id	sid	tid	token	lemma	pos
ejpam-5107	1	1	european	european	PROPN
ejpam-5107	1	2	journal	journal	PROPN
ejpam-5107	1	3	of	of	ADP
ejpam-5107	1	4	pure	pure	ADJ
ejpam-5107	1	5	and	and	CCONJ
ejpam-5107	1	6	applied	apply	VERB
ejpam-5107	1	7	mathematics	mathematic	NOUN
ejpam-5107	1	8	vol	vol	NOUN
ejpam-5107	1	9	.	.	PROPN
ejpam-5107	2	1	17	17	NUM
ejpam-5107	2	2	,	,	PUNCT
ejpam-5107	2	3	no	no	INTJ
ejpam-5107	2	4	.	.	NOUN
ejpam-5107	2	5	3	3	NUM
ejpam-5107	2	6	,	,	PUNCT
ejpam-5107	2	7	2024	2024	NUM
ejpam-5107	2	8	,	,	PUNCT
ejpam-5107	2	9	2299	2299	NUM
ejpam-5107	2	10	-	-	SYM
ejpam-5107	2	11	2310	2310	NUM
ejpam-5107	2	12	issn	issn	PROPN
ejpam-5107	2	13	1307	1307	NUM
ejpam-5107	2	14	-	-	SYM
ejpam-5107	2	15	5543	5543	NUM
ejpam-5107	2	16	–	–	PUNCT
ejpam-5107	2	17	ejpam.com	ejpam.com	X
ejpam-5107	2	18	published	publish	VERB
ejpam-5107	2	19	by	by	ADP
ejpam-5107	2	20	new	new	PROPN
ejpam-5107	2	21	york	york	PROPN
ejpam-5107	2	22	business	business	PROPN
ejpam-5107	2	23	global	global	ADJ
ejpam-5107	2	24	european	european	ADJ
ejpam-5107	2	25	call	call	NOUN
ejpam-5107	2	26	option	option	NOUN
ejpam-5107	2	27	under	under	ADP
ejpam-5107	2	28	stochastic	stochastic	ADJ
ejpam-5107	2	29	interest	interest	NOUN
ejpam-5107	2	30	rate	rate	NOUN
ejpam-5107	2	31	in	in	ADP
ejpam-5107	2	32	a	a	DET
ejpam-5107	2	33	fractional	fractional	ADJ
ejpam-5107	2	34	brownian	brownian	ADJ
ejpam-5107	2	35	motion	motion	NOUN
ejpam-5107	2	36	with	with	ADP
ejpam-5107	2	37	transaction	transaction	NOUN
ejpam-5107	2	38	cost	cost	VERB
ejpam-5107	2	39	felipe	felipe	PROPN
ejpam-5107	2	40	r.	r.	PROPN
ejpam-5107	2	41	sumalpong	sumalpong	PROPN
ejpam-5107	2	42	,	,	PUNCT
ejpam-5107	2	43	jr.1,∗	jr.1,∗	PROPN
ejpam-5107	2	44	,	,	PUNCT
ejpam-5107	2	45	eric	eric	PROPN
ejpam-5107	2	46	g.	g.	PROPN
ejpam-5107	2	47	lauron2	lauron2	PROPN
ejpam-5107	2	48	1	1	NUM
ejpam-5107	2	49	department	department	NOUN
ejpam-5107	2	50	of	of	ADP
ejpam-5107	2	51	mathematics	mathematic	NOUN
ejpam-5107	2	52	and	and	CCONJ
ejpam-5107	2	53	statistics	statistic	NOUN
ejpam-5107	2	54	,	,	PUNCT
ejpam-5107	2	55	faculty	faculty	NOUN
ejpam-5107	2	56	/	/	SYM
ejpam-5107	2	57	mindanao	mindanao	PROPN
ejpam-5107	2	58	state	state	PROPN
ejpam-5107	2	59	university	university	PROPN
ejpam-5107	2	60	iligan	iligan	PROPN
ejpam-5107	2	61	institute	institute	PROPN
ejpam-5107	2	62	of	of	ADP
ejpam-5107	2	63	technology	technology	PROPN
ejpam-5107	2	64	,	,	PUNCT
ejpam-5107	2	65	iligan	iligan	PROPN
ejpam-5107	2	66	city	city	PROPN
ejpam-5107	2	67	,	,	PUNCT
ejpam-5107	2	68	philippines	philippine	NOUN
ejpam-5107	2	69	2	2	NUM
ejpam-5107	2	70	j.h	j.h	PROPN
ejpam-5107	2	71	cerilles	cerille	VERB
ejpam-5107	2	72	state	state	PROPN
ejpam-5107	2	73	college	college	PROPN
ejpam-5107	2	74	dumingag	dumingag	PROPN
ejpam-5107	2	75	campus	campus	NOUN
ejpam-5107	2	76	,	,	PUNCT
ejpam-5107	2	77	zamboanga	zamboanga	PROPN
ejpam-5107	2	78	del	del	PROPN
ejpam-5107	2	79	sur	sur	PROPN
ejpam-5107	2	80	,	,	PUNCT
ejpam-5107	2	81	philippines	philippine	NOUN
ejpam-5107	2	82	abstract	abstract	ADJ
ejpam-5107	2	83	.	.	PUNCT
ejpam-5107	3	1	this	this	DET
ejpam-5107	3	2	paper	paper	NOUN
ejpam-5107	3	3	deals	deal	NOUN
ejpam-5107	3	4	on	on	ADP
ejpam-5107	3	5	the	the	DET
ejpam-5107	3	6	valuation	valuation	NOUN
ejpam-5107	3	7	of	of	ADP
ejpam-5107	3	8	european	european	ADJ
ejpam-5107	3	9	call	call	NOUN
ejpam-5107	3	10	option	option	NOUN
ejpam-5107	3	11	price	price	NOUN
ejpam-5107	3	12	in	in	ADP
ejpam-5107	3	13	a	a	DET
ejpam-5107	3	14	stochastic	stochastic	ADJ
ejpam-5107	3	15	environment	environment	NOUN
ejpam-5107	3	16	by	by	ADP
ejpam-5107	3	17	employing	employ	VERB
ejpam-5107	3	18	three	three	NUM
ejpam-5107	3	19	factors	factor	NOUN
ejpam-5107	3	20	which	which	PRON
ejpam-5107	3	21	are	be	AUX
ejpam-5107	3	22	the	the	DET
ejpam-5107	3	23	stochastic	stochastic	ADJ
ejpam-5107	3	24	model	model	NOUN
ejpam-5107	3	25	of	of	ADP
ejpam-5107	3	26	the	the	DET
ejpam-5107	3	27	asset	asset	NOUN
ejpam-5107	3	28	value	value	NOUN
ejpam-5107	3	29	,	,	PUNCT
ejpam-5107	3	30	the	the	DET
ejpam-5107	3	31	stochastic	stochastic	ADJ
ejpam-5107	3	32	interest	interest	NOUN
ejpam-5107	3	33	rate	rate	NOUN
ejpam-5107	3	34	and	and	CCONJ
ejpam-5107	3	35	the	the	DET
ejpam-5107	3	36	transaction	transaction	NOUN
ejpam-5107	3	37	cost	cost	NOUN
ejpam-5107	3	38	.	.	PUNCT
ejpam-5107	4	1	we	we	PRON
ejpam-5107	4	2	specify	specify	VERB
ejpam-5107	4	3	that	that	SCONJ
ejpam-5107	4	4	our	our	PRON
ejpam-5107	4	5	underlying	underlie	VERB
ejpam-5107	4	6	asset	asset	NOUN
ejpam-5107	4	7	and	and	CCONJ
ejpam-5107	4	8	the	the	DET
ejpam-5107	4	9	stochastic	stochastic	ADJ
ejpam-5107	4	10	interest	interest	NOUN
ejpam-5107	4	11	rate	rate	NOUN
ejpam-5107	4	12	,	,	PUNCT
ejpam-5107	4	13	particularly	particularly	ADV
ejpam-5107	4	14	hull	hull	NOUN
ejpam-5107	4	15	-	-	PUNCT
ejpam-5107	4	16	white	white	ADJ
ejpam-5107	4	17	model	model	NOUN
ejpam-5107	4	18	,	,	PUNCT
ejpam-5107	4	19	follows	follow	VERB
ejpam-5107	4	20	a	a	DET
ejpam-5107	4	21	fractional	fractional	ADJ
ejpam-5107	4	22	brownian	brownian	ADJ
ejpam-5107	4	23	motion	motion	NOUN
ejpam-5107	4	24	governed	govern	VERB
ejpam-5107	4	25	by	by	ADP
ejpam-5107	4	26	hurst	hurst	PROPN
ejpam-5107	4	27	parameter	parameter	PROPN
ejpam-5107	4	28	h.	h.	PROPN
ejpam-5107	4	29	we	we	PRON
ejpam-5107	4	30	used	use	VERB
ejpam-5107	4	31	the	the	DET
ejpam-5107	4	32	hedging	hedging	NOUN
ejpam-5107	4	33	and	and	CCONJ
ejpam-5107	4	34	replicating	replicate	VERB
ejpam-5107	4	35	technique	technique	NOUN
ejpam-5107	4	36	to	to	AUX
ejpam-5107	4	37	established	establish	VERB
ejpam-5107	4	38	the	the	DET
ejpam-5107	4	39	zero	zero	NUM
ejpam-5107	4	40	-	-	PUNCT
ejpam-5107	4	41	coupon	coupon	NOUN
ejpam-5107	4	42	bond	bond	NOUN
ejpam-5107	4	43	on	on	ADP
ejpam-5107	4	44	the	the	DET
ejpam-5107	4	45	european	european	ADJ
ejpam-5107	4	46	option	option	NOUN
ejpam-5107	4	47	.	.	PUNCT
ejpam-5107	5	1	finally	finally	ADV
ejpam-5107	5	2	,	,	PUNCT
ejpam-5107	5	3	we	we	PRON
ejpam-5107	5	4	give	give	VERB
ejpam-5107	5	5	a	a	DET
ejpam-5107	5	6	closed	closed	ADJ
ejpam-5107	5	7	-	-	PUNCT
ejpam-5107	5	8	form	form	NOUN
ejpam-5107	5	9	formula	formula	NOUN
ejpam-5107	5	10	of	of	ADP
ejpam-5107	5	11	the	the	DET
ejpam-5107	5	12	european	european	ADJ
ejpam-5107	5	13	call	call	NOUN
ejpam-5107	5	14	option	option	NOUN
ejpam-5107	5	15	price	price	NOUN
ejpam-5107	5	16	.	.	PUNCT
ejpam-5107	6	1	2020	2020	NUM
ejpam-5107	6	2	mathematics	mathematic	NOUN
ejpam-5107	6	3	subject	subject	NOUN
ejpam-5107	6	4	classifications	classification	NOUN
ejpam-5107	6	5	:	:	PUNCT
ejpam-5107	6	6	62p05	62p05	NUM
ejpam-5107	6	7	,	,	PUNCT
ejpam-5107	6	8	97m30	97m30	NUM
ejpam-5107	6	9	key	key	ADJ
ejpam-5107	6	10	words	word	NOUN
ejpam-5107	6	11	and	and	CCONJ
ejpam-5107	6	12	phrases	phrase	NOUN
ejpam-5107	6	13	:	:	PUNCT
ejpam-5107	6	14	european	european	ADJ
ejpam-5107	6	15	call	call	NOUN
ejpam-5107	6	16	option	option	NOUN
ejpam-5107	6	17	,	,	PUNCT
ejpam-5107	6	18	fractional	fractional	ADJ
ejpam-5107	6	19	brownian	brownian	ADJ
ejpam-5107	6	20	motion	motion	NOUN
ejpam-5107	6	21	,	,	PUNCT
ejpam-5107	6	22	fractional	fractional	ADJ
ejpam-5107	6	23	hullwhite	hullwhite	ADJ
ejpam-5107	6	24	interest	interest	NOUN
ejpam-5107	6	25	rate	rate	NOUN
ejpam-5107	6	26	model	model	NOUN
ejpam-5107	6	27	,	,	PUNCT
ejpam-5107	6	28	transaction	transaction	NOUN
ejpam-5107	6	29	cost	cost	NOUN
ejpam-5107	6	30	,	,	PUNCT
ejpam-5107	6	31	hedging	hedging	NOUN
ejpam-5107	6	32	,	,	PUNCT
ejpam-5107	6	33	option	option	NOUN
ejpam-5107	6	34	replication	replication	NOUN
ejpam-5107	6	35	1	1	NUM
ejpam-5107	6	36	.	.	PUNCT
ejpam-5107	6	37	introduction	introduction	NOUN
ejpam-5107	6	38	the	the	DET
ejpam-5107	6	39	study	study	NOUN
ejpam-5107	6	40	of	of	ADP
ejpam-5107	6	41	option	option	NOUN
ejpam-5107	6	42	pricing	pricing	NOUN
ejpam-5107	6	43	can	can	AUX
ejpam-5107	6	44	be	be	AUX
ejpam-5107	6	45	traced	trace	VERB
ejpam-5107	6	46	back	back	ADV
ejpam-5107	6	47	to	to	ADP
ejpam-5107	6	48	the	the	DET
ejpam-5107	6	49	seminal	seminal	ADJ
ejpam-5107	6	50	papers	paper	NOUN
ejpam-5107	6	51	of	of	ADP
ejpam-5107	6	52	black	black	ADJ
ejpam-5107	6	53	and	and	CCONJ
ejpam-5107	6	54	scholes[1	scholes[1	PRON
ejpam-5107	6	55	]	]	PUNCT
ejpam-5107	6	56	and	and	CCONJ
ejpam-5107	6	57	merton[2	merton[2	PROPN
ejpam-5107	6	58	]	]	X
ejpam-5107	6	59	.	.	PUNCT
ejpam-5107	7	1	the	the	DET
ejpam-5107	7	2	black	black	ADJ
ejpam-5107	7	3	-	-	PUNCT
ejpam-5107	7	4	scholes	schole	NOUN
ejpam-5107	7	5	-	-	PUNCT
ejpam-5107	7	6	merton(bsm	merton(bsm	NOUN
ejpam-5107	7	7	)	)	PUNCT
ejpam-5107	7	8	model	model	NOUN
ejpam-5107	7	9	is	be	AUX
ejpam-5107	7	10	a	a	DET
ejpam-5107	7	11	known	know	VERB
ejpam-5107	7	12	mathematical	mathematical	ADJ
ejpam-5107	7	13	model	model	NOUN
ejpam-5107	7	14	to	to	PART
ejpam-5107	7	15	evaluate	evaluate	VERB
ejpam-5107	7	16	the	the	DET
ejpam-5107	7	17	price	price	NOUN
ejpam-5107	7	18	of	of	ADP
ejpam-5107	7	19	the	the	DET
ejpam-5107	7	20	option	option	NOUN
ejpam-5107	7	21	that	that	PRON
ejpam-5107	7	22	utilizes	utilize	VERB
ejpam-5107	7	23	five	five	NUM
ejpam-5107	7	24	inputs	input	NOUN
ejpam-5107	7	25	namely	namely	ADV
ejpam-5107	7	26	as	as	ADP
ejpam-5107	7	27	:	:	PUNCT
ejpam-5107	7	28	the	the	DET
ejpam-5107	7	29	asset	asset	NOUN
ejpam-5107	7	30	price	price	NOUN
ejpam-5107	7	31	,	,	PUNCT
ejpam-5107	7	32	the	the	DET
ejpam-5107	7	33	strike	strike	NOUN
ejpam-5107	7	34	price	price	NOUN
ejpam-5107	7	35	,	,	PUNCT
ejpam-5107	7	36	the	the	DET
ejpam-5107	7	37	risk	risk	NOUN
ejpam-5107	7	38	-	-	PUNCT
ejpam-5107	7	39	free	free	ADJ
ejpam-5107	7	40	interest	interest	NOUN
ejpam-5107	7	41	rates	rate	NOUN
ejpam-5107	7	42	,	,	PUNCT
ejpam-5107	7	43	time	time	NOUN
ejpam-5107	7	44	of	of	ADP
ejpam-5107	7	45	expiration	expiration	NOUN
ejpam-5107	7	46	and	and	CCONJ
ejpam-5107	7	47	the	the	DET
ejpam-5107	7	48	volatility	volatility	NOUN
ejpam-5107	7	49	.	.	PUNCT
ejpam-5107	8	1	the	the	DET
ejpam-5107	8	2	initial	initial	ADJ
ejpam-5107	8	3	equation	equation	NOUN
ejpam-5107	8	4	of	of	ADP
ejpam-5107	8	5	the	the	DET
ejpam-5107	8	6	bsm	bsm	PROPN
ejpam-5107	8	7	model	model	NOUN
ejpam-5107	8	8	was	be	AUX
ejpam-5107	8	9	published	publish	VERB
ejpam-5107	8	10	in	in	ADP
ejpam-5107	8	11	1973	1973	NUM
ejpam-5107	8	12	on	on	ADP
ejpam-5107	8	13	the	the	DET
ejpam-5107	8	14	paper	paper	NOUN
ejpam-5107	8	15	“	"	PUNCT
ejpam-5107	8	16	the	the	DET
ejpam-5107	8	17	pricing	pricing	NOUN
ejpam-5107	8	18	of	of	ADP
ejpam-5107	8	19	options	option	NOUN
ejpam-5107	8	20	and	and	CCONJ
ejpam-5107	8	21	corporate	corporate	ADJ
ejpam-5107	8	22	liabilities	liability	NOUN
ejpam-5107	8	23	”	"	PUNCT
ejpam-5107	8	24	in	in	ADP
ejpam-5107	8	25	journal	journal	NOUN
ejpam-5107	8	26	of	of	ADP
ejpam-5107	8	27	political	political	ADJ
ejpam-5107	8	28	economy	economy	NOUN
ejpam-5107	8	29	.	.	PUNCT
ejpam-5107	9	1	by	by	ADP
ejpam-5107	9	2	this	this	DET
ejpam-5107	9	3	model	model	NOUN
ejpam-5107	9	4	,	,	PUNCT
ejpam-5107	9	5	black	black	ADJ
ejpam-5107	9	6	,	,	PUNCT
ejpam-5107	9	7	scholes	schole	NOUN
ejpam-5107	9	8	and	and	CCONJ
ejpam-5107	9	9	merton	merton	PROPN
ejpam-5107	9	10	received	receive	VERB
ejpam-5107	9	11	a	a	DET
ejpam-5107	9	12	nobel	nobel	PROPN
ejpam-5107	9	13	prize	prize	PROPN
ejpam-5107	9	14	in	in	ADP
ejpam-5107	9	15	economics	economic	NOUN
ejpam-5107	9	16	in	in	ADP
ejpam-5107	9	17	1997	1997	NUM
ejpam-5107	9	18	.	.	PUNCT
ejpam-5107	10	1	however	however	ADV
ejpam-5107	10	2	,	,	PUNCT
ejpam-5107	10	3	there	there	PRON
ejpam-5107	10	4	are	be	VERB
ejpam-5107	10	5	several	several	ADJ
ejpam-5107	10	6	drawbacks	drawback	NOUN
ejpam-5107	10	7	of	of	ADP
ejpam-5107	10	8	the	the	DET
ejpam-5107	10	9	bsm	bsm	PROPN
ejpam-5107	10	10	model	model	NOUN
ejpam-5107	10	11	such	such	ADJ
ejpam-5107	10	12	as	as	ADP
ejpam-5107	10	13	the	the	DET
ejpam-5107	10	14	assumptions	assumption	NOUN
ejpam-5107	10	15	that	that	SCONJ
ejpam-5107	10	16	the	the	DET
ejpam-5107	10	17	interest	interest	NOUN
ejpam-5107	10	18	rate	rate	NOUN
ejpam-5107	10	19	and	and	CCONJ
ejpam-5107	10	20	the	the	DET
ejpam-5107	10	21	volatility	volatility	NOUN
ejpam-5107	10	22	rate	rate	NOUN
ejpam-5107	10	23	are	be	AUX
ejpam-5107	10	24	constant	constant	ADJ
ejpam-5107	10	25	over	over	ADP
ejpam-5107	10	26	the	the	DET
ejpam-5107	10	27	period	period	NOUN
ejpam-5107	10	28	of	of	ADP
ejpam-5107	10	29	the	the	DET
ejpam-5107	10	30	contract	contract	NOUN
ejpam-5107	10	31	does	do	AUX
ejpam-5107	10	32	not	not	PART
ejpam-5107	10	33	fit	fit	VERB
ejpam-5107	10	34	the	the	DET
ejpam-5107	10	35	actual	actual	ADJ
ejpam-5107	10	36	scenario	scenario	NOUN
ejpam-5107	10	37	of	of	ADP
ejpam-5107	10	38	the	the	DET
ejpam-5107	10	39	market	market	NOUN
ejpam-5107	10	40	,	,	PUNCT
ejpam-5107	10	41	transaction	transaction	NOUN
ejpam-5107	10	42	cost	cost	NOUN
ejpam-5107	10	43	may	may	AUX
ejpam-5107	10	44	not	not	PART
ejpam-5107	10	45	be	be	AUX
ejpam-5107	10	46	avoided	avoid	VERB
ejpam-5107	10	47	,	,	PUNCT
ejpam-5107	10	48	and	and	CCONJ
ejpam-5107	10	49	the	the	DET
ejpam-5107	10	50	evolution	evolution	NOUN
ejpam-5107	10	51	of	of	ADP
ejpam-5107	10	52	the	the	DET
ejpam-5107	10	53	asset	asset	NOUN
ejpam-5107	10	54	price	price	NOUN
ejpam-5107	10	55	does	do	AUX
ejpam-5107	10	56	not	not	PART
ejpam-5107	10	57	always	always	ADV
ejpam-5107	10	58	obey	obey	VERB
ejpam-5107	10	59	a	a	DET
ejpam-5107	10	60	standard	standard	ADJ
ejpam-5107	10	61	brownian	brownian	ADJ
ejpam-5107	10	62	motion(h	motion(h	NOUN
ejpam-5107	10	63	=	=	SYM
ejpam-5107	10	64	1/2	1/2	NUM
ejpam-5107	10	65	)	)	PUNCT
ejpam-5107	11	1	for	for	ADP
ejpam-5107	11	2	which	which	PRON
ejpam-5107	11	3	nualart[3	nualart[3	SYM
ejpam-5107	11	4	]	]	PUNCT
ejpam-5107	11	5	noted	note	VERB
ejpam-5107	11	6	that	that	SCONJ
ejpam-5107	11	7	for	for	ADP
ejpam-5107	11	8	some	some	DET
ejpam-5107	11	9	stock	stock	NOUN
ejpam-5107	11	10	process	process	NOUN
ejpam-5107	11	11	,	,	PUNCT
ejpam-5107	11	12	the	the	DET
ejpam-5107	11	13	hurst	hurst	PROPN
ejpam-5107	11	14	exponent	exponent	PROPN
ejpam-5107	11	15	h	h	PROPN
ejpam-5107	11	16	may	may	AUX
ejpam-5107	11	17	not	not	PART
ejpam-5107	11	18	∗corresponding	∗corresponde	VERB
ejpam-5107	11	19	author	author	NOUN
ejpam-5107	11	20	.	.	PUNCT
ejpam-5107	12	1	doi	doi	NOUN
ejpam-5107	12	2	:	:	PUNCT
ejpam-5107	12	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5107	https://doi.org/10.29020/nybg.ejpam.v17i3.5107	ADP
ejpam-5107	12	4	email	email	NOUN
ejpam-5107	12	5	addresses	address	VERB
ejpam-5107	12	6	:	:	PUNCT
ejpam-5107	12	7	felipejr.sumalpong@g.msuiit.edu.ph	felipejr.sumalpong@g.msuiit.edu.ph	PROPN
ejpam-5107	12	8	(	(	PUNCT
ejpam-5107	12	9	f.jr	f.jr	PROPN
ejpam-5107	12	10	.	.	PROPN
ejpam-5107	12	11	sumalpong	sumalpong	PROPN
ejpam-5107	12	12	)	)	PUNCT
ejpam-5107	12	13	,	,	PUNCT
ejpam-5107	12	14	eric.lauron@g.msuiit.edu.ph	eric.lauron@g.msuiit.edu.ph	PROPN
ejpam-5107	12	15	(	(	PUNCT
ejpam-5107	12	16	e.	e.	PROPN
ejpam-5107	12	17	lauron	lauron	PROPN
ejpam-5107	12	18	)	)	PUNCT
ejpam-5107	12	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5107	12	20	2299	2299	NUM
ejpam-5107	13	1	©	©	ADP
ejpam-5107	13	2	2024	2024	NUM
ejpam-5107	13	3	ejpam	ejpam	NOUN
ejpam-5107	13	4	all	all	DET
ejpam-5107	13	5	rights	right	NOUN
ejpam-5107	13	6	reserved	reserve	VERB
ejpam-5107	13	7	.	.	PUNCT
ejpam-5107	14	1	f.	f.	PROPN
ejpam-5107	14	2	sumalpong	sumalpong	PROPN
ejpam-5107	14	3	,	,	PUNCT
ejpam-5107	14	4	e.	e.	PROPN
ejpam-5107	14	5	lauron	lauron	PROPN
ejpam-5107	14	6	/	/	SYM
ejpam-5107	14	7	eur	eur	PROPN
ejpam-5107	14	8	.	.	PUNCT
ejpam-5107	15	1	j.	j.	PROPN
ejpam-5107	15	2	pure	pure	PROPN
ejpam-5107	15	3	appl	appl	PROPN
ejpam-5107	15	4	.	.	PROPN
ejpam-5107	15	5	math	math	PROPN
ejpam-5107	15	6	,	,	PUNCT
ejpam-5107	15	7	17	17	NUM
ejpam-5107	15	8	(	(	PUNCT
ejpam-5107	15	9	3	3	NUM
ejpam-5107	15	10	)	)	PUNCT
ejpam-5107	15	11	(	(	PUNCT
ejpam-5107	15	12	2024	2024	NUM
ejpam-5107	15	13	)	)	PUNCT
ejpam-5107	15	14	,	,	PUNCT
ejpam-5107	15	15	2299	2299	NUM
ejpam-5107	15	16	-	-	SYM
ejpam-5107	15	17	2310	2310	NUM
ejpam-5107	15	18	2300	2300	NUM
ejpam-5107	15	19	be	be	AUX
ejpam-5107	15	20	exactly	exactly	ADV
ejpam-5107	15	21	1/2	1/2	NUM
ejpam-5107	15	22	but	but	CCONJ
ejpam-5107	15	23	greater	great	ADJ
ejpam-5107	15	24	than	than	ADP
ejpam-5107	15	25	or	or	CCONJ
ejpam-5107	15	26	equal	equal	ADJ
ejpam-5107	15	27	to	to	ADP
ejpam-5107	15	28	1/2	1/2	NUM
ejpam-5107	15	29	.	.	PUNCT
ejpam-5107	16	1	hence	hence	ADV
ejpam-5107	16	2	,	,	PUNCT
ejpam-5107	16	3	the	the	DET
ejpam-5107	16	4	standard	standard	ADJ
ejpam-5107	16	5	brownian	brownian	ADJ
ejpam-5107	16	6	motion	motion	NOUN
ejpam-5107	16	7	where	where	SCONJ
ejpam-5107	16	8	h	h	NOUN
ejpam-5107	16	9	=	=	NOUN
ejpam-5107	16	10	1/2	1/2	NUM
ejpam-5107	16	11	may	may	AUX
ejpam-5107	16	12	not	not	PART
ejpam-5107	16	13	be	be	AUX
ejpam-5107	16	14	a	a	DET
ejpam-5107	16	15	fitting	fitting	ADJ
ejpam-5107	16	16	stochastic	stochastic	ADJ
ejpam-5107	16	17	process	process	NOUN
ejpam-5107	16	18	for	for	ADP
ejpam-5107	16	19	some	some	DET
ejpam-5107	16	20	stock	stock	NOUN
ejpam-5107	16	21	processes	process	NOUN
ejpam-5107	16	22	.	.	PUNCT
ejpam-5107	17	1	in	in	ADP
ejpam-5107	17	2	this	this	DET
ejpam-5107	17	3	paper	paper	NOUN
ejpam-5107	17	4	,	,	PUNCT
ejpam-5107	17	5	we	we	PRON
ejpam-5107	17	6	assumed	assume	VERB
ejpam-5107	17	7	that	that	SCONJ
ejpam-5107	17	8	both	both	CCONJ
ejpam-5107	17	9	the	the	DET
ejpam-5107	17	10	asset	asset	NOUN
ejpam-5107	17	11	value	value	NOUN
ejpam-5107	17	12	and	and	CCONJ
ejpam-5107	17	13	the	the	DET
ejpam-5107	17	14	interest	interest	NOUN
ejpam-5107	17	15	rate	rate	NOUN
ejpam-5107	17	16	follows	follow	VERB
ejpam-5107	17	17	the	the	DET
ejpam-5107	17	18	fractional	fractional	ADJ
ejpam-5107	17	19	brownian	brownian	ADJ
ejpam-5107	17	20	motion	motion	NOUN
ejpam-5107	17	21	.	.	PUNCT
ejpam-5107	18	1	we	we	PRON
ejpam-5107	18	2	specify	specify	VERB
ejpam-5107	18	3	that	that	SCONJ
ejpam-5107	18	4	the	the	DET
ejpam-5107	18	5	asset	asset	NOUN
ejpam-5107	18	6	value	value	NOUN
ejpam-5107	18	7	x(t	x(t	PROPN
ejpam-5107	18	8	)	)	PUNCT
ejpam-5107	18	9	follows	follow	VERB
ejpam-5107	18	10	dx(t	dx(t	NOUN
ejpam-5107	18	11	)	)	PUNCT
ejpam-5107	18	12	=	=	SYM
ejpam-5107	18	13	r(t)x(t)dt+	r(t)x(t)dt+	PROPN
ejpam-5107	18	14	σxx(t)dbh	σxx(t)dbh	PROPN
ejpam-5107	18	15	1	1	NUM
ejpam-5107	18	16	(	(	PUNCT
ejpam-5107	18	17	t	t	NOUN
ejpam-5107	18	18	)	)	PUNCT
ejpam-5107	18	19	(	(	PUNCT
ejpam-5107	18	20	1	1	X
ejpam-5107	18	21	)	)	PUNCT
ejpam-5107	18	22	and	and	CCONJ
ejpam-5107	18	23	the	the	DET
ejpam-5107	18	24	interest	interest	NOUN
ejpam-5107	18	25	rate	rate	NOUN
ejpam-5107	18	26	r(t	r(t	NOUN
ejpam-5107	18	27	)	)	PUNCT
ejpam-5107	18	28	follows	follow	VERB
ejpam-5107	18	29	the	the	DET
ejpam-5107	18	30	fractional	fractional	ADJ
ejpam-5107	18	31	hull	hull	NOUN
ejpam-5107	18	32	-	-	PUNCT
ejpam-5107	18	33	white	white	ADJ
ejpam-5107	18	34	model	model	NOUN
ejpam-5107	18	35	dr(t	dr(t	PUNCT
ejpam-5107	18	36	)	)	PUNCT
ejpam-5107	19	1	=	=	PUNCT
ejpam-5107	20	1	[	[	X
ejpam-5107	20	2	θ(t)−	θ(t)−	PROPN
ejpam-5107	20	3	ar(t)]dt+	ar(t)]dt+	ADP
ejpam-5107	20	4	σrdb	σrdb	PROPN
ejpam-5107	20	5	h	h	NOUN
ejpam-5107	20	6	2	2	NUM
ejpam-5107	20	7	(	(	PUNCT
ejpam-5107	20	8	t	t	NOUN
ejpam-5107	20	9	)	)	PUNCT
ejpam-5107	20	10	(	(	PUNCT
ejpam-5107	20	11	2	2	X
ejpam-5107	20	12	)	)	PUNCT
ejpam-5107	20	13	where	where	SCONJ
ejpam-5107	20	14	σx	σx	NOUN
ejpam-5107	20	15	is	be	AUX
ejpam-5107	20	16	the	the	DET
ejpam-5107	20	17	volatility	volatility	NOUN
ejpam-5107	20	18	of	of	ADP
ejpam-5107	20	19	the	the	DET
ejpam-5107	20	20	asset	asset	NOUN
ejpam-5107	20	21	price	price	NOUN
ejpam-5107	20	22	,	,	PUNCT
ejpam-5107	20	23	σr	σr	PROPN
ejpam-5107	20	24	is	be	AUX
ejpam-5107	20	25	the	the	DET
ejpam-5107	20	26	volatility	volatility	NOUN
ejpam-5107	20	27	of	of	ADP
ejpam-5107	20	28	the	the	DET
ejpam-5107	20	29	interest	interest	NOUN
ejpam-5107	20	30	rate	rate	NOUN
ejpam-5107	20	31	,	,	PUNCT
ejpam-5107	20	32	and	and	CCONJ
ejpam-5107	20	33	bh	bh	NOUN
ejpam-5107	20	34	is	be	AUX
ejpam-5107	20	35	a	a	DET
ejpam-5107	20	36	fractional	fractional	ADJ
ejpam-5107	20	37	brownian	brownian	ADJ
ejpam-5107	20	38	motion	motion	NOUN
ejpam-5107	20	39	with	with	ADP
ejpam-5107	20	40	hurst	hurst	PROPN
ejpam-5107	20	41	parameter	parameter	PROPN
ejpam-5107	20	42	h.	h.	PROPN
ejpam-5107	20	43	with	with	ADP
ejpam-5107	20	44	the	the	DET
ejpam-5107	20	45	transaction	transaction	NOUN
ejpam-5107	20	46	cost	cost	NOUN
ejpam-5107	20	47	cost	cost	NOUN
ejpam-5107	20	48	=	=	PUNCT
ejpam-5107	20	49	cx(t)|v(t)|	cx(t)|v(t)|	NUM
ejpam-5107	20	50	(	(	PUNCT
ejpam-5107	20	51	3	3	NUM
ejpam-5107	20	52	)	)	PUNCT
ejpam-5107	20	53	where	where	SCONJ
ejpam-5107	20	54	c	c	NOUN
ejpam-5107	20	55	is	be	AUX
ejpam-5107	20	56	a	a	DET
ejpam-5107	20	57	fixed	fix	VERB
ejpam-5107	20	58	proportion	proportion	NOUN
ejpam-5107	20	59	of	of	ADP
ejpam-5107	20	60	the	the	DET
ejpam-5107	20	61	trading	trading	NOUN
ejpam-5107	20	62	amount	amount	NOUN
ejpam-5107	20	63	for	for	ADP
ejpam-5107	20	64	the	the	DET
ejpam-5107	20	65	asset	asset	NOUN
ejpam-5107	20	66	agreed	agree	VERB
ejpam-5107	20	67	between	between	ADP
ejpam-5107	20	68	both	both	DET
ejpam-5107	20	69	parties	party	NOUN
ejpam-5107	20	70	,	,	PUNCT
ejpam-5107	20	71	and	and	CCONJ
ejpam-5107	20	72	v(t	v(t	NOUN
ejpam-5107	20	73	)	)	PUNCT
ejpam-5107	20	74	is	be	AUX
ejpam-5107	20	75	the	the	DET
ejpam-5107	20	76	number	number	NOUN
ejpam-5107	20	77	of	of	ADP
ejpam-5107	20	78	assets	asset	NOUN
ejpam-5107	20	79	sold	sell	VERB
ejpam-5107	20	80	or	or	CCONJ
ejpam-5107	20	81	bought	buy	VERB
ejpam-5107	20	82	,	,	PUNCT
ejpam-5107	20	83	we	we	PRON
ejpam-5107	20	84	formulate	formulate	VERB
ejpam-5107	20	85	a	a	DET
ejpam-5107	20	86	european	european	ADJ
ejpam-5107	20	87	option	option	NOUN
ejpam-5107	20	88	price	price	NOUN
ejpam-5107	20	89	model	model	NOUN
ejpam-5107	20	90	on	on	ADP
ejpam-5107	20	91	par	par	NOUN
ejpam-5107	20	92	with	with	ADP
ejpam-5107	20	93	the	the	DET
ejpam-5107	20	94	bsm	bsm	PROPN
ejpam-5107	20	95	model	model	PROPN
ejpam-5107	20	96	.	.	PUNCT
ejpam-5107	21	1	for	for	ADP
ejpam-5107	21	2	simplicity	simplicity	NOUN
ejpam-5107	21	3	,	,	PUNCT
ejpam-5107	21	4	we	we	PRON
ejpam-5107	21	5	assumed	assume	VERB
ejpam-5107	21	6	that	that	SCONJ
ejpam-5107	21	7	the	the	DET
ejpam-5107	21	8	volatilities	volatility	NOUN
ejpam-5107	21	9	for	for	ADP
ejpam-5107	21	10	both	both	CCONJ
ejpam-5107	21	11	the	the	DET
ejpam-5107	21	12	asset	asset	NOUN
ejpam-5107	21	13	price	price	NOUN
ejpam-5107	21	14	and	and	CCONJ
ejpam-5107	21	15	the	the	DET
ejpam-5107	21	16	interest	interest	NOUN
ejpam-5107	21	17	rate	rate	NOUN
ejpam-5107	21	18	are	be	AUX
ejpam-5107	21	19	constant	constant	ADJ
ejpam-5107	21	20	,	,	PUNCT
ejpam-5107	21	21	no	no	DET
ejpam-5107	21	22	dividend	dividend	NOUN
ejpam-5107	21	23	and	and	CCONJ
ejpam-5107	21	24	coupon	coupon	NOUN
ejpam-5107	21	25	payments	payment	NOUN
ejpam-5107	21	26	,	,	PUNCT
ejpam-5107	21	27	and	and	CCONJ
ejpam-5107	21	28	we	we	PRON
ejpam-5107	21	29	limit	limit	VERB
ejpam-5107	21	30	our	our	PRON
ejpam-5107	21	31	analysis	analysis	NOUN
ejpam-5107	21	32	to	to	ADP
ejpam-5107	21	33	european	european	ADJ
ejpam-5107	21	34	options	option	NOUN
ejpam-5107	21	35	only	only	ADV
ejpam-5107	21	36	.	.	PUNCT
ejpam-5107	22	1	2	2	X
ejpam-5107	22	2	.	.	X
ejpam-5107	22	3	model	model	NOUN
ejpam-5107	22	4	formulation	formulation	NOUN
ejpam-5107	22	5	this	this	DET
ejpam-5107	22	6	section	section	NOUN
ejpam-5107	22	7	presents	present	VERB
ejpam-5107	22	8	our	our	PRON
ejpam-5107	22	9	assumptions	assumption	NOUN
ejpam-5107	22	10	for	for	ADP
ejpam-5107	22	11	the	the	DET
ejpam-5107	22	12	computations	computation	NOUN
ejpam-5107	22	13	of	of	ADP
ejpam-5107	22	14	the	the	DET
ejpam-5107	22	15	option	option	NOUN
ejpam-5107	22	16	price	price	NOUN
ejpam-5107	22	17	.	.	PUNCT
ejpam-5107	23	1	the	the	DET
ejpam-5107	23	2	following	follow	VERB
ejpam-5107	23	3	assumptions	assumption	NOUN
ejpam-5107	23	4	are	be	AUX
ejpam-5107	23	5	made	make	VERB
ejpam-5107	23	6	:	:	PUNCT
ejpam-5107	23	7	1	1	X
ejpam-5107	23	8	.	.	X
ejpam-5107	23	9	asset	asset	NOUN
ejpam-5107	23	10	price	price	NOUN
ejpam-5107	23	11	model	model	NOUN
ejpam-5107	23	12	the	the	DET
ejpam-5107	23	13	asset	asset	NOUN
ejpam-5107	23	14	price	price	NOUN
ejpam-5107	23	15	x(t	x(t	PROPN
ejpam-5107	23	16	)	)	PUNCT
ejpam-5107	23	17	follows	follow	VERB
ejpam-5107	23	18	a	a	DET
ejpam-5107	23	19	fractional	fractional	ADJ
ejpam-5107	23	20	brownian	brownian	ADJ
ejpam-5107	23	21	motion	motion	NOUN
ejpam-5107	23	22	given	give	VERB
ejpam-5107	23	23	by	by	ADP
ejpam-5107	23	24	dx(t	dx(t	NOUN
ejpam-5107	23	25	)	)	PUNCT
ejpam-5107	23	26	=	=	SYM
ejpam-5107	23	27	r(t)x(t)dt+	r(t)x(t)dt+	PROPN
ejpam-5107	23	28	σxx(t)dbh	σxx(t)dbh	PROPN
ejpam-5107	23	29	1	1	NUM
ejpam-5107	23	30	(	(	PUNCT
ejpam-5107	23	31	t	t	NOUN
ejpam-5107	23	32	)	)	PUNCT
ejpam-5107	23	33	(	(	PUNCT
ejpam-5107	23	34	4	4	X
ejpam-5107	23	35	)	)	PUNCT
ejpam-5107	23	36	where	where	SCONJ
ejpam-5107	23	37	r(t	r(t	NOUN
ejpam-5107	23	38	)	)	PUNCT
ejpam-5107	23	39	is	be	AUX
ejpam-5107	23	40	the	the	DET
ejpam-5107	23	41	total	total	ADJ
ejpam-5107	23	42	expected	expect	VERB
ejpam-5107	23	43	rate	rate	NOUN
ejpam-5107	23	44	of	of	ADP
ejpam-5107	23	45	return	return	NOUN
ejpam-5107	23	46	,	,	PUNCT
ejpam-5107	23	47	σx	σx	NOUN
ejpam-5107	23	48	is	be	AUX
ejpam-5107	23	49	the	the	DET
ejpam-5107	23	50	volatility	volatility	NOUN
ejpam-5107	23	51	of	of	ADP
ejpam-5107	23	52	the	the	DET
ejpam-5107	23	53	price	price	NOUN
ejpam-5107	23	54	and	and	CCONJ
ejpam-5107	23	55	bh	bh	PROPN
ejpam-5107	23	56	1	1	NUM
ejpam-5107	23	57	(	(	PUNCT
ejpam-5107	23	58	t	t	PROPN
ejpam-5107	23	59	)	)	PUNCT
ejpam-5107	23	60	is	be	AUX
ejpam-5107	23	61	a	a	DET
ejpam-5107	23	62	fractional	fractional	ADJ
ejpam-5107	23	63	brownian	brownian	ADJ
ejpam-5107	23	64	motion	motion	NOUN
ejpam-5107	23	65	with	with	ADP
ejpam-5107	23	66	hurst	hurst	PROPN
ejpam-5107	23	67	parameter	parameter	PROPN
ejpam-5107	23	68	h.	h.	PROPN
ejpam-5107	23	69	2	2	X
ejpam-5107	23	70	.	.	PUNCT
ejpam-5107	23	71	interest	interest	NOUN
ejpam-5107	23	72	rate	rate	NOUN
ejpam-5107	23	73	model	model	NOUN
ejpam-5107	23	74	the	the	DET
ejpam-5107	23	75	risk	risk	NOUN
ejpam-5107	23	76	-	-	PUNCT
ejpam-5107	23	77	free	free	ADJ
ejpam-5107	23	78	interest	interest	NOUN
ejpam-5107	23	79	rate	rate	NOUN
ejpam-5107	23	80	r(t	r(t	NOUN
ejpam-5107	23	81	)	)	PUNCT
ejpam-5107	23	82	follows	follow	VERB
ejpam-5107	23	83	a	a	DET
ejpam-5107	23	84	fractional	fractional	ADJ
ejpam-5107	23	85	hull	hull	NOUN
ejpam-5107	23	86	-	-	PUNCT
ejpam-5107	23	87	white	white	ADJ
ejpam-5107	23	88	model	model	NOUN
ejpam-5107	23	89	given	give	VERB
ejpam-5107	23	90	by	by	ADP
ejpam-5107	23	91	dr(t	dr(t	NOUN
ejpam-5107	23	92	)	)	PUNCT
ejpam-5107	23	93	=	=	PUNCT
ejpam-5107	24	1	[	[	X
ejpam-5107	24	2	θ(t)−	θ(t)−	PROPN
ejpam-5107	24	3	ar(t)]dt+	ar(t)]dt+	ADP
ejpam-5107	24	4	σrdb	σrdb	PROPN
ejpam-5107	24	5	h	h	NOUN
ejpam-5107	24	6	2	2	NUM
ejpam-5107	24	7	(	(	PUNCT
ejpam-5107	24	8	t	t	NOUN
ejpam-5107	24	9	)	)	PUNCT
ejpam-5107	24	10	(	(	PUNCT
ejpam-5107	24	11	5	5	NUM
ejpam-5107	24	12	)	)	PUNCT
ejpam-5107	24	13	where	where	SCONJ
ejpam-5107	24	14	θ(t	θ(t	NOUN
ejpam-5107	24	15	)	)	PUNCT
ejpam-5107	24	16	is	be	AUX
ejpam-5107	24	17	a	a	DET
ejpam-5107	24	18	deterministic	deterministic	ADJ
ejpam-5107	24	19	function	function	NOUN
ejpam-5107	24	20	of	of	ADP
ejpam-5107	24	21	time	time	NOUN
ejpam-5107	24	22	,	,	PUNCT
ejpam-5107	24	23	a	a	PRON
ejpam-5107	24	24	is	be	AUX
ejpam-5107	24	25	constant	constant	ADJ
ejpam-5107	24	26	,	,	PUNCT
ejpam-5107	24	27	σr	σr	PROPN
ejpam-5107	24	28	is	be	AUX
ejpam-5107	24	29	the	the	DET
ejpam-5107	24	30	volatility	volatility	NOUN
ejpam-5107	24	31	of	of	ADP
ejpam-5107	24	32	the	the	DET
ejpam-5107	24	33	interest	interest	NOUN
ejpam-5107	24	34	rate	rate	NOUN
ejpam-5107	24	35	which	which	PRON
ejpam-5107	24	36	is	be	AUX
ejpam-5107	24	37	assumed	assume	VERB
ejpam-5107	24	38	to	to	PART
ejpam-5107	24	39	be	be	AUX
ejpam-5107	24	40	constant	constant	ADJ
ejpam-5107	24	41	and	and	CCONJ
ejpam-5107	24	42	bh	bh	PROPN
ejpam-5107	24	43	2	2	NUM
ejpam-5107	24	44	(	(	PUNCT
ejpam-5107	24	45	t	t	PROPN
ejpam-5107	24	46	)	)	PUNCT
ejpam-5107	24	47	is	be	AUX
ejpam-5107	24	48	a	a	DET
ejpam-5107	24	49	fractional	fractional	ADJ
ejpam-5107	24	50	brownian	brownian	ADJ
ejpam-5107	24	51	motion	motion	NOUN
ejpam-5107	24	52	with	with	ADP
ejpam-5107	24	53	hurst	hurst	PROPN
ejpam-5107	24	54	parameter	parameter	PROPN
ejpam-5107	24	55	h.	h.	PROPN
ejpam-5107	24	56	under	under	ADP
ejpam-5107	24	57	the	the	DET
ejpam-5107	24	58	fractional	fractional	ADJ
ejpam-5107	24	59	brownian	brownian	ADJ
ejpam-5107	24	60	motion	motion	NOUN
ejpam-5107	24	61	,	,	PUNCT
ejpam-5107	24	62	the	the	DET
ejpam-5107	24	63	correlation	correlation	NOUN
ejpam-5107	24	64	coefficient	coefficient	NOUN
ejpam-5107	24	65	between	between	ADP
ejpam-5107	24	66	bh	bh	NOUN
ejpam-5107	24	67	1	1	NUM
ejpam-5107	24	68	(	(	PUNCT
ejpam-5107	24	69	t	t	PROPN
ejpam-5107	24	70	)	)	PUNCT
ejpam-5107	24	71	f.	f.	PROPN
ejpam-5107	24	72	sumalpong	sumalpong	PROPN
ejpam-5107	24	73	,	,	PUNCT
ejpam-5107	24	74	e.	e.	PROPN
ejpam-5107	24	75	lauron	lauron	PROPN
ejpam-5107	24	76	/	/	SYM
ejpam-5107	24	77	eur	eur	PROPN
ejpam-5107	24	78	.	.	PUNCT
ejpam-5107	25	1	j.	j.	PROPN
ejpam-5107	25	2	pure	pure	PROPN
ejpam-5107	25	3	appl	appl	PROPN
ejpam-5107	25	4	.	.	PROPN
ejpam-5107	25	5	math	math	PROPN
ejpam-5107	25	6	,	,	PUNCT
ejpam-5107	25	7	17	17	NUM
ejpam-5107	25	8	(	(	PUNCT
ejpam-5107	25	9	3	3	NUM
ejpam-5107	25	10	)	)	PUNCT
ejpam-5107	25	11	(	(	PUNCT
ejpam-5107	25	12	2024	2024	NUM
ejpam-5107	25	13	)	)	PUNCT
ejpam-5107	25	14	,	,	PUNCT
ejpam-5107	25	15	2299	2299	NUM
ejpam-5107	25	16	-	-	SYM
ejpam-5107	25	17	2310	2310	NUM
ejpam-5107	25	18	2301	2301	NUM
ejpam-5107	25	19	and	and	CCONJ
ejpam-5107	25	20	bh	bh	PROPN
ejpam-5107	25	21	2	2	NUM
ejpam-5107	25	22	(	(	PUNCT
ejpam-5107	25	23	t	t	PROPN
ejpam-5107	25	24	)	)	PUNCT
ejpam-5107	25	25	for	for	ADP
ejpam-5107	25	26	t	t	PROPN
ejpam-5107	25	27	≥	≥	X
ejpam-5107	25	28	0	0	NUM
ejpam-5107	25	29	is	be	AUX
ejpam-5107	25	30	given	give	VERB
ejpam-5107	25	31	by	by	ADP
ejpam-5107	25	32	cov(bh	cov(bh	PRON
ejpam-5107	25	33	1	1	NUM
ejpam-5107	25	34	(	(	PUNCT
ejpam-5107	25	35	t	t	PROPN
ejpam-5107	25	36	)	)	PUNCT
ejpam-5107	25	37	,	,	PUNCT
ejpam-5107	25	38	bh	bh	NOUN
ejpam-5107	25	39	2	2	NUM
ejpam-5107	25	40	(	(	PUNCT
ejpam-5107	25	41	t	t	PROPN
ejpam-5107	25	42	)	)	PUNCT
ejpam-5107	25	43	)	)	PUNCT
ejpam-5107	26	1	=	=	PUNCT
ejpam-5107	26	2	ρ(dt)2h	ρ(dt)2h	NOUN
ejpam-5107	26	3	.	.	PUNCT
ejpam-5107	27	1	(	(	PUNCT
ejpam-5107	27	2	6	6	NUM
ejpam-5107	27	3	)	)	PUNCT
ejpam-5107	27	4	moreover	moreover	ADV
ejpam-5107	27	5	,	,	PUNCT
ejpam-5107	27	6	the	the	DET
ejpam-5107	27	7	following	follow	VERB
ejpam-5107	27	8	properties	property	NOUN
ejpam-5107	27	9	are	be	AUX
ejpam-5107	27	10	applied	apply	VERB
ejpam-5107	27	11	to	to	ADP
ejpam-5107	27	12	the	the	DET
ejpam-5107	27	13	fractional	fractional	ADJ
ejpam-5107	27	14	brownian	brownian	ADJ
ejpam-5107	27	15	motion	motion	NOUN
ejpam-5107	27	16	:	:	PUNCT
ejpam-5107	27	17	e[dbh(t	e[dbh(t	NOUN
ejpam-5107	27	18	)	)	PUNCT
ejpam-5107	27	19	]	]	PUNCT
ejpam-5107	28	1	=	=	PUNCT
ejpam-5107	28	2	0	0	NUM
ejpam-5107	28	3	,	,	PUNCT
ejpam-5107	28	4	(	(	PUNCT
ejpam-5107	28	5	7	7	X
ejpam-5107	28	6	)	)	PUNCT
ejpam-5107	28	7	e[dtdbh(t	e[dtdbh(t	NOUN
ejpam-5107	28	8	)	)	PUNCT
ejpam-5107	28	9	]	]	PUNCT
ejpam-5107	29	1	=	=	PUNCT
ejpam-5107	29	2	0	0	NUM
ejpam-5107	29	3	,	,	PUNCT
ejpam-5107	29	4	(	(	PUNCT
ejpam-5107	29	5	8)	8)	NUM
ejpam-5107	29	6	e[dbh	e[dbh	NOUN
ejpam-5107	29	7	1	1	NUM
ejpam-5107	29	8	(	(	PUNCT
ejpam-5107	29	9	t)dbh	t)dbh	ADV
ejpam-5107	29	10	2	2	NUM
ejpam-5107	29	11	(	(	PUNCT
ejpam-5107	29	12	t	t	NOUN
ejpam-5107	29	13	)	)	PUNCT
ejpam-5107	29	14	]	]	PUNCT
ejpam-5107	30	1	=	=	PUNCT
ejpam-5107	30	2	ρdt2h	ρdt2h	PROPN
ejpam-5107	30	3	,	,	PUNCT
ejpam-5107	30	4	(	(	PUNCT
ejpam-5107	30	5	9	9	X
ejpam-5107	30	6	)	)	PUNCT
ejpam-5107	30	7	e[(dbh(t))2	e[(dbh(t))2	NOUN
ejpam-5107	30	8	]	]	PUNCT
ejpam-5107	31	1	=	=	SYM
ejpam-5107	31	2	(	(	PUNCT
ejpam-5107	31	3	dt)2h	dt)2h	NOUN
ejpam-5107	31	4	,	,	PUNCT
ejpam-5107	31	5	(	(	PUNCT
ejpam-5107	31	6	10	10	NUM
ejpam-5107	31	7	)	)	PUNCT
ejpam-5107	31	8	e[(dt)2	e[(dt)2	VERB
ejpam-5107	31	9	]	]	X
ejpam-5107	31	10	=	=	SYM
ejpam-5107	31	11	0	0	X
ejpam-5107	31	12	.	.	PUNCT
ejpam-5107	32	1	(	(	PUNCT
ejpam-5107	32	2	11	11	NUM
ejpam-5107	32	3	)	)	PUNCT
ejpam-5107	32	4	lemma	lemma	PROPN
ejpam-5107	32	5	1	1	NUM
ejpam-5107	32	6	.	.	PUNCT
ejpam-5107	33	1	the	the	DET
ejpam-5107	33	2	zero	zero	NUM
ejpam-5107	33	3	-	-	PUNCT
ejpam-5107	33	4	coupon	coupon	NOUN
ejpam-5107	33	5	bond	bond	NOUN
ejpam-5107	33	6	model	model	NOUN
ejpam-5107	33	7	with	with	ADP
ejpam-5107	33	8	the	the	DET
ejpam-5107	33	9	terminal	terminal	ADJ
ejpam-5107	33	10	condition	condition	NOUN
ejpam-5107	33	11	p	p	X
ejpam-5107	33	12	(	(	PUNCT
ejpam-5107	33	13	r	r	NOUN
ejpam-5107	33	14	,	,	PUNCT
ejpam-5107	33	15	t;t	t;t	NOUN
ejpam-5107	33	16	)	)	PUNCT
ejpam-5107	34	1	=	=	SYM
ejpam-5107	34	2	1	1	NUM
ejpam-5107	34	3	can	can	AUX
ejpam-5107	34	4	derive	derive	VERB
ejpam-5107	34	5	the	the	DET
ejpam-5107	34	6	following	follow	VERB
ejpam-5107	34	7	formula	formula	NOUN
ejpam-5107	34	8	p	p	X
ejpam-5107	34	9	(	(	PUNCT
ejpam-5107	34	10	r	r	NOUN
ejpam-5107	34	11	,	,	PUNCT
ejpam-5107	34	12	t;t	t;t	NOUN
ejpam-5107	34	13	)	)	PUNCT
ejpam-5107	35	1	=	=	PUNCT
ejpam-5107	35	2	e−rb(t	e−rb(t	PROPN
ejpam-5107	35	3	,	,	PUNCT
ejpam-5107	35	4	t	t	NOUN
ejpam-5107	35	5	)	)	PUNCT
ejpam-5107	35	6	−a(t	−a(t	NOUN
ejpam-5107	35	7	,	,	PUNCT
ejpam-5107	35	8	t	t	PROPN
ejpam-5107	35	9	)	)	PUNCT
ejpam-5107	35	10	,	,	PUNCT
ejpam-5107	35	11	(	(	PUNCT
ejpam-5107	35	12	12	12	NUM
ejpam-5107	35	13	)	)	PUNCT
ejpam-5107	35	14	with	with	ADP
ejpam-5107	35	15	b(t	b(t	PROPN
ejpam-5107	35	16	,	,	PUNCT
ejpam-5107	35	17	t	t	NOUN
ejpam-5107	35	18	)	)	PUNCT
ejpam-5107	35	19	=	=	PUNCT
ejpam-5107	36	1	1	1	NUM
ejpam-5107	36	2	a	a	PRON
ejpam-5107	36	3	[	[	PUNCT
ejpam-5107	36	4	1−	1−	NUM
ejpam-5107	36	5	e−a(t−t	e−a(t−t	NUM
ejpam-5107	36	6	)	)	PUNCT
ejpam-5107	36	7	]	]	PUNCT
ejpam-5107	37	1	a(t	a(t	PROPN
ejpam-5107	37	2	,	,	PUNCT
ejpam-5107	37	3	t	t	NOUN
ejpam-5107	37	4	)	)	PUNCT
ejpam-5107	37	5	=	=	PUNCT
ejpam-5107	38	1	−	−	PROPN
ejpam-5107	38	2	∫	∫	PROPN
ejpam-5107	38	3	t	t	PROPN
ejpam-5107	38	4	t	t	PROPN
ejpam-5107	38	5	θ(u)b(u	θ(u)b(u	VERB
ejpam-5107	38	6	,	,	PUNCT
ejpam-5107	38	7	t	t	NOUN
ejpam-5107	38	8	)	)	PUNCT
ejpam-5107	38	9	du+	du+	NOUN
ejpam-5107	39	1	1	1	NUM
ejpam-5107	39	2	2	2	NUM
ejpam-5107	39	3	dt2h	dt2h	NOUN
ejpam-5107	39	4	[	[	X
ejpam-5107	39	5	∫	∫	X
ejpam-5107	39	6	t	t	PROPN
ejpam-5107	39	7	t	t	PROPN
ejpam-5107	39	8	σ2rb	σ2rb	X
ejpam-5107	39	9	2(u	2(u	NUM
ejpam-5107	39	10	,	,	PUNCT
ejpam-5107	39	11	t	t	NOUN
ejpam-5107	39	12	)	)	PUNCT
ejpam-5107	39	13	du	du	PROPN
ejpam-5107	39	14	]	]	PUNCT
ejpam-5107	39	15	where	where	SCONJ
ejpam-5107	39	16	σr	σr	PROPN
ejpam-5107	39	17	is	be	AUX
ejpam-5107	39	18	the	the	DET
ejpam-5107	39	19	volatility	volatility	NOUN
ejpam-5107	39	20	of	of	ADP
ejpam-5107	39	21	the	the	DET
ejpam-5107	39	22	interest	interest	NOUN
ejpam-5107	39	23	rate	rate	NOUN
ejpam-5107	39	24	,	,	PUNCT
ejpam-5107	39	25	θ(t	θ(t	PROPN
ejpam-5107	39	26	)	)	PUNCT
ejpam-5107	39	27	is	be	AUX
ejpam-5107	39	28	a	a	DET
ejpam-5107	39	29	deterministic	deterministic	ADJ
ejpam-5107	39	30	function	function	NOUN
ejpam-5107	39	31	of	of	ADP
ejpam-5107	39	32	time	time	NOUN
ejpam-5107	39	33	,	,	PUNCT
ejpam-5107	39	34	and	and	CCONJ
ejpam-5107	39	35	a	a	PRON
ejpam-5107	39	36	is	be	AUX
ejpam-5107	39	37	a	a	DET
ejpam-5107	39	38	constant	constant	ADJ
ejpam-5107	39	39	assumed	assume	VERB
ejpam-5107	39	40	to	to	PART
ejpam-5107	39	41	be	be	AUX
ejpam-5107	39	42	nonzero	nonzero	ADJ
ejpam-5107	39	43	.	.	PUNCT
ejpam-5107	40	1	3	3	X
ejpam-5107	40	2	.	.	X
ejpam-5107	40	3	transaction	transaction	NOUN
ejpam-5107	40	4	cost	cost	NOUN
ejpam-5107	40	5	transaction	transaction	NOUN
ejpam-5107	40	6	cost	cost	NOUN
ejpam-5107	40	7	is	be	AUX
ejpam-5107	40	8	a	a	DET
ejpam-5107	40	9	fixed	fix	VERB
ejpam-5107	40	10	proportion	proportion	NOUN
ejpam-5107	40	11	c	c	NOUN
ejpam-5107	40	12	,	,	PUNCT
ejpam-5107	40	13	depending	depend	VERB
ejpam-5107	40	14	on	on	ADP
ejpam-5107	40	15	the	the	DET
ejpam-5107	40	16	individual	individual	ADJ
ejpam-5107	40	17	investor	investor	NOUN
ejpam-5107	40	18	,	,	PUNCT
ejpam-5107	40	19	of	of	ADP
ejpam-5107	40	20	the	the	DET
ejpam-5107	40	21	trading	trading	NOUN
ejpam-5107	40	22	amount	amount	NOUN
ejpam-5107	40	23	for	for	ADP
ejpam-5107	40	24	the	the	DET
ejpam-5107	40	25	asset	asset	NOUN
ejpam-5107	40	26	.	.	PUNCT
ejpam-5107	41	1	we	we	PRON
ejpam-5107	41	2	have	have	VERB
ejpam-5107	41	3	cost	cost	NOUN
ejpam-5107	41	4	=	=	PUNCT
ejpam-5107	41	5	cx(t)|v(t)|	cx(t)|v(t)|	NUM
ejpam-5107	41	6	where	where	SCONJ
ejpam-5107	41	7	v(t	v(t	NOUN
ejpam-5107	41	8	)	)	PUNCT
ejpam-5107	41	9	is	be	AUX
ejpam-5107	41	10	the	the	DET
ejpam-5107	41	11	number	number	NOUN
ejpam-5107	41	12	of	of	ADP
ejpam-5107	41	13	shares	share	NOUN
ejpam-5107	41	14	of	of	ADP
ejpam-5107	41	15	the	the	DET
ejpam-5107	41	16	sold	sell	VERB
ejpam-5107	41	17	or	or	CCONJ
ejpam-5107	41	18	bought	buy	VERB
ejpam-5107	41	19	at	at	ADP
ejpam-5107	41	20	the	the	DET
ejpam-5107	41	21	price	price	NOUN
ejpam-5107	41	22	xt	xt	PROPN
ejpam-5107	41	23	.	.	PUNCT
ejpam-5107	42	1	specifically	specifically	ADV
ejpam-5107	42	2	,	,	PUNCT
ejpam-5107	42	3	v(t	v(t	NOUN
ejpam-5107	42	4	)	)	PUNCT
ejpam-5107	42	5	>	>	X
ejpam-5107	42	6	0	0	NUM
ejpam-5107	42	7	indicates	indicate	VERB
ejpam-5107	42	8	a	a	DET
ejpam-5107	42	9	bought	buy	VERB
ejpam-5107	42	10	share	share	NOUN
ejpam-5107	42	11	while	while	SCONJ
ejpam-5107	42	12	v(t	v(t	NOUN
ejpam-5107	42	13	)	)	PUNCT
ejpam-5107	42	14	<	<	X
ejpam-5107	42	15	0	0	NUM
ejpam-5107	42	16	indicates	indicate	VERB
ejpam-5107	42	17	a	a	DET
ejpam-5107	42	18	sold	sell	VERB
ejpam-5107	42	19	shares	share	NOUN
ejpam-5107	42	20	.	.	PUNCT
ejpam-5107	43	1	4	4	X
ejpam-5107	43	2	.	.	X
ejpam-5107	43	3	portfolio	portfolio	NOUN
ejpam-5107	43	4	the	the	DET
ejpam-5107	43	5	portfolio	portfolio	NOUN
ejpam-5107	43	6	is	be	AUX
ejpam-5107	43	7	revised	revise	VERB
ejpam-5107	43	8	at	at	ADP
ejpam-5107	43	9	time	time	NOUN
ejpam-5107	43	10	dt	dt	X
ejpam-5107	43	11	,	,	PUNCT
ejpam-5107	43	12	where	where	SCONJ
ejpam-5107	43	13	dt	dt	PROPN
ejpam-5107	43	14	is	be	AUX
ejpam-5107	43	15	a	a	DET
ejpam-5107	43	16	small	small	ADJ
ejpam-5107	43	17	time	time	NOUN
ejpam-5107	43	18	step	step	NOUN
ejpam-5107	43	19	from	from	ADP
ejpam-5107	43	20	t	t	PROPN
ejpam-5107	43	21	to	to	ADP
ejpam-5107	43	22	t+	t+	NOUN
ejpam-5107	43	23	dt	dt	PROPN
ejpam-5107	43	24	.	.	PROPN
ejpam-5107	43	25	5	5	X
ejpam-5107	43	26	.	.	PUNCT
ejpam-5107	43	27	expected	expect	VERB
ejpam-5107	43	28	return	return	NOUN
ejpam-5107	43	29	of	of	ADP
ejpam-5107	43	30	the	the	DET
ejpam-5107	43	31	portfolio	portfolio	NOUN
ejpam-5107	43	32	the	the	DET
ejpam-5107	43	33	expected	expect	VERB
ejpam-5107	43	34	return	return	NOUN
ejpam-5107	43	35	of	of	ADP
ejpam-5107	43	36	the	the	DET
ejpam-5107	43	37	portfolio	portfolio	NOUN
ejpam-5107	43	38	π(t	π(t	PROPN
ejpam-5107	43	39	)	)	PUNCT
ejpam-5107	43	40	satisfies	satisfy	VERB
ejpam-5107	43	41	the	the	DET
ejpam-5107	43	42	equality	equality	NOUN
ejpam-5107	43	43	e[dπ(t	e[dπ(t	PROPN
ejpam-5107	43	44	)	)	PUNCT
ejpam-5107	43	45	]	]	PUNCT
ejpam-5107	44	1	=	=	PUNCT
ejpam-5107	44	2	r(t)π(t)dt	r(t)π(t)dt	PROPN
ejpam-5107	44	3	(	(	PUNCT
ejpam-5107	44	4	13	13	NUM
ejpam-5107	44	5	)	)	PUNCT
ejpam-5107	44	6	where	where	SCONJ
ejpam-5107	44	7	r(t	r(t	NOUN
ejpam-5107	44	8	)	)	PUNCT
ejpam-5107	44	9	is	be	AUX
ejpam-5107	44	10	the	the	DET
ejpam-5107	44	11	interest	interest	NOUN
ejpam-5107	44	12	rate	rate	NOUN
ejpam-5107	44	13	.	.	PUNCT
ejpam-5107	45	1	f.	f.	PROPN
ejpam-5107	45	2	sumalpong	sumalpong	PROPN
ejpam-5107	45	3	,	,	PUNCT
ejpam-5107	45	4	e.	e.	PROPN
ejpam-5107	45	5	lauron	lauron	PROPN
ejpam-5107	45	6	/	/	SYM
ejpam-5107	45	7	eur	eur	PROPN
ejpam-5107	45	8	.	.	PUNCT
ejpam-5107	46	1	j.	j.	PROPN
ejpam-5107	46	2	pure	pure	PROPN
ejpam-5107	46	3	appl	appl	PROPN
ejpam-5107	46	4	.	.	PROPN
ejpam-5107	46	5	math	math	PROPN
ejpam-5107	46	6	,	,	PUNCT
ejpam-5107	46	7	17	17	NUM
ejpam-5107	46	8	(	(	PUNCT
ejpam-5107	46	9	3	3	NUM
ejpam-5107	46	10	)	)	PUNCT
ejpam-5107	46	11	(	(	PUNCT
ejpam-5107	46	12	2024	2024	NUM
ejpam-5107	46	13	)	)	PUNCT
ejpam-5107	46	14	,	,	PUNCT
ejpam-5107	46	15	2299	2299	NUM
ejpam-5107	46	16	-	-	SYM
ejpam-5107	46	17	2310	2310	NUM
ejpam-5107	46	18	2302	2302	NUM
ejpam-5107	46	19	from	from	ADP
ejpam-5107	46	20	these	these	DET
ejpam-5107	46	21	assumptions	assumption	NOUN
ejpam-5107	47	1	,	,	PUNCT
ejpam-5107	47	2	we	we	PRON
ejpam-5107	47	3	can	can	AUX
ejpam-5107	47	4	now	now	ADV
ejpam-5107	47	5	begin	begin	VERB
ejpam-5107	47	6	to	to	PART
ejpam-5107	47	7	price	price	VERB
ejpam-5107	47	8	the	the	DET
ejpam-5107	47	9	zero	zero	NUM
ejpam-5107	47	10	-	-	PUNCT
ejpam-5107	47	11	coupon	coupon	NOUN
ejpam-5107	47	12	bond	bond	NOUN
ejpam-5107	47	13	of	of	ADP
ejpam-5107	47	14	the	the	DET
ejpam-5107	47	15	fractional	fractional	ADJ
ejpam-5107	47	16	hull	hull	NOUN
ejpam-5107	47	17	-	-	PUNCT
ejpam-5107	47	18	white	white	NOUN
ejpam-5107	47	19	which	which	PRON
ejpam-5107	47	20	we	we	PRON
ejpam-5107	47	21	will	will	AUX
ejpam-5107	47	22	use	use	VERB
ejpam-5107	47	23	to	to	PART
ejpam-5107	47	24	come	come	VERB
ejpam-5107	47	25	up	up	ADP
ejpam-5107	47	26	an	an	DET
ejpam-5107	47	27	option	option	NOUN
ejpam-5107	47	28	price	price	NOUN
ejpam-5107	47	29	.	.	PUNCT
ejpam-5107	48	1	theorem	theorem	NOUN
ejpam-5107	48	2	1	1	NUM
ejpam-5107	48	3	.	.	PUNCT
ejpam-5107	49	1	under	under	ADP
ejpam-5107	49	2	the	the	DET
ejpam-5107	49	3	fractional	fractional	ADJ
ejpam-5107	49	4	hull	hull	NOUN
ejpam-5107	49	5	-	-	PUNCT
ejpam-5107	49	6	white	white	ADJ
ejpam-5107	49	7	interest	interest	NOUN
ejpam-5107	49	8	rate	rate	NOUN
ejpam-5107	49	9	model	model	PROPN
ejpam-5107	49	10	,	,	PUNCT
ejpam-5107	49	11	the	the	DET
ejpam-5107	49	12	zero	zero	NUM
ejpam-5107	49	13	-	-	PUNCT
ejpam-5107	49	14	coupon	coupon	NOUN
ejpam-5107	49	15	bond	bond	NOUN
ejpam-5107	49	16	price	price	NOUN
ejpam-5107	49	17	p	p	NOUN
ejpam-5107	49	18	(	(	PUNCT
ejpam-5107	49	19	r(t	r(t	NOUN
ejpam-5107	49	20	)	)	PUNCT
ejpam-5107	49	21	,	,	PUNCT
ejpam-5107	49	22	t;t	t;t	NUM
ejpam-5107	49	23	)	)	PUNCT
ejpam-5107	49	24	obeys	obey	VERB
ejpam-5107	49	25	the	the	DET
ejpam-5107	49	26	following	follow	VERB
ejpam-5107	49	27	equation	equation	NOUN
ejpam-5107	49	28	:	:	PUNCT
ejpam-5107	49	29	∂p	∂p	PROPN
ejpam-5107	49	30	∂t	∂t	PROPN
ejpam-5107	50	1	+	+	PUNCT
ejpam-5107	50	2	[	[	X
ejpam-5107	50	3	θ(t)−	θ(t)−	PROPN
ejpam-5107	50	4	ar(t)−	ar(t)−	PROPN
ejpam-5107	50	5	ψσr	ψσr	PROPN
ejpam-5107	50	6	]	]	X
ejpam-5107	51	1	∂p	∂p	PROPN
ejpam-5107	52	1	∂r	∂r	PROPN
ejpam-5107	53	1	+	+	CCONJ
ejpam-5107	53	2	1	1	NUM
ejpam-5107	53	3	2	2	NUM
ejpam-5107	53	4	∂2p	∂2p	NOUN
ejpam-5107	53	5	∂r2	∂r2	PROPN
ejpam-5107	53	6	(	(	PUNCT
ejpam-5107	53	7	σr	σr	PROPN
ejpam-5107	53	8	)	)	PUNCT
ejpam-5107	53	9	2(dt)2h−1	2(dt)2h−1	NUM
ejpam-5107	53	10	−	−	NOUN
ejpam-5107	53	11	rp	rp	NOUN
ejpam-5107	53	12	=	=	NOUN
ejpam-5107	53	13	0	0	PROPN
ejpam-5107	53	14	.	.	PUNCT
ejpam-5107	53	15	where	where	SCONJ
ejpam-5107	53	16	r(t	r(t	NOUN
ejpam-5107	53	17	)	)	PUNCT
ejpam-5107	53	18	is	be	AUX
ejpam-5107	53	19	the	the	DET
ejpam-5107	53	20	interest	interest	NOUN
ejpam-5107	53	21	rate	rate	NOUN
ejpam-5107	53	22	under	under	ADP
ejpam-5107	53	23	hull	hull	NOUN
ejpam-5107	53	24	-	-	PUNCT
ejpam-5107	53	25	white	white	ADJ
ejpam-5107	53	26	model	model	NOUN
ejpam-5107	53	27	,	,	PUNCT
ejpam-5107	53	28	θ(t	θ(t	PROPN
ejpam-5107	53	29	)	)	PUNCT
ejpam-5107	53	30	is	be	AUX
ejpam-5107	53	31	a	a	DET
ejpam-5107	53	32	deterministic	deterministic	ADJ
ejpam-5107	53	33	function	function	NOUN
ejpam-5107	53	34	of	of	ADP
ejpam-5107	53	35	time	time	NOUN
ejpam-5107	53	36	,	,	PUNCT
ejpam-5107	53	37	a	a	PRON
ejpam-5107	53	38	is	be	AUX
ejpam-5107	53	39	constant	constant	ADJ
ejpam-5107	53	40	,	,	PUNCT
ejpam-5107	53	41	ψ	ψ	X
ejpam-5107	53	42	is	be	AUX
ejpam-5107	53	43	the	the	DET
ejpam-5107	53	44	market	market	NOUN
ejpam-5107	53	45	price	price	NOUN
ejpam-5107	53	46	of	of	ADP
ejpam-5107	53	47	the	the	DET
ejpam-5107	53	48	risk	risk	NOUN
ejpam-5107	53	49	with	with	ADP
ejpam-5107	53	50	volatility	volatility	NOUN
ejpam-5107	53	51	σ	σ	PROPN
ejpam-5107	53	52	and	and	CCONJ
ejpam-5107	53	53	σr	σr	PROPN
ejpam-5107	53	54	is	be	AUX
ejpam-5107	53	55	the	the	DET
ejpam-5107	53	56	volatility	volatility	NOUN
ejpam-5107	53	57	of	of	ADP
ejpam-5107	53	58	the	the	DET
ejpam-5107	53	59	interest	interest	NOUN
ejpam-5107	53	60	rate	rate	NOUN
ejpam-5107	53	61	which	which	PRON
ejpam-5107	53	62	is	be	AUX
ejpam-5107	53	63	assumed	assume	VERB
ejpam-5107	53	64	to	to	PART
ejpam-5107	53	65	be	be	AUX
ejpam-5107	53	66	constant	constant	ADJ
ejpam-5107	53	67	.	.	PUNCT
ejpam-5107	54	1	proof	proof	NOUN
ejpam-5107	54	2	:	:	PUNCT
ejpam-5107	54	3	the	the	DET
ejpam-5107	54	4	equation	equation	NOUN
ejpam-5107	54	5	can	can	AUX
ejpam-5107	54	6	be	be	AUX
ejpam-5107	54	7	attained	attain	VERB
ejpam-5107	54	8	by	by	ADP
ejpam-5107	54	9	constructing	construct	VERB
ejpam-5107	54	10	a	a	DET
ejpam-5107	54	11	deterministic	deterministic	ADJ
ejpam-5107	54	12	hedged	hedge	VERB
ejpam-5107	54	13	portfolio	portfolio	NOUN
ejpam-5107	54	14	that	that	PRON
ejpam-5107	54	15	employs	employ	VERB
ejpam-5107	54	16	two	two	NUM
ejpam-5107	54	17	coupon	coupon	NOUN
ejpam-5107	54	18	bonds	bond	NOUN
ejpam-5107	54	19	p1(t	p1(t	NOUN
ejpam-5107	54	20	)	)	PUNCT
ejpam-5107	54	21	,	,	PUNCT
ejpam-5107	54	22	p2(t	p2(t	PROPN
ejpam-5107	54	23	)	)	PUNCT
ejpam-5107	54	24	,	,	PUNCT
ejpam-5107	54	25	that	that	ADV
ejpam-5107	54	26	is	is	ADV
ejpam-5107	54	27	,	,	PUNCT
ejpam-5107	54	28	π(t	π(t	PROPN
ejpam-5107	54	29	)	)	PUNCT
ejpam-5107	54	30	=	=	PUNCT
ejpam-5107	54	31	p1(t)−∆p2(t	p1(t)−∆p2(t	NUM
ejpam-5107	54	32	)	)	PUNCT
ejpam-5107	54	33	(	(	PUNCT
ejpam-5107	54	34	14	14	NUM
ejpam-5107	54	35	)	)	PUNCT
ejpam-5107	54	36	with	with	ADP
ejpam-5107	54	37	different	different	ADJ
ejpam-5107	54	38	maturity	maturity	NOUN
ejpam-5107	54	39	t1	t1	NOUN
ejpam-5107	54	40	and	and	CCONJ
ejpam-5107	54	41	t2	t2	NOUN
ejpam-5107	54	42	respectively	respectively	ADV
ejpam-5107	54	43	.	.	PUNCT
ejpam-5107	55	1	we	we	PRON
ejpam-5107	55	2	long	long	VERB
ejpam-5107	55	3	one	one	NUM
ejpam-5107	55	4	share	share	NOUN
ejpam-5107	55	5	of	of	ADP
ejpam-5107	55	6	bond	bond	NOUN
ejpam-5107	55	7	p1(t	p1(t	PART
ejpam-5107	55	8	)	)	PUNCT
ejpam-5107	55	9	and	and	CCONJ
ejpam-5107	55	10	short	short	ADJ
ejpam-5107	55	11	∆	∆	ADJ
ejpam-5107	55	12	shares	share	NOUN
ejpam-5107	55	13	of	of	ADP
ejpam-5107	55	14	p2(t	p2(t	NOUN
ejpam-5107	55	15	)	)	PUNCT
ejpam-5107	55	16	.	.	PUNCT
ejpam-5107	56	1	taking	take	VERB
ejpam-5107	56	2	the	the	DET
ejpam-5107	56	3	derivative	derivative	NOUN
ejpam-5107	56	4	of	of	ADP
ejpam-5107	56	5	equation	equation	NOUN
ejpam-5107	56	6	(	(	PUNCT
ejpam-5107	56	7	14	14	NUM
ejpam-5107	56	8	)	)	PUNCT
ejpam-5107	56	9	,	,	PUNCT
ejpam-5107	56	10	we	we	PRON
ejpam-5107	56	11	have	have	VERB
ejpam-5107	56	12	dπ(t	dπ(t	NOUN
ejpam-5107	56	13	)	)	PUNCT
ejpam-5107	56	14	=	=	SYM
ejpam-5107	56	15	dp1(t)−∆dp2(t	dp1(t)−∆dp2(t	NOUN
ejpam-5107	56	16	)	)	PUNCT
ejpam-5107	56	17	.	.	PUNCT
ejpam-5107	57	1	(	(	PUNCT
ejpam-5107	57	2	15	15	X
ejpam-5107	57	3	)	)	PUNCT
ejpam-5107	57	4	applying	apply	VERB
ejpam-5107	57	5	ito	ito	PROPN
ejpam-5107	57	6	’s	’s	PART
ejpam-5107	57	7	lemma	lemma	PROPN
ejpam-5107	57	8	to	to	ADP
ejpam-5107	57	9	the	the	DET
ejpam-5107	57	10	price	price	NOUN
ejpam-5107	57	11	function	function	NOUN
ejpam-5107	57	12	p	p	NOUN
ejpam-5107	57	13	(	(	PUNCT
ejpam-5107	57	14	r(t	r(t	NOUN
ejpam-5107	57	15	)	)	PUNCT
ejpam-5107	57	16	,	,	PUNCT
ejpam-5107	57	17	t;t	t;t	NOUN
ejpam-5107	57	18	)	)	PUNCT
ejpam-5107	57	19	,	,	PUNCT
ejpam-5107	57	20	the	the	DET
ejpam-5107	57	21	right	right	ADJ
ejpam-5107	57	22	-	-	PUNCT
ejpam-5107	57	23	hand	hand	NOUN
ejpam-5107	57	24	side	side	NOUN
ejpam-5107	57	25	of	of	ADP
ejpam-5107	57	26	the	the	DET
ejpam-5107	57	27	equality	equality	NOUN
ejpam-5107	57	28	in	in	ADP
ejpam-5107	57	29	equation	equation	NOUN
ejpam-5107	57	30	15	15	NUM
ejpam-5107	57	31	becomes	become	VERB
ejpam-5107	57	32	,	,	PUNCT
ejpam-5107	57	33	∂p1	∂p1	ADJ
ejpam-5107	57	34	∂t	∂t	PROPN
ejpam-5107	57	35	dt+	dt+	NOUN
ejpam-5107	58	1	[	[	X
ejpam-5107	58	2	θ(t)−	θ(t)−	PROPN
ejpam-5107	58	3	ar(t	ar(t	PUNCT
ejpam-5107	58	4	)	)	PUNCT
ejpam-5107	58	5	]	]	PUNCT
ejpam-5107	59	1	∂p1	∂p1	NOUN
ejpam-5107	59	2	∂r	∂r	ADJ
ejpam-5107	59	3	dt+	dt+	NOUN
ejpam-5107	59	4	1	1	NUM
ejpam-5107	59	5	2	2	NUM
ejpam-5107	59	6	∂2p1	∂2p1	NOUN
ejpam-5107	59	7	∂r2	∂r2	PROPN
ejpam-5107	59	8	(	(	PUNCT
ejpam-5107	59	9	[	[	X
ejpam-5107	59	10	θ(t)−	θ(t)−	PROPN
ejpam-5107	59	11	ar(t)]2(dt)2	ar(t)]2(dt)2	PROPN
ejpam-5107	59	12	+2[θ(t)−	+2[θ(t)−	PROPN
ejpam-5107	59	13	ar(t)]σrdtdb	ar(t)]σrdtdb	X
ejpam-5107	59	14	h	h	NOUN
ejpam-5107	59	15	2	2	NUM
ejpam-5107	59	16	+	+	CCONJ
ejpam-5107	59	17	(	(	PUNCT
ejpam-5107	59	18	σr	σr	PROPN
ejpam-5107	59	19	)	)	PUNCT
ejpam-5107	59	20	2(dbh	2(dbh	NUM
ejpam-5107	59	21	2	2	NUM
ejpam-5107	59	22	)	)	PUNCT
ejpam-5107	59	23	2	2	NUM
ejpam-5107	59	24	)	)	PUNCT
ejpam-5107	59	25	+	+	CCONJ
ejpam-5107	59	26	σr	σr	ADP
ejpam-5107	59	27	∂p1	∂p1	NOUN
ejpam-5107	59	28	∂r	∂r	PROPN
ejpam-5107	59	29	dbh	dbh	PROPN
ejpam-5107	59	30	2	2	NUM
ejpam-5107	59	31	−∆σr	−∆σr	NOUN
ejpam-5107	59	32	∂p1	∂p1	NOUN
ejpam-5107	59	33	∂r	∂r	PROPN
ejpam-5107	59	34	dbh	dbh	PROPN
ejpam-5107	59	35	2	2	NUM
ejpam-5107	59	36	−∆	−∆	NOUN
ejpam-5107	59	37	(	(	PUNCT
ejpam-5107	59	38	∂p2	∂p2	PROPN
ejpam-5107	59	39	∂t	∂t	PROPN
ejpam-5107	59	40	dt+	dt+	NOUN
ejpam-5107	59	41	[	[	X
ejpam-5107	59	42	θ(t)−	θ(t)−	PROPN
ejpam-5107	59	43	ar(t	ar(t	PUNCT
ejpam-5107	59	44	)	)	PUNCT
ejpam-5107	59	45	]	]	PUNCT
ejpam-5107	60	1	∂p2	∂p2	X
ejpam-5107	60	2	∂r	∂r	ADJ
ejpam-5107	60	3	dt+	dt+	NOUN
ejpam-5107	60	4	1	1	NUM
ejpam-5107	60	5	2	2	NUM
ejpam-5107	60	6	∂2p2	∂2p2	NUM
ejpam-5107	60	7	∂r2	∂r2	PROPN
ejpam-5107	60	8	(	(	PUNCT
ejpam-5107	60	9	[	[	X
ejpam-5107	60	10	θ(t)−	θ(t)−	PROPN
ejpam-5107	60	11	ar(t)]2(dt)2	ar(t)]2(dt)2	PROPN
ejpam-5107	60	12	+	+	NUM
ejpam-5107	60	13	2[θ(t)−	2[θ(t)−	NUM
ejpam-5107	60	14	ar(t)]σrdtdb	ar(t)]σrdtdb	X
ejpam-5107	60	15	h	h	NOUN
ejpam-5107	60	16	2	2	NUM
ejpam-5107	60	17	+	+	CCONJ
ejpam-5107	60	18	(	(	PUNCT
ejpam-5107	60	19	σr	σr	PROPN
ejpam-5107	60	20	)	)	PUNCT
ejpam-5107	60	21	2(dbh	2(dbh	NUM
ejpam-5107	60	22	2	2	NUM
ejpam-5107	60	23	)	)	PUNCT
ejpam-5107	60	24	2	2	NUM
ejpam-5107	60	25	)	)	PUNCT
ejpam-5107	60	26	)	)	PUNCT
ejpam-5107	60	27	to	to	PART
ejpam-5107	60	28	eliminate	eliminate	VERB
ejpam-5107	60	29	the	the	DET
ejpam-5107	60	30	risk	risk	NOUN
ejpam-5107	60	31	,	,	PUNCT
ejpam-5107	60	32	take	take	VERB
ejpam-5107	60	33	∆	∆	X
ejpam-5107	60	34	=	=	PUNCT
ejpam-5107	61	1	∂p1	∂p1	NOUN
ejpam-5107	61	2	∂r	∂r	PROPN
ejpam-5107	61	3	/	/	SYM
ejpam-5107	61	4	∂p2	∂p2	PROPN
ejpam-5107	62	1	∂r	∂r	INTJ
ejpam-5107	62	2	,	,	PUNCT
ejpam-5107	62	3	(	(	PUNCT
ejpam-5107	62	4	16	16	NUM
ejpam-5107	62	5	)	)	PUNCT
ejpam-5107	62	6	such	such	ADJ
ejpam-5107	62	7	that	that	SCONJ
ejpam-5107	62	8	∂p2	∂p2	PROPN
ejpam-5107	63	1	∂r	∂r	PROPN
ejpam-5107	63	2	̸=	̸=	PROPN
ejpam-5107	63	3	0	0	NUM
ejpam-5107	63	4	.	.	PUNCT
ejpam-5107	64	1	thus	thus	ADV
ejpam-5107	64	2	,	,	PUNCT
ejpam-5107	64	3	∂p1	∂p1	ADJ
ejpam-5107	64	4	∂t	∂t	PROPN
ejpam-5107	64	5	dt+	dt+	NOUN
ejpam-5107	64	6	[	[	X
ejpam-5107	64	7	θ(t)−	θ(t)−	PROPN
ejpam-5107	64	8	ar(t	ar(t	PUNCT
ejpam-5107	64	9	)	)	PUNCT
ejpam-5107	64	10	]	]	PUNCT
ejpam-5107	65	1	∂p1	∂p1	NOUN
ejpam-5107	65	2	∂r	∂r	ADJ
ejpam-5107	65	3	dt+	dt+	NOUN
ejpam-5107	65	4	[	[	X
ejpam-5107	65	5	θ(t)−	θ(t)−	PROPN
ejpam-5107	65	6	ar(t)]2(dt)2	ar(t)]2(dt)2	PROPN
ejpam-5107	66	1	+	+	PROPN
ejpam-5107	66	2	[	[	X
ejpam-5107	66	3	θ(t)−	θ(t)−	PROPN
ejpam-5107	66	4	ar(t)]σr	ar(t)]σr	PROPN
ejpam-5107	66	5	∂2p1	∂2p1	X
ejpam-5107	66	6	∂r2	∂r2	PROPN
ejpam-5107	66	7	dtdbh	dtdbh	VERB
ejpam-5107	66	8	2	2	NUM
ejpam-5107	66	9	+	+	CCONJ
ejpam-5107	66	10	(	(	PUNCT
ejpam-5107	66	11	σr	σr	ADJ
ejpam-5107	66	12	)	)	PUNCT
ejpam-5107	66	13	2	2	NUM
ejpam-5107	66	14	1	1	NUM
ejpam-5107	66	15	2	2	NUM
ejpam-5107	66	16	∂2p1	∂2p1	NOUN
ejpam-5107	66	17	∂r2	∂r2	PROPN
ejpam-5107	66	18	(	(	PUNCT
ejpam-5107	66	19	dbh	dbh	PROPN
ejpam-5107	66	20	2	2	NUM
ejpam-5107	66	21	)	)	PUNCT
ejpam-5107	66	22	2	2	NUM
ejpam-5107	66	23	−	−	PROPN
ejpam-5107	66	24	(	(	PUNCT
ejpam-5107	66	25	∂p1	∂p1	NOUN
ejpam-5107	66	26	∂r	∂r	PROPN
ejpam-5107	66	27	/	/	SYM
ejpam-5107	66	28	∂p2	∂p2	PROPN
ejpam-5107	67	1	∂r	∂r	PROPN
ejpam-5107	67	2	)	)	PUNCT
ejpam-5107	68	1	∂p2	∂p2	PROPN
ejpam-5107	68	2	∂t	∂t	PROPN
ejpam-5107	68	3	dt−	dt−	PROPN
ejpam-5107	68	4	[	[	X
ejpam-5107	68	5	θ(t)−	θ(t)−	PROPN
ejpam-5107	68	6	ar(t	ar(t	PUNCT
ejpam-5107	68	7	)	)	PUNCT
ejpam-5107	68	8	]	]	PUNCT
ejpam-5107	69	1	∂p2	∂p2	PROPN
ejpam-5107	70	1	∂r	∂r	INTJ
ejpam-5107	70	2	(	(	PUNCT
ejpam-5107	70	3	∂p1	∂p1	NOUN
ejpam-5107	70	4	∂r	∂r	PROPN
ejpam-5107	70	5	/	/	SYM
ejpam-5107	70	6	∂p2	∂p2	PROPN
ejpam-5107	70	7	∂r	∂r	PROPN
ejpam-5107	70	8	)	)	PUNCT
ejpam-5107	70	9	dt	dt	PROPN
ejpam-5107	70	10	f.	f.	PROPN
ejpam-5107	70	11	sumalpong	sumalpong	PROPN
ejpam-5107	70	12	,	,	PUNCT
ejpam-5107	70	13	e.	e.	PROPN
ejpam-5107	70	14	lauron	lauron	PROPN
ejpam-5107	70	15	/	/	SYM
ejpam-5107	70	16	eur	eur	PROPN
ejpam-5107	70	17	.	.	PUNCT
ejpam-5107	71	1	j.	j.	PROPN
ejpam-5107	71	2	pure	pure	PROPN
ejpam-5107	71	3	appl	appl	PROPN
ejpam-5107	71	4	.	.	PROPN
ejpam-5107	71	5	math	math	PROPN
ejpam-5107	71	6	,	,	PUNCT
ejpam-5107	71	7	17	17	NUM
ejpam-5107	71	8	(	(	PUNCT
ejpam-5107	71	9	3	3	NUM
ejpam-5107	71	10	)	)	PUNCT
ejpam-5107	71	11	(	(	PUNCT
ejpam-5107	71	12	2024	2024	NUM
ejpam-5107	71	13	)	)	PUNCT
ejpam-5107	71	14	,	,	PUNCT
ejpam-5107	71	15	2299	2299	NUM
ejpam-5107	71	16	-	-	SYM
ejpam-5107	71	17	2310	2310	NUM
ejpam-5107	71	18	2303	2303	NUM
ejpam-5107	71	19	−	−	NOUN
ejpam-5107	71	20	1	1	NUM
ejpam-5107	71	21	2	2	NUM
ejpam-5107	71	22	∂2p2	∂2p2	NUM
ejpam-5107	71	23	∂r2	∂r2	PROPN
ejpam-5107	71	24	(	(	PUNCT
ejpam-5107	71	25	∂p1	∂p1	NOUN
ejpam-5107	71	26	∂r	∂r	PROPN
ejpam-5107	71	27	/	/	SYM
ejpam-5107	71	28	∂p2	∂p2	PROPN
ejpam-5107	72	1	∂r	∂r	PROPN
ejpam-5107	72	2	)	)	PUNCT
ejpam-5107	73	1	[	[	X
ejpam-5107	73	2	θ(t)−	θ(t)−	PROPN
ejpam-5107	73	3	ar(t)]2(dt)2	ar(t)]2(dt)2	PROPN
ejpam-5107	73	4	−	−	PROPN
ejpam-5107	73	5	[	[	X
ejpam-5107	73	6	θ(t)−	θ(t)−	PROPN
ejpam-5107	73	7	ar(t)]σr	ar(t)]σr	PROPN
ejpam-5107	73	8	∂2p2	∂2p2	PUNCT
ejpam-5107	73	9	∂r2	∂r2	PROPN
ejpam-5107	73	10	(	(	PUNCT
ejpam-5107	73	11	∂p1	∂p1	NOUN
ejpam-5107	73	12	∂r	∂r	PROPN
ejpam-5107	73	13	/	/	SYM
ejpam-5107	73	14	∂p2	∂p2	PROPN
ejpam-5107	73	15	∂r	∂r	PROPN
ejpam-5107	73	16	)	)	PUNCT
ejpam-5107	73	17	dtdbh	dtdbh	VERB
ejpam-5107	73	18	2	2	NUM
ejpam-5107	73	19	−	−	NOUN
ejpam-5107	73	20	(	(	PUNCT
ejpam-5107	73	21	σr	σr	NOUN
ejpam-5107	73	22	)	)	PUNCT
ejpam-5107	73	23	2	2	NUM
ejpam-5107	73	24	1	1	NUM
ejpam-5107	73	25	2	2	NUM
ejpam-5107	73	26	∂2p2	∂2p2	NUM
ejpam-5107	73	27	∂r2	∂r2	PROPN
ejpam-5107	73	28	(	(	PUNCT
ejpam-5107	73	29	∂p1	∂p1	NOUN
ejpam-5107	73	30	∂r	∂r	PROPN
ejpam-5107	73	31	/	/	SYM
ejpam-5107	73	32	∂p2	∂p2	PROPN
ejpam-5107	73	33	∂r	∂r	PROPN
ejpam-5107	73	34	)	)	PUNCT
ejpam-5107	73	35	(	(	PUNCT
ejpam-5107	73	36	dbh	dbh	PROPN
ejpam-5107	73	37	2	2	NUM
ejpam-5107	73	38	)	)	PUNCT
ejpam-5107	73	39	2	2	NUM
ejpam-5107	73	40	.	.	PUNCT
ejpam-5107	73	41	by	by	ADP
ejpam-5107	73	42	non	non	ADJ
ejpam-5107	73	43	-	-	ADJ
ejpam-5107	73	44	arbitrage	arbitrage	ADJ
ejpam-5107	73	45	principle	principle	NOUN
ejpam-5107	73	46	,	,	PUNCT
ejpam-5107	73	47	∂p1	∂p1	PROPN
ejpam-5107	73	48	∂t	∂t	PROPN
ejpam-5107	74	1	+	+	PUNCT
ejpam-5107	74	2	[	[	X
ejpam-5107	74	3	θ(t)−	θ(t)−	PROPN
ejpam-5107	74	4	ar(t	ar(t	PUNCT
ejpam-5107	74	5	)	)	PUNCT
ejpam-5107	74	6	]	]	PUNCT
ejpam-5107	75	1	∂p1	∂p1	PROPN
ejpam-5107	76	1	∂r	∂r	PROPN
ejpam-5107	77	1	+	+	CCONJ
ejpam-5107	77	2	(	(	PUNCT
ejpam-5107	77	3	σr	σr	ADJ
ejpam-5107	77	4	)	)	PUNCT
ejpam-5107	77	5	2	2	NUM
ejpam-5107	77	6	1	1	NUM
ejpam-5107	77	7	2	2	NUM
ejpam-5107	77	8	∂2p1	∂2p1	NOUN
ejpam-5107	77	9	∂r2	∂r2	PROPN
ejpam-5107	77	10	(	(	PUNCT
ejpam-5107	77	11	dt)2h−1	dt)2h−1	ADP
ejpam-5107	77	12	−	−	PROPN
ejpam-5107	77	13	rp1(t	rp1(t	PROPN
ejpam-5107	77	14	)	)	PUNCT
ejpam-5107	77	15	=	=	PRON
ejpam-5107	78	1	(	(	PUNCT
ejpam-5107	78	2	∂p1	∂p1	NOUN
ejpam-5107	78	3	∂r	∂r	PROPN
ejpam-5107	78	4	/	/	SYM
ejpam-5107	78	5	∂p2	∂p2	PROPN
ejpam-5107	78	6	∂r	∂r	PROPN
ejpam-5107	78	7	)	)	PUNCT
ejpam-5107	79	1	[	[	PUNCT
ejpam-5107	79	2	∂p2	∂p2	PROPN
ejpam-5107	79	3	∂t	∂t	PROPN
ejpam-5107	79	4	+	+	PROPN
ejpam-5107	80	1	[	[	X
ejpam-5107	80	2	θ(t)−	θ(t)−	PROPN
ejpam-5107	80	3	ar(t	ar(t	PUNCT
ejpam-5107	80	4	)	)	PUNCT
ejpam-5107	80	5	]	]	PUNCT
ejpam-5107	81	1	∂p2	∂p2	PROPN
ejpam-5107	82	1	∂r	∂r	NOUN
ejpam-5107	83	1	+	+	CCONJ
ejpam-5107	83	2	(	(	PUNCT
ejpam-5107	83	3	σr	σr	ADJ
ejpam-5107	83	4	)	)	PUNCT
ejpam-5107	83	5	2	2	NUM
ejpam-5107	83	6	1	1	NUM
ejpam-5107	83	7	2	2	NUM
ejpam-5107	83	8	∂2p2	∂2p2	NUM
ejpam-5107	83	9	∂r2	∂r2	PROPN
ejpam-5107	83	10	(	(	PUNCT
ejpam-5107	83	11	dt)2h−1	dt)2h−1	ADP
ejpam-5107	83	12	−	−	PROPN
ejpam-5107	83	13	rp2(t	rp2(t	NOUN
ejpam-5107	83	14	)	)	PUNCT
ejpam-5107	83	15	]	]	PUNCT
ejpam-5107	83	16	.	.	PUNCT
ejpam-5107	84	1	this	this	PRON
ejpam-5107	84	2	is	be	AUX
ejpam-5107	84	3	one	one	NUM
ejpam-5107	84	4	equation	equation	NOUN
ejpam-5107	84	5	in	in	ADP
ejpam-5107	84	6	two	two	NUM
ejpam-5107	84	7	unknowns	unknown	NOUN
ejpam-5107	84	8	.	.	PUNCT
ejpam-5107	85	1	however	however	ADV
ejpam-5107	85	2	,	,	PUNCT
ejpam-5107	85	3	the	the	DET
ejpam-5107	85	4	left	left	ADJ
ejpam-5107	85	5	-	-	PUNCT
ejpam-5107	85	6	hand	hand	NOUN
ejpam-5107	85	7	side	side	NOUN
ejpam-5107	85	8	is	be	AUX
ejpam-5107	85	9	a	a	DET
ejpam-5107	85	10	function	function	NOUN
ejpam-5107	85	11	of	of	ADP
ejpam-5107	85	12	t1	t1	NOUN
ejpam-5107	85	13	and	and	CCONJ
ejpam-5107	85	14	the	the	DET
ejpam-5107	85	15	right	right	ADJ
ejpam-5107	85	16	-	-	PUNCT
ejpam-5107	85	17	hand	hand	NOUN
ejpam-5107	85	18	side	side	NOUN
ejpam-5107	85	19	is	be	AUX
ejpam-5107	85	20	a	a	DET
ejpam-5107	85	21	function	function	NOUN
ejpam-5107	85	22	of	of	ADP
ejpam-5107	85	23	t2	t2	NOUN
ejpam-5107	85	24	.	.	PUNCT
ejpam-5107	86	1	the	the	DET
ejpam-5107	86	2	only	only	ADJ
ejpam-5107	86	3	way	way	NOUN
ejpam-5107	86	4	for	for	SCONJ
ejpam-5107	86	5	this	this	DET
ejpam-5107	86	6	equality	equality	NOUN
ejpam-5107	86	7	to	to	PART
ejpam-5107	86	8	be	be	AUX
ejpam-5107	86	9	possible	possible	ADJ
ejpam-5107	86	10	is	be	AUX
ejpam-5107	86	11	for	for	SCONJ
ejpam-5107	86	12	both	both	DET
ejpam-5107	86	13	side	side	NOUN
ejpam-5107	86	14	to	to	PART
ejpam-5107	86	15	be	be	AUX
ejpam-5107	86	16	independent	independent	ADJ
ejpam-5107	86	17	of	of	ADP
ejpam-5107	86	18	the	the	DET
ejpam-5107	86	19	maturity	maturity	NOUN
ejpam-5107	86	20	date	date	NOUN
ejpam-5107	86	21	.	.	PUNCT
ejpam-5107	87	1	thus	thus	ADV
ejpam-5107	87	2	dropping	drop	VERB
ejpam-5107	87	3	the	the	DET
ejpam-5107	87	4	subscripts	subscript	NOUN
ejpam-5107	87	5	of	of	ADP
ejpam-5107	87	6	p	p	NOUN
ejpam-5107	87	7	and	and	CCONJ
ejpam-5107	87	8	introducing	introduce	VERB
ejpam-5107	87	9	the	the	DET
ejpam-5107	87	10	market	market	NOUN
ejpam-5107	87	11	price	price	NOUN
ejpam-5107	87	12	of	of	ADP
ejpam-5107	87	13	the	the	DET
ejpam-5107	87	14	risk	risk	NOUN
ejpam-5107	87	15	ψ	ψ	NOUN
ejpam-5107	87	16	,	,	PUNCT
ejpam-5107	87	17	we	we	PRON
ejpam-5107	87	18	have	have	VERB
ejpam-5107	87	19	∂p	∂p	PROPN
ejpam-5107	87	20	∂t	∂t	PROPN
ejpam-5107	88	1	+	+	PUNCT
ejpam-5107	88	2	[	[	X
ejpam-5107	88	3	θ(t)−	θ(t)−	PROPN
ejpam-5107	88	4	ar(t)]∂p∂r	ar(t)]∂p∂r	PROPN
ejpam-5107	88	5	+	+	X
ejpam-5107	88	6	(	(	PUNCT
ejpam-5107	88	7	σr	σr	ADJ
ejpam-5107	88	8	)	)	PUNCT
ejpam-5107	88	9	2	2	NUM
ejpam-5107	88	10	1	1	NUM
ejpam-5107	88	11	2	2	NUM
ejpam-5107	88	12	∂2p	∂2p	NOUN
ejpam-5107	88	13	∂r2	∂r2	PROPN
ejpam-5107	88	14	(	(	PUNCT
ejpam-5107	88	15	dt)2h−1	dt)2h−1	ADP
ejpam-5107	88	16	−	−	PROPN
ejpam-5107	88	17	rp	rp	NOUN
ejpam-5107	88	18	(	(	PUNCT
ejpam-5107	88	19	t	t	NOUN
ejpam-5107	88	20	)	)	PUNCT
ejpam-5107	88	21	∂p	∂p	PROPN
ejpam-5107	89	1	∂r	∂r	NOUN
ejpam-5107	89	2	=	=	NOUN
ejpam-5107	89	3	ψσr	ψσr	PROPN
ejpam-5107	89	4	.	.	PUNCT
ejpam-5107	90	1	simplifying	simplify	VERB
ejpam-5107	90	2	this	this	PRON
ejpam-5107	90	3	,	,	PUNCT
ejpam-5107	90	4	the	the	DET
ejpam-5107	90	5	equation	equation	NOUN
ejpam-5107	90	6	in	in	ADP
ejpam-5107	90	7	the	the	DET
ejpam-5107	90	8	theorem	theorem	NOUN
ejpam-5107	90	9	can	can	AUX
ejpam-5107	90	10	be	be	AUX
ejpam-5107	90	11	arrived	arrive	VERB
ejpam-5107	90	12	.	.	PUNCT
ejpam-5107	91	1	theorem	theorem	VERB
ejpam-5107	91	2	2	2	NUM
ejpam-5107	91	3	.	.	PUNCT
ejpam-5107	92	1	if	if	SCONJ
ejpam-5107	92	2	the	the	DET
ejpam-5107	92	3	number	number	NOUN
ejpam-5107	92	4	of	of	ADP
ejpam-5107	92	5	assets	asset	NOUN
ejpam-5107	92	6	traded	trade	VERB
ejpam-5107	92	7	during	during	ADP
ejpam-5107	92	8	the	the	DET
ejpam-5107	92	9	time	time	NOUN
ejpam-5107	92	10	interval	interval	NOUN
ejpam-5107	92	11	[	[	X
ejpam-5107	92	12	t	t	X
ejpam-5107	92	13	,	,	PUNCT
ejpam-5107	92	14	dt	dt	X
ejpam-5107	92	15	]	]	X
ejpam-5107	92	16	is	be	AUX
ejpam-5107	92	17	v	v	NOUN
ejpam-5107	92	18	,	,	PUNCT
ejpam-5107	92	19	then	then	ADV
ejpam-5107	92	20	e[|v|	e[|v|	ADJ
ejpam-5107	92	21	]	]	X
ejpam-5107	92	22	=	=	PUNCT
ejpam-5107	92	23	√	√	NUM
ejpam-5107	92	24	2	2	NUM
ejpam-5107	92	25	π	π	NOUN
ejpam-5107	92	26	(	(	PUNCT
ejpam-5107	92	27	dt)h	dt)h	PROPN
ejpam-5107	92	28	(	(	PUNCT
ejpam-5107	92	29	(	(	PUNCT
ejpam-5107	92	30	∂2v	∂2v	X
ejpam-5107	92	31	∂x2	∂x2	NOUN
ejpam-5107	92	32	)	)	PUNCT
ejpam-5107	92	33	2	2	NUM
ejpam-5107	92	34	σ2xx	σ2xx	NOUN
ejpam-5107	92	35	2(t	2(t	NUM
ejpam-5107	92	36	)	)	PUNCT
ejpam-5107	93	1	+	+	CCONJ
ejpam-5107	93	2	(	(	PUNCT
ejpam-5107	93	3	∂2v	∂2v	PROPN
ejpam-5107	93	4	∂r∂x	∂r∂x	PROPN
ejpam-5107	93	5	)	)	PUNCT
ejpam-5107	93	6	2	2	NUM
ejpam-5107	93	7	σ2r	σ2r	ADP
ejpam-5107	93	8	+	+	NOUN
ejpam-5107	93	9	2ρσxσrx(t	2ρσxσrx(t	NUM
ejpam-5107	93	10	)	)	PUNCT
ejpam-5107	93	11	∂2v	∂2v	NOUN
ejpam-5107	93	12	∂x2	∂x2	NOUN
ejpam-5107	93	13	∂2v	∂2v	X
ejpam-5107	93	14	∂r∂x	∂r∂x	NOUN
ejpam-5107	93	15	)	)	PUNCT
ejpam-5107	93	16	1	1	NUM
ejpam-5107	93	17	2	2	NUM
ejpam-5107	93	18	where	where	SCONJ
ejpam-5107	93	19	v	v	NOUN
ejpam-5107	93	20	(	(	PUNCT
ejpam-5107	93	21	t	t	PROPN
ejpam-5107	93	22	)	)	PUNCT
ejpam-5107	93	23	is	be	AUX
ejpam-5107	93	24	the	the	DET
ejpam-5107	93	25	option	option	NOUN
ejpam-5107	93	26	price	price	NOUN
ejpam-5107	93	27	,	,	PUNCT
ejpam-5107	93	28	x(t	x(t	PROPN
ejpam-5107	93	29	)	)	PUNCT
ejpam-5107	93	30	is	be	AUX
ejpam-5107	93	31	the	the	DET
ejpam-5107	93	32	market	market	NOUN
ejpam-5107	93	33	price	price	NOUN
ejpam-5107	93	34	of	of	ADP
ejpam-5107	93	35	the	the	DET
ejpam-5107	93	36	asset	asset	NOUN
ejpam-5107	93	37	at	at	ADP
ejpam-5107	93	38	time	time	NOUN
ejpam-5107	93	39	t	t	PROPN
ejpam-5107	93	40	,	,	PUNCT
ejpam-5107	93	41	r(t	r(t	NOUN
ejpam-5107	93	42	)	)	PUNCT
ejpam-5107	93	43	is	be	AUX
ejpam-5107	93	44	the	the	DET
ejpam-5107	93	45	interest	interest	NOUN
ejpam-5107	93	46	rate	rate	NOUN
ejpam-5107	93	47	that	that	PRON
ejpam-5107	93	48	follows	follow	VERB
ejpam-5107	93	49	the	the	DET
ejpam-5107	93	50	fractional	fractional	ADJ
ejpam-5107	93	51	hull	hull	NOUN
ejpam-5107	93	52	-	-	PUNCT
ejpam-5107	93	53	white	white	ADJ
ejpam-5107	93	54	model	model	NOUN
ejpam-5107	93	55	with	with	ADP
ejpam-5107	93	56	hurst	hurst	PROPN
ejpam-5107	93	57	parameter	parameter	PROPN
ejpam-5107	93	58	h	h	PROPN
ejpam-5107	93	59	,	,	PUNCT
ejpam-5107	93	60	σx	σx	PRON
ejpam-5107	93	61	is	be	AUX
ejpam-5107	93	62	the	the	DET
ejpam-5107	93	63	volatility	volatility	NOUN
ejpam-5107	93	64	of	of	ADP
ejpam-5107	93	65	the	the	DET
ejpam-5107	93	66	asset	asset	NOUN
ejpam-5107	93	67	price	price	NOUN
ejpam-5107	93	68	,	,	PUNCT
ejpam-5107	93	69	σr	σr	PROPN
ejpam-5107	93	70	is	be	AUX
ejpam-5107	93	71	the	the	DET
ejpam-5107	93	72	volatility	volatility	NOUN
ejpam-5107	93	73	of	of	ADP
ejpam-5107	93	74	the	the	DET
ejpam-5107	93	75	interest	interest	NOUN
ejpam-5107	93	76	rate	rate	NOUN
ejpam-5107	93	77	and	and	CCONJ
ejpam-5107	93	78	ρ	ρ	NOUN
ejpam-5107	93	79	is	be	AUX
ejpam-5107	93	80	the	the	DET
ejpam-5107	93	81	correlation	correlation	NOUN
ejpam-5107	93	82	coefficient	coefficient	NOUN
ejpam-5107	93	83	between	between	ADP
ejpam-5107	93	84	the	the	DET
ejpam-5107	93	85	interest	interest	NOUN
ejpam-5107	93	86	rate	rate	NOUN
ejpam-5107	93	87	and	and	CCONJ
ejpam-5107	93	88	the	the	DET
ejpam-5107	93	89	asset	asset	NOUN
ejpam-5107	93	90	price	price	NOUN
ejpam-5107	93	91	.	.	PUNCT
ejpam-5107	94	1	proof	proof	NOUN
ejpam-5107	94	2	:	:	PUNCT
ejpam-5107	94	3	suppose	suppose	VERB
ejpam-5107	94	4	v	v	NOUN
ejpam-5107	94	5	is	be	AUX
ejpam-5107	94	6	the	the	DET
ejpam-5107	94	7	number	number	NOUN
ejpam-5107	94	8	of	of	ADP
ejpam-5107	94	9	asset	asset	NOUN
ejpam-5107	94	10	traded	trade	VERB
ejpam-5107	94	11	during	during	ADP
ejpam-5107	94	12	the	the	DET
ejpam-5107	94	13	time	time	NOUN
ejpam-5107	94	14	interval	interval	NOUN
ejpam-5107	94	15	[	[	X
ejpam-5107	94	16	t	t	X
ejpam-5107	94	17	,	,	PUNCT
ejpam-5107	94	18	dt	dt	X
ejpam-5107	94	19	]	]	PUNCT
ejpam-5107	94	20	.	.	PUNCT
ejpam-5107	95	1	at	at	ADP
ejpam-5107	95	2	the	the	DET
ejpam-5107	95	3	short	short	ADJ
ejpam-5107	95	4	time	time	NOUN
ejpam-5107	95	5	t	t	PROPN
ejpam-5107	95	6	,	,	PUNCT
ejpam-5107	95	7	the	the	DET
ejpam-5107	95	8	number	number	NOUN
ejpam-5107	95	9	of	of	ADP
ejpam-5107	95	10	assets	asset	NOUN
ejpam-5107	95	11	hold	hold	VERB
ejpam-5107	95	12	is	be	AUX
ejpam-5107	95	13	given	give	VERB
ejpam-5107	95	14	by	by	ADP
ejpam-5107	95	15	∆1	∆1	PROPN
ejpam-5107	95	16	=	=	SYM
ejpam-5107	95	17	∂v	∂v	PROPN
ejpam-5107	95	18	∂x	∂x	PROPN
ejpam-5107	95	19	(	(	PUNCT
ejpam-5107	95	20	x	x	NOUN
ejpam-5107	95	21	,	,	PUNCT
ejpam-5107	95	22	r	r	NOUN
ejpam-5107	95	23	,	,	PUNCT
ejpam-5107	95	24	t	t	PROPN
ejpam-5107	95	25	)	)	PUNCT
ejpam-5107	95	26	.	.	PUNCT
ejpam-5107	96	1	(	(	PUNCT
ejpam-5107	96	2	17	17	NUM
ejpam-5107	96	3	)	)	PUNCT
ejpam-5107	96	4	f.	f.	PROPN
ejpam-5107	96	5	sumalpong	sumalpong	PROPN
ejpam-5107	96	6	,	,	PUNCT
ejpam-5107	96	7	e.	e.	PROPN
ejpam-5107	96	8	lauron	lauron	PROPN
ejpam-5107	96	9	/	/	SYM
ejpam-5107	96	10	eur	eur	PROPN
ejpam-5107	96	11	.	.	PUNCT
ejpam-5107	97	1	j.	j.	PROPN
ejpam-5107	97	2	pure	pure	PROPN
ejpam-5107	97	3	appl	appl	PROPN
ejpam-5107	97	4	.	.	PROPN
ejpam-5107	97	5	math	math	PROPN
ejpam-5107	97	6	,	,	PUNCT
ejpam-5107	97	7	17	17	NUM
ejpam-5107	97	8	(	(	PUNCT
ejpam-5107	97	9	3	3	NUM
ejpam-5107	97	10	)	)	PUNCT
ejpam-5107	97	11	(	(	PUNCT
ejpam-5107	97	12	2024	2024	NUM
ejpam-5107	97	13	)	)	PUNCT
ejpam-5107	97	14	,	,	PUNCT
ejpam-5107	97	15	2299	2299	NUM
ejpam-5107	97	16	-	-	SYM
ejpam-5107	97	17	2310	2310	NUM
ejpam-5107	97	18	2304	2304	NUM
ejpam-5107	97	19	after	after	ADP
ejpam-5107	97	20	the	the	DET
ejpam-5107	97	21	time	time	NOUN
ejpam-5107	97	22	step	step	NOUN
ejpam-5107	97	23	dt	dt	PROPN
ejpam-5107	97	24	,	,	PUNCT
ejpam-5107	97	25	the	the	DET
ejpam-5107	97	26	number	number	NOUN
ejpam-5107	97	27	of	of	ADP
ejpam-5107	97	28	assets	asset	NOUN
ejpam-5107	97	29	held	hold	VERB
ejpam-5107	97	30	is	be	AUX
ejpam-5107	97	31	∆t+dt	∆t+dt	NOUN
ejpam-5107	97	32	=	=	SYM
ejpam-5107	97	33	∂v	∂v	PROPN
ejpam-5107	97	34	∂x	∂x	PROPN
ejpam-5107	97	35	(	(	PUNCT
ejpam-5107	97	36	x	x	SYM
ejpam-5107	97	37	+	+	NUM
ejpam-5107	97	38	dt	dt	NOUN
ejpam-5107	97	39	,	,	PUNCT
ejpam-5107	97	40	r	r	NOUN
ejpam-5107	97	41	+	+	NUM
ejpam-5107	97	42	dt	dt	PROPN
ejpam-5107	97	43	,	,	PUNCT
ejpam-5107	97	44	t+	t+	NOUN
ejpam-5107	97	45	dt	dt	PROPN
ejpam-5107	97	46	)	)	PUNCT
ejpam-5107	97	47	.	.	PUNCT
ejpam-5107	98	1	(	(	PUNCT
ejpam-5107	98	2	18	18	NUM
ejpam-5107	98	3	)	)	PUNCT
ejpam-5107	98	4	since	since	SCONJ
ejpam-5107	98	5	the	the	DET
ejpam-5107	98	6	time	time	NOUN
ejpam-5107	98	7	step	step	NOUN
ejpam-5107	98	8	dt	dt	NOUN
ejpam-5107	98	9	is	be	AUX
ejpam-5107	98	10	assumed	assume	VERB
ejpam-5107	98	11	to	to	PART
ejpam-5107	98	12	be	be	AUX
ejpam-5107	98	13	so	so	ADV
ejpam-5107	98	14	small	small	ADJ
ejpam-5107	98	15	,	,	PUNCT
ejpam-5107	98	16	we	we	PRON
ejpam-5107	98	17	have	have	VERB
ejpam-5107	98	18	dx	dx	PROPN
ejpam-5107	98	19	≃	≃	ADJ
ejpam-5107	98	20	σxx(t)dbh	σxx(t)dbh	PROPN
ejpam-5107	98	21	1	1	NUM
ejpam-5107	98	22	(	(	PUNCT
ejpam-5107	98	23	t	t	NOUN
ejpam-5107	98	24	)	)	PUNCT
ejpam-5107	98	25	(	(	PUNCT
ejpam-5107	98	26	19	19	NUM
ejpam-5107	98	27	)	)	PUNCT
ejpam-5107	98	28	and	and	CCONJ
ejpam-5107	98	29	dr	dr	PROPN
ejpam-5107	98	30	≃	≃	PROPN
ejpam-5107	98	31	σrdb	σrdb	PROPN
ejpam-5107	98	32	h	h	PROPN
ejpam-5107	98	33	2	2	NUM
ejpam-5107	98	34	.	.	PUNCT
ejpam-5107	99	1	(	(	PUNCT
ejpam-5107	99	2	20	20	NUM
ejpam-5107	99	3	)	)	PUNCT
ejpam-5107	99	4	the	the	DET
ejpam-5107	99	5	number	number	NOUN
ejpam-5107	99	6	of	of	ADP
ejpam-5107	99	7	assets	asset	NOUN
ejpam-5107	99	8	traded	trade	VERB
ejpam-5107	99	9	v	v	NOUN
ejpam-5107	99	10	during	during	ADP
ejpam-5107	99	11	the	the	DET
ejpam-5107	99	12	time	time	NOUN
ejpam-5107	99	13	interval	interval	NOUN
ejpam-5107	99	14	[	[	X
ejpam-5107	99	15	t	t	PROPN
ejpam-5107	99	16	,	,	PUNCT
ejpam-5107	99	17	t+	t+	PUNCT
ejpam-5107	99	18	dt	dt	X
ejpam-5107	99	19	]	]	PUNCT
ejpam-5107	99	20	given	give	VERB
ejpam-5107	99	21	by	by	ADP
ejpam-5107	99	22	v	v	NOUN
ejpam-5107	99	23	=	=	SYM
ejpam-5107	99	24	∂2v	∂2v	NOUN
ejpam-5107	99	25	∂x2	∂x2	NOUN
ejpam-5107	99	26	σxx(t)dbh	σxx(t)dbh	ADJ
ejpam-5107	99	27	1	1	NUM
ejpam-5107	99	28	(	(	PUNCT
ejpam-5107	99	29	t	t	NOUN
ejpam-5107	99	30	)	)	PUNCT
ejpam-5107	99	31	+	+	CCONJ
ejpam-5107	99	32	∂2v	∂2v	PROPN
ejpam-5107	99	33	∂r∂x	∂r∂x	PROPN
ejpam-5107	99	34	σrdb	σrdb	PROPN
ejpam-5107	99	35	h	h	NOUN
ejpam-5107	99	36	2	2	NUM
ejpam-5107	99	37	(	(	PUNCT
ejpam-5107	99	38	t	t	NOUN
ejpam-5107	99	39	)	)	PUNCT
ejpam-5107	99	40	(	(	PUNCT
ejpam-5107	99	41	21	21	NUM
ejpam-5107	99	42	)	)	PUNCT
ejpam-5107	99	43	with	with	ADP
ejpam-5107	99	44	mean	mean	PROPN
ejpam-5107	99	45	e[v	e[v	X
ejpam-5107	99	46	]	]	X
ejpam-5107	99	47	=	=	SYM
ejpam-5107	99	48	0	0	NUM
ejpam-5107	99	49	,	,	PUNCT
ejpam-5107	99	50	(	(	PUNCT
ejpam-5107	99	51	22	22	NUM
ejpam-5107	99	52	)	)	PUNCT
ejpam-5107	99	53	and	and	CCONJ
ejpam-5107	99	54	variance	variance	VERB
ejpam-5107	99	55	e[v2	e[v2	ADV
ejpam-5107	99	56	]	]	X
ejpam-5107	99	57	=	=	SYM
ejpam-5107	99	58	(	(	PUNCT
ejpam-5107	99	59	∂2v	∂2v	X
ejpam-5107	99	60	∂x2	∂x2	NOUN
ejpam-5107	99	61	)	)	PUNCT
ejpam-5107	99	62	2	2	NUM
ejpam-5107	99	63	σ2xx	σ2xx	NOUN
ejpam-5107	99	64	2(t)(dt)2h	2(t)(dt)2h	NOUN
ejpam-5107	99	65	+	+	CCONJ
ejpam-5107	99	66	(	(	PUNCT
ejpam-5107	99	67	∂2v	∂2v	PROPN
ejpam-5107	99	68	∂r∂x	∂r∂x	PROPN
ejpam-5107	99	69	)	)	PUNCT
ejpam-5107	100	1	2	2	NUM
ejpam-5107	100	2	σ2r	σ2r	X
ejpam-5107	100	3	(	(	PUNCT
ejpam-5107	100	4	dt	dt	NOUN
ejpam-5107	100	5	)	)	PUNCT
ejpam-5107	100	6	2h	2h	NUM
ejpam-5107	100	7	+	+	SYM
ejpam-5107	100	8	2ρσxσrx(t	2ρσxσrx(t	NUM
ejpam-5107	100	9	)	)	PUNCT
ejpam-5107	100	10	∂2v	∂2v	NOUN
ejpam-5107	100	11	∂x2	∂x2	NOUN
ejpam-5107	100	12	∂2v	∂2v	X
ejpam-5107	100	13	∂r∂x	∂r∂x	NOUN
ejpam-5107	100	14	(	(	PUNCT
ejpam-5107	100	15	dt)2h	dt)2h	NOUN
ejpam-5107	100	16	.	.	PUNCT
ejpam-5107	101	1	if	if	SCONJ
ejpam-5107	101	2	we	we	PRON
ejpam-5107	101	3	let	let	VERB
ejpam-5107	101	4	the	the	DET
ejpam-5107	101	5	variance	variance	NOUN
ejpam-5107	101	6	of	of	ADP
ejpam-5107	101	7	v	v	NOUN
ejpam-5107	101	8	to	to	PART
ejpam-5107	101	9	be	be	AUX
ejpam-5107	101	10	β2	β2	VERB
ejpam-5107	101	11	,	,	PUNCT
ejpam-5107	101	12	then	then	ADV
ejpam-5107	101	13	we	we	PRON
ejpam-5107	101	14	have	have	VERB
ejpam-5107	101	15	e[v2	e[v2	ADV
ejpam-5107	101	16	]	]	PUNCT
ejpam-5107	101	17	=	=	SYM
ejpam-5107	101	18	β2	β2	VERB
ejpam-5107	101	19	.	.	PUNCT
ejpam-5107	102	1	since	since	SCONJ
ejpam-5107	102	2	v	v	NOUN
ejpam-5107	102	3	is	be	AUX
ejpam-5107	102	4	normally	normally	ADV
ejpam-5107	102	5	distributed	distribute	VERB
ejpam-5107	102	6	,	,	PUNCT
ejpam-5107	102	7	the	the	DET
ejpam-5107	102	8	probability	probability	NOUN
ejpam-5107	102	9	density	density	NOUN
ejpam-5107	102	10	function	function	NOUN
ejpam-5107	102	11	of	of	ADP
ejpam-5107	102	12	v	v	NOUN
ejpam-5107	102	13	is	be	AUX
ejpam-5107	102	14	given	give	VERB
ejpam-5107	102	15	as	as	ADP
ejpam-5107	102	16	f(v	f(v	NOUN
ejpam-5107	102	17	)	)	PUNCT
ejpam-5107	102	18	=	=	SYM
ejpam-5107	102	19	1	1	NUM
ejpam-5107	102	20	β	β	SYM
ejpam-5107	102	21	√	√	ADP
ejpam-5107	102	22	2π	2π	PROPN
ejpam-5107	102	23	e	e	NOUN
ejpam-5107	102	24	−(v)2	−(v)2	PUNCT
ejpam-5107	102	25	2β2	2β2	NUM
ejpam-5107	102	26	.	.	PUNCT
ejpam-5107	103	1	(	(	PUNCT
ejpam-5107	103	2	23	23	NUM
ejpam-5107	103	3	)	)	PUNCT
ejpam-5107	103	4	hence	hence	ADV
ejpam-5107	103	5	,	,	PUNCT
ejpam-5107	103	6	we	we	PRON
ejpam-5107	103	7	have	have	VERB
ejpam-5107	103	8	e[|v|	e[|v|	ADJ
ejpam-5107	103	9	]	]	X
ejpam-5107	104	1	=	=	PUNCT
ejpam-5107	104	2	∫	∫	PROPN
ejpam-5107	105	1	+	+	NUM
ejpam-5107	105	2	∞	∞	PROPN
ejpam-5107	105	3	−∞	−∞	ADP
ejpam-5107	105	4	|v|f(v)dv	|v|f(v)dv	NOUN
ejpam-5107	105	5	=	=	PUNCT
ejpam-5107	105	6	∫	∫	PROPN
ejpam-5107	106	1	+	+	NOUN
ejpam-5107	106	2	∞	∞	PROPN
ejpam-5107	106	3	−∞	−∞	X
ejpam-5107	106	4	|v|	|v|	NUM
ejpam-5107	106	5	1	1	NUM
ejpam-5107	106	6	β	β	NOUN
ejpam-5107	106	7	√	√	ADP
ejpam-5107	106	8	2π	2π	PROPN
ejpam-5107	106	9	e	e	NOUN
ejpam-5107	106	10	−(v)2	−(v)2	PUNCT
ejpam-5107	106	11	2β2	2β2	NUM
ejpam-5107	106	12	dv	dv	PROPN
ejpam-5107	106	13	by	by	ADP
ejpam-5107	106	14	letting	let	VERB
ejpam-5107	106	15	u	u	NOUN
ejpam-5107	106	16	=	=	PUNCT
ejpam-5107	106	17	−(v)2	−(v)2	PUNCT
ejpam-5107	106	18	2β2	2β2	NUM
ejpam-5107	106	19	,	,	PUNCT
ejpam-5107	106	20	we	we	PRON
ejpam-5107	106	21	have	have	VERB
ejpam-5107	106	22	dv	dv	PROPN
ejpam-5107	106	23	=	=	SYM
ejpam-5107	106	24	−β2du	−β2du	NUM
ejpam-5107	106	25	v	v	NOUN
ejpam-5107	106	26	.	.	PUNCT
ejpam-5107	107	1	substituting	substitute	VERB
ejpam-5107	107	2	we	we	PRON
ejpam-5107	107	3	have	have	VERB
ejpam-5107	107	4	e[|v|	e[|v|	ADJ
ejpam-5107	107	5	]	]	X
ejpam-5107	108	1	=	=	SYM
ejpam-5107	108	2	√	√	NUM
ejpam-5107	108	3	2	2	NUM
ejpam-5107	108	4	π	π	X
ejpam-5107	108	5	(	(	PUNCT
ejpam-5107	108	6	dt)h	dt)h	ADJ
ejpam-5107	108	7	×	×	NOUN
ejpam-5107	108	8	[	[	X
ejpam-5107	108	9	(	(	PUNCT
ejpam-5107	108	10	∂2v	∂2v	PROPN
ejpam-5107	108	11	∂x2	∂x2	NOUN
ejpam-5107	108	12	)	)	PUNCT
ejpam-5107	108	13	2	2	NUM
ejpam-5107	108	14	σ2xx	σ2xx	NOUN
ejpam-5107	108	15	2(t	2(t	NUM
ejpam-5107	108	16	)	)	PUNCT
ejpam-5107	108	17	f.	f.	PROPN
ejpam-5107	108	18	sumalpong	sumalpong	PROPN
ejpam-5107	108	19	,	,	PUNCT
ejpam-5107	108	20	e.	e.	PROPN
ejpam-5107	108	21	lauron	lauron	PROPN
ejpam-5107	108	22	/	/	SYM
ejpam-5107	108	23	eur	eur	PROPN
ejpam-5107	108	24	.	.	PUNCT
ejpam-5107	109	1	j.	j.	PROPN
ejpam-5107	109	2	pure	pure	PROPN
ejpam-5107	109	3	appl	appl	PROPN
ejpam-5107	109	4	.	.	PROPN
ejpam-5107	109	5	math	math	PROPN
ejpam-5107	109	6	,	,	PUNCT
ejpam-5107	109	7	17	17	NUM
ejpam-5107	109	8	(	(	PUNCT
ejpam-5107	109	9	3	3	NUM
ejpam-5107	109	10	)	)	PUNCT
ejpam-5107	109	11	(	(	PUNCT
ejpam-5107	109	12	2024	2024	NUM
ejpam-5107	109	13	)	)	PUNCT
ejpam-5107	109	14	,	,	PUNCT
ejpam-5107	109	15	2299	2299	NUM
ejpam-5107	109	16	-	-	SYM
ejpam-5107	109	17	2310	2310	NUM
ejpam-5107	109	18	2305	2305	NUM
ejpam-5107	109	19	+	+	CCONJ
ejpam-5107	109	20	(	(	PUNCT
ejpam-5107	109	21	∂2v	∂2v	PROPN
ejpam-5107	109	22	∂r∂x	∂r∂x	PROPN
ejpam-5107	109	23	)	)	PUNCT
ejpam-5107	109	24	2	2	NUM
ejpam-5107	109	25	σ2r	σ2r	ADP
ejpam-5107	109	26	+	+	NOUN
ejpam-5107	109	27	2ρσxσrx(t	2ρσxσrx(t	NUM
ejpam-5107	109	28	)	)	PUNCT
ejpam-5107	109	29	∂2v	∂2v	NOUN
ejpam-5107	109	30	∂x2	∂x2	NOUN
ejpam-5107	109	31	∂2v	∂2v	X
ejpam-5107	109	32	∂r∂x	∂r∂x	PROPN
ejpam-5107	109	33	]	]	PUNCT
ejpam-5107	109	34	.	.	PUNCT
ejpam-5107	110	1	theorem	theorem	NOUN
ejpam-5107	110	2	3	3	NUM
ejpam-5107	110	3	.	.	PUNCT
ejpam-5107	110	4	using	use	VERB
ejpam-5107	110	5	the	the	DET
ejpam-5107	110	6	hull	hull	NOUN
ejpam-5107	110	7	-	-	PUNCT
ejpam-5107	110	8	white	white	ADJ
ejpam-5107	110	9	interest	interest	NOUN
ejpam-5107	110	10	rate	rate	NOUN
ejpam-5107	110	11	model	model	NOUN
ejpam-5107	110	12	and	and	CCONJ
ejpam-5107	110	13	with	with	ADP
ejpam-5107	110	14	transaction	transaction	NOUN
ejpam-5107	110	15	cost	cost	NOUN
ejpam-5107	110	16	in	in	ADP
ejpam-5107	110	17	a	a	DET
ejpam-5107	110	18	fractional	fractional	ADJ
ejpam-5107	110	19	brownian	brownian	ADJ
ejpam-5107	110	20	motion	motion	NOUN
ejpam-5107	110	21	,	,	PUNCT
ejpam-5107	110	22	the	the	DET
ejpam-5107	110	23	value	value	NOUN
ejpam-5107	110	24	of	of	ADP
ejpam-5107	110	25	the	the	DET
ejpam-5107	110	26	option	option	NOUN
ejpam-5107	110	27	is	be	AUX
ejpam-5107	110	28	modeled	model	VERB
ejpam-5107	110	29	as	as	ADP
ejpam-5107	110	30	:	:	PUNCT
ejpam-5107	110	31	∂v	∂v	PROPN
ejpam-5107	110	32	∂t	∂t	PROPN
ejpam-5107	111	1	+	+	CCONJ
ejpam-5107	111	2	1	1	NUM
ejpam-5107	111	3	2	2	NUM
ejpam-5107	111	4	∂2v	∂2v	NOUN
ejpam-5107	111	5	∂x2	∂x2	NOUN
ejpam-5107	111	6	σ2x(x(t))2(dt)2h−1	σ2x(x(t))2(dt)2h−1	NOUN
ejpam-5107	111	7	+	+	NOUN
ejpam-5107	111	8	1	1	NUM
ejpam-5107	111	9	2	2	NUM
ejpam-5107	111	10	∂2v	∂2v	NOUN
ejpam-5107	111	11	∂r2	∂r2	PROPN
ejpam-5107	111	12	σ2r	σ2r	VERB
ejpam-5107	111	13	(	(	PUNCT
ejpam-5107	111	14	dt	dt	NOUN
ejpam-5107	111	15	)	)	PUNCT
ejpam-5107	111	16	2h−1	2h−1	PROPN
ejpam-5107	112	1	+	+	CCONJ
ejpam-5107	112	2	∂v	∂v	PROPN
ejpam-5107	112	3	∂x	∂x	PROPN
ejpam-5107	112	4	rx(t	rx(t	NOUN
ejpam-5107	112	5	)	)	PUNCT
ejpam-5107	113	1	+	+	NUM
ejpam-5107	113	2	∂2v	∂2v	NOUN
ejpam-5107	113	3	∂x∂r	∂x∂r	NOUN
ejpam-5107	113	4	σrσxx(t)ρ(t)(dt)2h−1	σrσxx(t)ρ(t)(dt)2h−1	X
ejpam-5107	114	1	+	+	CCONJ
ejpam-5107	115	1	∂v	∂v	PROPN
ejpam-5107	115	2	∂r	∂r	PROPN
ejpam-5107	116	1	[	[	X
ejpam-5107	116	2	θ(t)−	θ(t)−	PROPN
ejpam-5107	116	3	ar(t)−	ar(t)−	PROPN
ejpam-5107	116	4	ψσr	ψσr	PROPN
ejpam-5107	116	5	]	]	PUNCT
ejpam-5107	116	6	−	−	PROPN
ejpam-5107	116	7	rv	rv	PROPN
ejpam-5107	116	8	(	(	PUNCT
ejpam-5107	116	9	t	t	PROPN
ejpam-5107	116	10	)	)	PUNCT
ejpam-5107	116	11	+	+	NUM
ejpam-5107	116	12	cx(t	cx(t	NOUN
ejpam-5107	116	13	)	)	PUNCT
ejpam-5107	116	14	√	√	ADV
ejpam-5107	116	15	2	2	NUM
ejpam-5107	116	16	π	π	NOUN
ejpam-5107	116	17	(	(	PUNCT
ejpam-5107	116	18	dt)h	dt)h	ADJ
ejpam-5107	116	19	×	×	NOUN
ejpam-5107	116	20	[	[	X
ejpam-5107	116	21	(	(	PUNCT
ejpam-5107	116	22	∂2v	∂2v	PROPN
ejpam-5107	116	23	∂x2	∂x2	NOUN
ejpam-5107	116	24	)	)	PUNCT
ejpam-5107	116	25	2	2	NUM
ejpam-5107	116	26	σ2xx	σ2xx	NOUN
ejpam-5107	116	27	2(t	2(t	NUM
ejpam-5107	116	28	)	)	PUNCT
ejpam-5107	117	1	+	+	CCONJ
ejpam-5107	117	2	(	(	PUNCT
ejpam-5107	117	3	∂2v	∂2v	PROPN
ejpam-5107	117	4	∂r∂x	∂r∂x	PROPN
ejpam-5107	117	5	)	)	PUNCT
ejpam-5107	117	6	2	2	NUM
ejpam-5107	117	7	σ2r	σ2r	ADP
ejpam-5107	117	8	+2ρσxσrx(t	+2ρσxσrx(t	PROPN
ejpam-5107	117	9	)	)	PUNCT
ejpam-5107	117	10	∂2v	∂2v	PROPN
ejpam-5107	117	11	∂x2	∂x2	NOUN
ejpam-5107	117	12	∂2v	∂2v	X
ejpam-5107	117	13	∂r∂x	∂r∂x	NOUN
ejpam-5107	117	14	]	]	PUNCT
ejpam-5107	117	15	1	1	NUM
ejpam-5107	117	16	2	2	NUM
ejpam-5107	117	17	=	=	SYM
ejpam-5107	117	18	0	0	NUM
ejpam-5107	117	19	.	.	PUNCT
ejpam-5107	118	1	where	where	SCONJ
ejpam-5107	118	2	v	v	NOUN
ejpam-5107	118	3	(	(	PUNCT
ejpam-5107	118	4	t	t	PROPN
ejpam-5107	118	5	)	)	PUNCT
ejpam-5107	118	6	is	be	AUX
ejpam-5107	118	7	the	the	DET
ejpam-5107	118	8	option	option	NOUN
ejpam-5107	118	9	price	price	NOUN
ejpam-5107	118	10	,	,	PUNCT
ejpam-5107	118	11	x(t	x(t	PROPN
ejpam-5107	118	12	)	)	PUNCT
ejpam-5107	118	13	is	be	AUX
ejpam-5107	118	14	the	the	DET
ejpam-5107	118	15	market	market	NOUN
ejpam-5107	118	16	value	value	NOUN
ejpam-5107	118	17	of	of	ADP
ejpam-5107	118	18	the	the	DET
ejpam-5107	118	19	asset	asset	NOUN
ejpam-5107	118	20	at	at	ADP
ejpam-5107	118	21	time	time	NOUN
ejpam-5107	118	22	t	t	PROPN
ejpam-5107	118	23	,	,	PUNCT
ejpam-5107	118	24	r(t	r(t	NOUN
ejpam-5107	118	25	)	)	PUNCT
ejpam-5107	118	26	is	be	AUX
ejpam-5107	118	27	the	the	DET
ejpam-5107	118	28	interest	interest	NOUN
ejpam-5107	118	29	rate	rate	NOUN
ejpam-5107	118	30	,	,	PUNCT
ejpam-5107	118	31	σx	σx	NOUN
ejpam-5107	118	32	is	be	AUX
ejpam-5107	118	33	the	the	DET
ejpam-5107	118	34	volatility	volatility	NOUN
ejpam-5107	118	35	of	of	ADP
ejpam-5107	118	36	the	the	DET
ejpam-5107	118	37	asset	asset	NOUN
ejpam-5107	118	38	,	,	PUNCT
ejpam-5107	118	39	σr	σr	PROPN
ejpam-5107	118	40	is	be	AUX
ejpam-5107	118	41	the	the	DET
ejpam-5107	118	42	volatility	volatility	NOUN
ejpam-5107	118	43	of	of	ADP
ejpam-5107	118	44	the	the	DET
ejpam-5107	118	45	interest	interest	NOUN
ejpam-5107	118	46	rate	rate	NOUN
ejpam-5107	118	47	,	,	PUNCT
ejpam-5107	118	48	c	c	PROPN
ejpam-5107	118	49	is	be	AUX
ejpam-5107	118	50	fixed	fix	VERB
ejpam-5107	118	51	proportion	proportion	NOUN
ejpam-5107	118	52	of	of	ADP
ejpam-5107	118	53	the	the	DET
ejpam-5107	118	54	trading	trading	NOUN
ejpam-5107	118	55	amount	amount	NOUN
ejpam-5107	118	56	for	for	ADP
ejpam-5107	118	57	the	the	DET
ejpam-5107	118	58	asset	asset	NOUN
ejpam-5107	118	59	agreed	agree	VERB
ejpam-5107	118	60	by	by	ADP
ejpam-5107	118	61	both	both	DET
ejpam-5107	118	62	parties	party	NOUN
ejpam-5107	118	63	,	,	PUNCT
ejpam-5107	118	64	and	and	CCONJ
ejpam-5107	118	65	h	h	NOUN
ejpam-5107	118	66	is	be	AUX
ejpam-5107	118	67	the	the	DET
ejpam-5107	118	68	hurst	hurst	PROPN
ejpam-5107	118	69	parameter	parameter	NOUN
ejpam-5107	118	70	.	.	PUNCT
ejpam-5107	119	1	proof	proof	NOUN
ejpam-5107	119	2	:	:	PUNCT
ejpam-5107	119	3	let	let	VERB
ejpam-5107	119	4	v	v	X
ejpam-5107	119	5	(	(	PUNCT
ejpam-5107	119	6	t	t	NOUN
ejpam-5107	119	7	)	)	PUNCT
ejpam-5107	119	8	=	=	NOUN
ejpam-5107	119	9	v	v	X
ejpam-5107	119	10	(	(	PUNCT
ejpam-5107	119	11	t	t	PROPN
ejpam-5107	119	12	,	,	PUNCT
ejpam-5107	119	13	x(t	x(t	PROPN
ejpam-5107	119	14	)	)	PUNCT
ejpam-5107	119	15	,	,	PUNCT
ejpam-5107	119	16	r(t	r(t	NOUN
ejpam-5107	119	17	)	)	PUNCT
ejpam-5107	119	18	)	)	PUNCT
ejpam-5107	119	19	be	be	AUX
ejpam-5107	119	20	the	the	DET
ejpam-5107	119	21	option	option	NOUN
ejpam-5107	119	22	price	price	NOUN
ejpam-5107	119	23	.	.	PUNCT
ejpam-5107	120	1	define	define	VERB
ejpam-5107	120	2	the	the	DET
ejpam-5107	120	3	portfolio	portfolio	NOUN
ejpam-5107	120	4	π(t	π(t	PROPN
ejpam-5107	120	5	)	)	PUNCT
ejpam-5107	120	6	=	=	SYM
ejpam-5107	120	7	v	v	X
ejpam-5107	120	8	(	(	PUNCT
ejpam-5107	120	9	t)−∆1x(t)−∆2p	t)−∆1x(t)−∆2p	PROPN
ejpam-5107	120	10	(	(	PUNCT
ejpam-5107	120	11	t	t	PROPN
ejpam-5107	120	12	)	)	PUNCT
ejpam-5107	120	13	where	where	SCONJ
ejpam-5107	120	14	∆1,∆2	∆1,∆2	NOUN
ejpam-5107	120	15	are	be	AUX
ejpam-5107	120	16	the	the	DET
ejpam-5107	120	17	respective	respective	ADJ
ejpam-5107	120	18	shares	share	NOUN
ejpam-5107	120	19	of	of	ADP
ejpam-5107	120	20	the	the	DET
ejpam-5107	120	21	asset	asset	NOUN
ejpam-5107	120	22	price	price	NOUN
ejpam-5107	120	23	x(t	x(t	PROPN
ejpam-5107	120	24	)	)	PUNCT
ejpam-5107	120	25	and	and	CCONJ
ejpam-5107	120	26	the	the	DET
ejpam-5107	120	27	zero	zero	NUM
ejpam-5107	120	28	-	-	PUNCT
ejpam-5107	120	29	coupon	coupon	NOUN
ejpam-5107	120	30	bond	bond	NOUN
ejpam-5107	120	31	p	p	NOUN
ejpam-5107	120	32	(	(	PUNCT
ejpam-5107	120	33	t	t	PROPN
ejpam-5107	120	34	)	)	PUNCT
ejpam-5107	120	35	.	.	PUNCT
ejpam-5107	121	1	the	the	DET
ejpam-5107	121	2	value	value	NOUN
ejpam-5107	121	3	of	of	ADP
ejpam-5107	121	4	the	the	DET
ejpam-5107	121	5	change	change	NOUN
ejpam-5107	121	6	of	of	ADP
ejpam-5107	121	7	portfolio	portfolio	NOUN
ejpam-5107	121	8	at	at	ADP
ejpam-5107	121	9	time	time	NOUN
ejpam-5107	121	10	[	[	X
ejpam-5107	121	11	t	t	X
ejpam-5107	121	12	,	,	PUNCT
ejpam-5107	121	13	t+	t+	PUNCT
ejpam-5107	121	14	dt	dt	X
ejpam-5107	121	15	]	]	PUNCT
ejpam-5107	121	16	with	with	ADP
ejpam-5107	121	17	transaction	transaction	NOUN
ejpam-5107	121	18	cost	cost	NOUN
ejpam-5107	121	19	is	be	AUX
ejpam-5107	121	20	now	now	ADV
ejpam-5107	121	21	dπ(t	dπ(t	VERB
ejpam-5107	121	22	)	)	PUNCT
ejpam-5107	121	23	=	=	SYM
ejpam-5107	121	24	v	v	X
ejpam-5107	121	25	(	(	PUNCT
ejpam-5107	121	26	t)−∆1dx(t)−∆2dp	t)−∆1dx(t)−∆2dp	PROPN
ejpam-5107	121	27	(	(	PUNCT
ejpam-5107	121	28	t	t	PROPN
ejpam-5107	121	29	)	)	PUNCT
ejpam-5107	121	30	+	+	CCONJ
ejpam-5107	121	31	c|v(t)|x(t	c|v(t)|x(t	PROPN
ejpam-5107	121	32	)	)	PUNCT
ejpam-5107	121	33	.	.	PUNCT
ejpam-5107	122	1	taking	take	VERB
ejpam-5107	122	2	the	the	DET
ejpam-5107	122	3	expectation	expectation	NOUN
ejpam-5107	122	4	we	we	PRON
ejpam-5107	122	5	have	have	VERB
ejpam-5107	122	6	e[dπ(t	e[dπ(t	PROPN
ejpam-5107	122	7	)	)	PUNCT
ejpam-5107	122	8	]	]	PUNCT
ejpam-5107	123	1	=	=	PUNCT
ejpam-5107	123	2	e	e	X
ejpam-5107	124	1	[	[	X
ejpam-5107	124	2	v	v	X
ejpam-5107	124	3	(	(	PUNCT
ejpam-5107	124	4	t)]−	t)]−	NOUN
ejpam-5107	124	5	e	e	X
ejpam-5107	125	1	[	[	X
ejpam-5107	125	2	∆1dx(t)]−	∆1dx(t)]−	X
ejpam-5107	125	3	e	e	PROPN
ejpam-5107	125	4	[	[	X
ejpam-5107	125	5	∆2dp	∆2dp	PROPN
ejpam-5107	125	6	(	(	PUNCT
ejpam-5107	125	7	t	t	PROPN
ejpam-5107	125	8	)	)	PUNCT
ejpam-5107	125	9	]	]	PUNCT
ejpam-5107	126	1	+	+	CCONJ
ejpam-5107	126	2	cx(t)e	cx(t)e	PUNCT
ejpam-5107	127	1	[	[	X
ejpam-5107	127	2	|v(t)|	|v(t)|	X
ejpam-5107	127	3	]	]	PUNCT
ejpam-5107	127	4	.	.	PUNCT
ejpam-5107	128	1	by	by	ADP
ejpam-5107	128	2	non	non	ADJ
ejpam-5107	128	3	-	-	ADJ
ejpam-5107	128	4	arbitrage	arbitrage	ADJ
ejpam-5107	128	5	principle	principle	NOUN
ejpam-5107	128	6	,	,	PUNCT
ejpam-5107	128	7	e	e	X
ejpam-5107	128	8	[	[	X
ejpam-5107	128	9	v	v	X
ejpam-5107	128	10	(	(	PUNCT
ejpam-5107	128	11	t)]−	t)]−	NOUN
ejpam-5107	128	12	e	e	X
ejpam-5107	129	1	[	[	X
ejpam-5107	129	2	∆1dx(t)]−	∆1dx(t)]−	X
ejpam-5107	129	3	e	e	PROPN
ejpam-5107	129	4	[	[	X
ejpam-5107	129	5	∆2dp	∆2dp	PROPN
ejpam-5107	129	6	(	(	PUNCT
ejpam-5107	129	7	t)]−	t)]−	NOUN
ejpam-5107	129	8	rv	rv	PROPN
ejpam-5107	129	9	(	(	PUNCT
ejpam-5107	129	10	t)dt+∆1rx(t)dt	t)dt+∆1rx(t)dt	ADP
ejpam-5107	129	11	+	+	ADJ
ejpam-5107	129	12	∆2rp	∆2rp	ADJ
ejpam-5107	129	13	(	(	PUNCT
ejpam-5107	129	14	t)dt+	t)dt+	NOUN
ejpam-5107	129	15	cx(t)e	cx(t)e	PUNCT
ejpam-5107	130	1	[	[	X
ejpam-5107	130	2	|v(t)|	|v(t)|	X
ejpam-5107	130	3	]	]	X
ejpam-5107	130	4	=	=	SYM
ejpam-5107	130	5	0	0	NUM
ejpam-5107	130	6	to	to	PART
ejpam-5107	130	7	eliminate	eliminate	VERB
ejpam-5107	130	8	the	the	DET
ejpam-5107	130	9	risk	risk	NOUN
ejpam-5107	130	10	,	,	PUNCT
ejpam-5107	130	11	take	take	VERB
ejpam-5107	130	12	∆1	∆1	NOUN
ejpam-5107	130	13	=	=	SYM
ejpam-5107	130	14	∂v	∂v	PROPN
ejpam-5107	130	15	∂x	∂x	PROPN
ejpam-5107	130	16	(	(	PUNCT
ejpam-5107	130	17	24	24	NUM
ejpam-5107	130	18	)	)	PUNCT
ejpam-5107	130	19	f.	f.	PROPN
ejpam-5107	130	20	sumalpong	sumalpong	PROPN
ejpam-5107	130	21	,	,	PUNCT
ejpam-5107	130	22	e.	e.	PROPN
ejpam-5107	130	23	lauron	lauron	PROPN
ejpam-5107	130	24	/	/	SYM
ejpam-5107	130	25	eur	eur	PROPN
ejpam-5107	130	26	.	.	PUNCT
ejpam-5107	131	1	j.	j.	PROPN
ejpam-5107	131	2	pure	pure	PROPN
ejpam-5107	131	3	appl	appl	PROPN
ejpam-5107	131	4	.	.	PROPN
ejpam-5107	131	5	math	math	PROPN
ejpam-5107	131	6	,	,	PUNCT
ejpam-5107	131	7	17	17	NUM
ejpam-5107	131	8	(	(	PUNCT
ejpam-5107	131	9	3	3	NUM
ejpam-5107	131	10	)	)	PUNCT
ejpam-5107	131	11	(	(	PUNCT
ejpam-5107	131	12	2024	2024	NUM
ejpam-5107	131	13	)	)	PUNCT
ejpam-5107	131	14	,	,	PUNCT
ejpam-5107	131	15	2299	2299	NUM
ejpam-5107	131	16	-	-	SYM
ejpam-5107	131	17	2310	2310	NUM
ejpam-5107	131	18	2306	2306	NUM
ejpam-5107	131	19	and	and	CCONJ
ejpam-5107	131	20	∆2	∆2	X
ejpam-5107	132	1	=	=	SYM
ejpam-5107	132	2	∂v	∂v	PROPN
ejpam-5107	133	1	∂r	∂r	PROPN
ejpam-5107	133	2	/	/	SYM
ejpam-5107	133	3	∂p	∂p	PROPN
ejpam-5107	133	4	∂r	∂r	INTJ
ejpam-5107	133	5	.	.	PUNCT
ejpam-5107	134	1	(	(	PUNCT
ejpam-5107	134	2	25	25	NUM
ejpam-5107	134	3	)	)	PUNCT
ejpam-5107	134	4	hence	hence	ADV
ejpam-5107	134	5	,	,	PUNCT
ejpam-5107	134	6	∂v	∂v	PROPN
ejpam-5107	134	7	∂t	∂t	PROPN
ejpam-5107	135	1	+	+	CCONJ
ejpam-5107	135	2	1	1	NUM
ejpam-5107	135	3	2	2	NUM
ejpam-5107	135	4	∂2v	∂2v	NOUN
ejpam-5107	135	5	∂x2	∂x2	NOUN
ejpam-5107	135	6	σ2x(x(t))2(dt)2h−1	σ2x(x(t))2(dt)2h−1	NOUN
ejpam-5107	135	7	+	+	NOUN
ejpam-5107	135	8	1	1	NUM
ejpam-5107	135	9	2	2	NUM
ejpam-5107	135	10	∂2v	∂2v	NOUN
ejpam-5107	135	11	∂r2	∂r2	PROPN
ejpam-5107	135	12	σ2r	σ2r	VERB
ejpam-5107	135	13	(	(	PUNCT
ejpam-5107	135	14	dt	dt	NOUN
ejpam-5107	135	15	)	)	PUNCT
ejpam-5107	135	16	2h−1	2h−1	PROPN
ejpam-5107	136	1	+	+	CCONJ
ejpam-5107	136	2	∂v	∂v	PROPN
ejpam-5107	136	3	∂x	∂x	PROPN
ejpam-5107	136	4	rx(t	rx(t	NOUN
ejpam-5107	136	5	)	)	PUNCT
ejpam-5107	137	1	+	+	NUM
ejpam-5107	137	2	∂2v	∂2v	NOUN
ejpam-5107	137	3	∂x∂r	∂x∂r	NOUN
ejpam-5107	137	4	σrσxx(t)ρ(t)(dt)2h−1	σrσxx(t)ρ(t)(dt)2h−1	X
ejpam-5107	138	1	+	+	CCONJ
ejpam-5107	139	1	∂v	∂v	PROPN
ejpam-5107	139	2	∂r	∂r	PROPN
ejpam-5107	140	1	[	[	X
ejpam-5107	140	2	θ(t)−	θ(t)−	PROPN
ejpam-5107	140	3	ar(t)−	ar(t)−	PROPN
ejpam-5107	140	4	ψσr	ψσr	PROPN
ejpam-5107	140	5	]	]	PUNCT
ejpam-5107	140	6	−	−	PROPN
ejpam-5107	140	7	rv	rv	PROPN
ejpam-5107	140	8	(	(	PUNCT
ejpam-5107	140	9	t	t	PROPN
ejpam-5107	140	10	)	)	PUNCT
ejpam-5107	140	11	+	+	PUNCT
ejpam-5107	140	12	cx(t)e	cx(t)e	PUNCT
ejpam-5107	141	1	[	[	X
ejpam-5107	141	2	|v(t)|	|v(t)|	X
ejpam-5107	141	3	]	]	X
ejpam-5107	141	4	=	=	SYM
ejpam-5107	141	5	0	0	X
ejpam-5107	141	6	.	.	X
ejpam-5107	141	7	employing	employ	VERB
ejpam-5107	141	8	the	the	DET
ejpam-5107	141	9	transaction	transaction	NOUN
ejpam-5107	141	10	cost	cost	NOUN
ejpam-5107	141	11	,	,	PUNCT
ejpam-5107	141	12	we	we	PRON
ejpam-5107	141	13	have	have	AUX
ejpam-5107	141	14	can	can	AUX
ejpam-5107	141	15	derived	derive	VERB
ejpam-5107	141	16	the	the	DET
ejpam-5107	141	17	equation	equation	NOUN
ejpam-5107	141	18	in	in	ADP
ejpam-5107	141	19	the	the	DET
ejpam-5107	141	20	theorem	theorem	NOUN
ejpam-5107	141	21	.	.	PROPN
ejpam-5107	142	1	3	3	X
ejpam-5107	142	2	.	.	X
ejpam-5107	142	3	the	the	DET
ejpam-5107	142	4	model	model	NOUN
ejpam-5107	142	5	theorem	theorem	VERB
ejpam-5107	142	6	4	4	NUM
ejpam-5107	142	7	.	.	PUNCT
ejpam-5107	142	8	based	base	VERB
ejpam-5107	142	9	on	on	ADP
ejpam-5107	142	10	the	the	DET
ejpam-5107	142	11	price	price	NOUN
ejpam-5107	142	12	model	model	NOUN
ejpam-5107	142	13	in	in	ADP
ejpam-5107	142	14	theorem	theorem	NOUN
ejpam-5107	142	15	3	3	NUM
ejpam-5107	142	16	under	under	ADP
ejpam-5107	142	17	a	a	DET
ejpam-5107	142	18	fractional	fractional	ADJ
ejpam-5107	142	19	brownian	brownian	ADJ
ejpam-5107	142	20	motion	motion	NOUN
ejpam-5107	142	21	,	,	PUNCT
ejpam-5107	142	22	the	the	DET
ejpam-5107	142	23	closed	closed	ADJ
ejpam-5107	142	24	form	form	NOUN
ejpam-5107	142	25	formula	formula	NOUN
ejpam-5107	142	26	for	for	ADP
ejpam-5107	142	27	the	the	DET
ejpam-5107	142	28	european	european	ADJ
ejpam-5107	142	29	call	call	NOUN
ejpam-5107	142	30	option	option	NOUN
ejpam-5107	142	31	price	price	NOUN
ejpam-5107	142	32	is	be	AUX
ejpam-5107	142	33	given	give	VERB
ejpam-5107	142	34	by	by	ADP
ejpam-5107	142	35	vc(x	vc(x	NOUN
ejpam-5107	142	36	,	,	PUNCT
ejpam-5107	142	37	r	r	NOUN
ejpam-5107	142	38	,	,	PUNCT
ejpam-5107	142	39	t	t	PROPN
ejpam-5107	142	40	)	)	PUNCT
ejpam-5107	142	41	=	=	SYM
ejpam-5107	143	1	xn(d1)−kp	xn(d1)−kp	PROPN
ejpam-5107	143	2	(	(	PUNCT
ejpam-5107	143	3	r	r	NOUN
ejpam-5107	143	4	,	,	PUNCT
ejpam-5107	143	5	t	t	PROPN
ejpam-5107	143	6	,	,	PUNCT
ejpam-5107	143	7	t	t	NOUN
ejpam-5107	143	8	)	)	PUNCT
ejpam-5107	143	9	n(d2	n(d2	PROPN
ejpam-5107	143	10	)	)	PUNCT
ejpam-5107	143	11	(	(	PUNCT
ejpam-5107	143	12	26	26	NUM
ejpam-5107	143	13	)	)	PUNCT
ejpam-5107	144	1	where	where	SCONJ
ejpam-5107	144	2	d1	d1	PROPN
ejpam-5107	144	3	=	=	SYM
ejpam-5107	144	4	d2	d2	PROPN
ejpam-5107	144	5	+	+	PROPN
ejpam-5107	144	6	m	m	PROPN
ejpam-5107	144	7	d2	d2	NOUN
ejpam-5107	144	8	=	=	SYM
ejpam-5107	144	9	ln	ln	PROPN
ejpam-5107	144	10	x	x	VERB
ejpam-5107	144	11	kp	kp	X
ejpam-5107	144	12	(	(	PUNCT
ejpam-5107	144	13	r	r	NOUN
ejpam-5107	144	14	,	,	PUNCT
ejpam-5107	144	15	t;t	t;t	NUM
ejpam-5107	144	16	)	)	PUNCT
ejpam-5107	144	17	−m	−m	ADP
ejpam-5107	144	18	n	n	CCONJ
ejpam-5107	144	19	σ̂2	σ̂2	NOUN
ejpam-5107	144	20	=	=	SYM
ejpam-5107	144	21	σ2x	σ2x	NOUN
ejpam-5107	144	22	+	+	CCONJ
ejpam-5107	144	23	σ22b	σ22b	NOUN
ejpam-5107	144	24	2	2	NUM
ejpam-5107	144	25	+	+	SYM
ejpam-5107	144	26	2ρσxσ2b	2ρσxσ2b	NUM
ejpam-5107	144	27	b	b	X
ejpam-5107	144	28	=	=	SYM
ejpam-5107	144	29	1	1	NUM
ejpam-5107	144	30	p	p	NOUN
ejpam-5107	144	31	∂p	∂p	NOUN
ejpam-5107	145	1	∂r	∂r	NOUN
ejpam-5107	145	2	m	m	NOUN
ejpam-5107	145	3	=	=	VERB
ejpam-5107	146	1	√√√√2	√√√√2	PROPN
ejpam-5107	147	1	∫	∫	PROPN
ejpam-5107	147	2	t	t	PROPN
ejpam-5107	147	3	t	t	PROPN
ejpam-5107	147	4	[	[	PUNCT
ejpam-5107	147	5	1	1	NUM
ejpam-5107	147	6	2	2	NUM
ejpam-5107	147	7	(	(	PUNCT
ejpam-5107	147	8	ds)2h−1σ̂2	ds)2h−1σ̂2	X
ejpam-5107	147	9	+	+	PUNCT
ejpam-5107	147	10	c(ds)h−1	c(ds)h−1	NOUN
ejpam-5107	147	11	√	√	ADV
ejpam-5107	147	12	2	2	NUM
ejpam-5107	147	13	π	π	X
ejpam-5107	147	14	σ̃	σ̃	PROPN
ejpam-5107	147	15	]	]	PUNCT
ejpam-5107	147	16	ds	ds	PROPN
ejpam-5107	147	17	n	n	NOUN
ejpam-5107	147	18	=	=	PUNCT
ejpam-5107	147	19	√√√√2	√√√√2	PROPN
ejpam-5107	148	1	∫	∫	PROPN
ejpam-5107	148	2	t	t	PROPN
ejpam-5107	148	3	t	t	PROPN
ejpam-5107	148	4	[	[	PUNCT
ejpam-5107	148	5	1	1	NUM
ejpam-5107	148	6	2	2	NUM
ejpam-5107	148	7	(	(	PUNCT
ejpam-5107	148	8	ds)2h−1σ̃2	ds)2h−1σ̃2	X
ejpam-5107	148	9	+	+	CCONJ
ejpam-5107	148	10	c(ds)h−1	c(ds)h−1	NOUN
ejpam-5107	148	11	√	√	ADV
ejpam-5107	148	12	2	2	NUM
ejpam-5107	148	13	π	π	X
ejpam-5107	148	14	σ̃	σ̃	PROPN
ejpam-5107	148	15	]	]	PUNCT
ejpam-5107	148	16	ds	ds	ADJ
ejpam-5107	148	17	proof	proof	NOUN
ejpam-5107	148	18	:	:	PUNCT
ejpam-5107	148	19	theorem	theorem	VERB
ejpam-5107	148	20	3	3	NUM
ejpam-5107	148	21	can	can	AUX
ejpam-5107	148	22	be	be	AUX
ejpam-5107	148	23	solved	solve	VERB
ejpam-5107	148	24	by	by	ADP
ejpam-5107	148	25	the	the	DET
ejpam-5107	148	26	transformation	transformation	NOUN
ejpam-5107	148	27	of	of	ADP
ejpam-5107	148	28	independent	independent	ADJ
ejpam-5107	148	29	variables	variable	NOUN
ejpam-5107	149	1	y	y	PROPN
ejpam-5107	150	1	=	=	PUNCT
ejpam-5107	151	1	x	x	SYM
ejpam-5107	152	1	p	p	X
ejpam-5107	152	2	(	(	PUNCT
ejpam-5107	152	3	r	r	NOUN
ejpam-5107	152	4	,	,	PUNCT
ejpam-5107	152	5	t;t	t;t	NUM
ejpam-5107	152	6	)	)	PUNCT
ejpam-5107	152	7	(	(	PUNCT
ejpam-5107	152	8	27	27	NUM
ejpam-5107	152	9	)	)	PUNCT
ejpam-5107	152	10	and	and	CCONJ
ejpam-5107	152	11	a	a	DET
ejpam-5107	152	12	new	new	ADJ
ejpam-5107	152	13	unknown	unknown	ADJ
ejpam-5107	152	14	function	function	NOUN
ejpam-5107	152	15	denoted	denote	VERB
ejpam-5107	152	16	as	as	ADP
ejpam-5107	152	17	v̂	v̂	PRON
ejpam-5107	152	18	(	(	PUNCT
ejpam-5107	152	19	y	y	PROPN
ejpam-5107	152	20	,	,	PUNCT
ejpam-5107	152	21	t	t	PROPN
ejpam-5107	152	22	)	)	PUNCT
ejpam-5107	152	23	=	=	NOUN
ejpam-5107	152	24	v	v	X
ejpam-5107	152	25	(	(	PUNCT
ejpam-5107	152	26	x	x	NOUN
ejpam-5107	152	27	,	,	PUNCT
ejpam-5107	152	28	r	r	NOUN
ejpam-5107	152	29	,	,	PUNCT
ejpam-5107	152	30	t	t	PROPN
ejpam-5107	152	31	)	)	PUNCT
ejpam-5107	152	32	p	p	NOUN
ejpam-5107	152	33	(	(	PUNCT
ejpam-5107	152	34	r	r	NOUN
ejpam-5107	152	35	,	,	PUNCT
ejpam-5107	152	36	t;t	t;t	NUM
ejpam-5107	152	37	)	)	PUNCT
ejpam-5107	152	38	.	.	PUNCT
ejpam-5107	153	1	(	(	PUNCT
ejpam-5107	153	2	28	28	NUM
ejpam-5107	153	3	)	)	PUNCT
ejpam-5107	153	4	f.	f.	PROPN
ejpam-5107	153	5	sumalpong	sumalpong	PROPN
ejpam-5107	153	6	,	,	PUNCT
ejpam-5107	153	7	e.	e.	PROPN
ejpam-5107	153	8	lauron	lauron	PROPN
ejpam-5107	153	9	/	/	SYM
ejpam-5107	153	10	eur	eur	PROPN
ejpam-5107	153	11	.	.	PUNCT
ejpam-5107	154	1	j.	j.	PROPN
ejpam-5107	154	2	pure	pure	PROPN
ejpam-5107	154	3	appl	appl	PROPN
ejpam-5107	154	4	.	.	PROPN
ejpam-5107	154	5	math	math	PROPN
ejpam-5107	154	6	,	,	PUNCT
ejpam-5107	154	7	17	17	NUM
ejpam-5107	154	8	(	(	PUNCT
ejpam-5107	154	9	3	3	NUM
ejpam-5107	154	10	)	)	PUNCT
ejpam-5107	154	11	(	(	PUNCT
ejpam-5107	154	12	2024	2024	NUM
ejpam-5107	154	13	)	)	PUNCT
ejpam-5107	154	14	,	,	PUNCT
ejpam-5107	154	15	2299	2299	NUM
ejpam-5107	154	16	-	-	SYM
ejpam-5107	154	17	2310	2310	NUM
ejpam-5107	154	18	2307	2307	NUM
ejpam-5107	154	19	we	we	PRON
ejpam-5107	154	20	have	have	VERB
ejpam-5107	154	21	the	the	DET
ejpam-5107	154	22	following	follow	VERB
ejpam-5107	154	23	computations	computation	NOUN
ejpam-5107	154	24	,	,	PUNCT
ejpam-5107	154	25	∂v	∂v	PROPN
ejpam-5107	154	26	∂t	∂t	PROPN
ejpam-5107	155	1	=	=	PUNCT
ejpam-5107	155	2	v̂	v̂	PUNCT
ejpam-5107	155	3	∂p	∂p	PROPN
ejpam-5107	155	4	∂t	∂t	PROPN
ejpam-5107	155	5	+	+	CCONJ
ejpam-5107	155	6	p	p	NOUN
ejpam-5107	155	7	∂v̂	∂v̂	NOUN
ejpam-5107	155	8	∂t	∂t	PROPN
ejpam-5107	155	9	−	−	PROPN
ejpam-5107	155	10	y	y	PROPN
ejpam-5107	155	11	∂p	∂p	PROPN
ejpam-5107	155	12	∂t	∂t	PROPN
ejpam-5107	155	13	∂v̂	∂v̂	NOUN
ejpam-5107	155	14	∂y	∂y	NOUN
ejpam-5107	155	15	,	,	PUNCT
ejpam-5107	155	16	∂v	∂v	PROPN
ejpam-5107	156	1	∂r	∂r	PROPN
ejpam-5107	156	2	=	=	PUNCT
ejpam-5107	157	1	v̂	v̂	X
ejpam-5107	157	2	∂p	∂p	PROPN
ejpam-5107	158	1	∂r	∂r	INTJ
ejpam-5107	158	2	−	−	PROPN
ejpam-5107	159	1	y	y	PROPN
ejpam-5107	159	2	∂p	∂p	PROPN
ejpam-5107	159	3	∂r	∂r	PROPN
ejpam-5107	159	4	∂v̂	∂v̂	NOUN
ejpam-5107	160	1	∂r	∂r	INTJ
ejpam-5107	160	2	,	,	PUNCT
ejpam-5107	160	3	∂v	∂v	PROPN
ejpam-5107	160	4	∂x	∂x	PROPN
ejpam-5107	160	5	=	=	SYM
ejpam-5107	160	6	∂v̂	∂v̂	NOUN
ejpam-5107	160	7	∂y	∂y	NOUN
ejpam-5107	160	8	,	,	PUNCT
ejpam-5107	160	9	∂2v	∂2v	X
ejpam-5107	160	10	∂r2	∂r2	NOUN
ejpam-5107	160	11	=	=	PROPN
ejpam-5107	160	12	v̂	v̂	X
ejpam-5107	160	13	∂2p	∂2p	NOUN
ejpam-5107	160	14	∂r2	∂r2	PROPN
ejpam-5107	160	15	−	−	PUNCT
ejpam-5107	160	16	y	y	PROPN
ejpam-5107	160	17	∂v̂	∂v̂	NOUN
ejpam-5107	160	18	∂y	∂y	PROPN
ejpam-5107	160	19	∂2p	∂2p	NOUN
ejpam-5107	160	20	∂r2	∂r2	PROPN
ejpam-5107	160	21	−	−	VERB
ejpam-5107	160	22	y2	y2	PROPN
ejpam-5107	161	1	∂2v̂	∂2v̂	PROPN
ejpam-5107	161	2	∂y2	∂y2	VERB
ejpam-5107	161	3	1	1	NUM
ejpam-5107	161	4	p	p	X
ejpam-5107	161	5	(	(	PUNCT
ejpam-5107	161	6	∂p	∂p	PROPN
ejpam-5107	161	7	∂r	∂r	PROPN
ejpam-5107	161	8	)	)	PUNCT
ejpam-5107	161	9	2	2	NUM
ejpam-5107	161	10	,	,	PUNCT
ejpam-5107	161	11	∂2v	∂2v	X
ejpam-5107	161	12	∂r∂x	∂r∂x	NOUN
ejpam-5107	161	13	=	=	PUNCT
ejpam-5107	161	14	−y∂	−y∂	PRON
ejpam-5107	161	15	2v̂	2v̂	NUM
ejpam-5107	161	16	∂y2	∂y2	VERB
ejpam-5107	162	1	1	1	NUM
ejpam-5107	162	2	p	p	NOUN
ejpam-5107	162	3	∂p	∂p	PROPN
ejpam-5107	162	4	∂r	∂r	PROPN
ejpam-5107	162	5	,	,	PUNCT
ejpam-5107	162	6	∂2v	∂2v	X
ejpam-5107	162	7	∂x2	∂x2	NOUN
ejpam-5107	162	8	=	=	SYM
ejpam-5107	162	9	1	1	NUM
ejpam-5107	162	10	p	p	DET
ejpam-5107	162	11	∂2v̂	∂2v̂	PROPN
ejpam-5107	162	12	∂y2	∂y2	ADJ
ejpam-5107	162	13	.	.	PUNCT
ejpam-5107	163	1	substituting	substitute	VERB
ejpam-5107	163	2	these	these	DET
ejpam-5107	163	3	equations	equation	NOUN
ejpam-5107	163	4	gives	give	VERB
ejpam-5107	163	5	,	,	PUNCT
ejpam-5107	163	6	∂v̂	∂v̂	NOUN
ejpam-5107	163	7	∂t	∂t	PROPN
ejpam-5107	164	1	+	+	CCONJ
ejpam-5107	164	2	[	[	PUNCT
ejpam-5107	164	3	1	1	NUM
ejpam-5107	164	4	2	2	NUM
ejpam-5107	164	5	y2(dt)2h−1∂	y2(dt)2h−1∂	NOUN
ejpam-5107	164	6	2v̂	2v̂	PROPN
ejpam-5107	164	7	∂y2	∂y2	NOUN
ejpam-5107	164	8	]	]	PUNCT
ejpam-5107	164	9	[	[	PUNCT
ejpam-5107	164	10	σ2x	σ2x	NOUN
ejpam-5107	164	11	+	+	CCONJ
ejpam-5107	164	12	1	1	NUM
ejpam-5107	164	13	p	p	NOUN
ejpam-5107	164	14	2	2	NUM
ejpam-5107	164	15	(	(	PUNCT
ejpam-5107	164	16	∂p	∂p	PROPN
ejpam-5107	164	17	∂r	∂r	PROPN
ejpam-5107	164	18	)	)	PUNCT
ejpam-5107	164	19	2	2	NUM
ejpam-5107	164	20	(	(	PUNCT
ejpam-5107	164	21	σr	σr	NOUN
ejpam-5107	164	22	)	)	PUNCT
ejpam-5107	164	23	2	2	NUM
ejpam-5107	164	24	−	−	NOUN
ejpam-5107	164	25	2	2	NUM
ejpam-5107	164	26	p	p	NOUN
ejpam-5107	164	27	∂p	∂p	PROPN
ejpam-5107	164	28	∂r	∂r	NOUN
ejpam-5107	164	29	σrσxρ(t	σrσxρ(t	PROPN
ejpam-5107	164	30	)	)	PUNCT
ejpam-5107	164	31	]	]	PUNCT
ejpam-5107	165	1	+	+	CCONJ
ejpam-5107	165	2	cy2	cy2	ADJ
ejpam-5107	165	3	√	√	ADV
ejpam-5107	165	4	2	2	NUM
ejpam-5107	165	5	π	π	NOUN
ejpam-5107	165	6	(	(	PUNCT
ejpam-5107	165	7	dt)h−1	dt)h−1	NOUN
ejpam-5107	165	8	∣∣∣∣∣∂2v̂∂y2	∣∣∣∣∣∂2v̂∂y2	PROPN
ejpam-5107	165	9	∣∣∣∣∣×	∣∣∣∣∣×	PROPN
ejpam-5107	165	10	[	[	PUNCT
ejpam-5107	165	11	σ2x	σ2x	NOUN
ejpam-5107	165	12	+	+	CCONJ
ejpam-5107	165	13	1	1	NUM
ejpam-5107	165	14	p	p	NOUN
ejpam-5107	165	15	2	2	NUM
ejpam-5107	165	16	(	(	PUNCT
ejpam-5107	165	17	∂p	∂p	PROPN
ejpam-5107	165	18	∂r	∂r	PROPN
ejpam-5107	165	19	)	)	PUNCT
ejpam-5107	165	20	2	2	NUM
ejpam-5107	165	21	σ2r	σ2r	ADP
ejpam-5107	165	22	−2ρσxσr	−2ρσxσr	NOUN
ejpam-5107	165	23	(	(	PUNCT
ejpam-5107	165	24	1	1	NUM
ejpam-5107	165	25	p	p	NOUN
ejpam-5107	165	26	)	)	PUNCT
ejpam-5107	165	27	(	(	PUNCT
ejpam-5107	165	28	∂p	∂p	SYM
ejpam-5107	165	29	∂r	∂r	PROPN
ejpam-5107	165	30	)	)	PUNCT
ejpam-5107	165	31	]	]	X
ejpam-5107	165	32	1/2	1/2	NUM
ejpam-5107	165	33	=	=	SYM
ejpam-5107	165	34	0	0	PUNCT
ejpam-5107	165	35	taking	take	VERB
ejpam-5107	165	36	another	another	DET
ejpam-5107	165	37	transformation	transformation	NOUN
ejpam-5107	165	38	by	by	ADP
ejpam-5107	165	39	letting	let	VERB
ejpam-5107	165	40	z	z	NOUN
ejpam-5107	165	41	=	=	PUNCT
ejpam-5107	165	42	ln	ln	PROPN
ejpam-5107	165	43	y.	y.	NOUN
ejpam-5107	165	44	hence	hence	ADV
ejpam-5107	165	45	we	we	PRON
ejpam-5107	165	46	have	have	AUX
ejpam-5107	165	47	,	,	PUNCT
ejpam-5107	165	48	∂v̂	∂v̂	VERB
ejpam-5107	165	49	∂y	∂y	NOUN
ejpam-5107	165	50	=	=	SYM
ejpam-5107	165	51	∂v̂	∂v̂	NOUN
ejpam-5107	165	52	∂z	∂z	PROPN
ejpam-5107	165	53	1	1	NUM
ejpam-5107	165	54	y	y	PROPN
ejpam-5107	165	55	(	(	PUNCT
ejpam-5107	165	56	29	29	NUM
ejpam-5107	165	57	)	)	PUNCT
ejpam-5107	165	58	and	and	CCONJ
ejpam-5107	165	59	∂2v̂	∂2v̂	VERB
ejpam-5107	165	60	∂y2	∂y2	ADJ
ejpam-5107	165	61	=	=	PUNCT
ejpam-5107	165	62	(	(	PUNCT
ejpam-5107	165	63	1	1	NUM
ejpam-5107	165	64	y	y	NOUN
ejpam-5107	165	65	)	)	PUNCT
ejpam-5107	165	66	2	2	NUM
ejpam-5107	165	67	(	(	PUNCT
ejpam-5107	165	68	∂2v̂	∂2v̂	PROPN
ejpam-5107	165	69	∂z2	∂z2	PROPN
ejpam-5107	165	70	−	−	PROPN
ejpam-5107	165	71	∂v̂	∂v̂	NOUN
ejpam-5107	165	72	∂z	∂z	PROPN
ejpam-5107	165	73	)	)	PUNCT
ejpam-5107	165	74	.	.	PUNCT
ejpam-5107	166	1	furthermore	furthermore	ADV
ejpam-5107	166	2	,	,	PUNCT
ejpam-5107	166	3	let	let	VERB
ejpam-5107	166	4	b	b	NOUN
ejpam-5107	166	5	=	=	SYM
ejpam-5107	166	6	1	1	NUM
ejpam-5107	166	7	p	p	NOUN
ejpam-5107	166	8	∂p	∂p	PROPN
ejpam-5107	166	9	∂r	∂r	PROPN
ejpam-5107	166	10	and	and	CCONJ
ejpam-5107	166	11	σ̃2	σ̃2	PROPN
ejpam-5107	166	12	=	=	SYM
ejpam-5107	166	13	σ2x	σ2x	NOUN
ejpam-5107	166	14	+	+	CCONJ
ejpam-5107	166	15	σ2rb	σ2rb	NOUN
ejpam-5107	166	16	2	2	NUM
ejpam-5107	166	17	+	+	SYM
ejpam-5107	166	18	2ρσxσrb	2ρσxσrb	NUM
ejpam-5107	166	19	.	.	PUNCT
ejpam-5107	167	1	therefore	therefore	ADV
ejpam-5107	167	2	,	,	PUNCT
ejpam-5107	167	3	we	we	PRON
ejpam-5107	167	4	have	have	AUX
ejpam-5107	167	5	∂v̂	∂v̂	VERB
ejpam-5107	167	6	∂t	∂t	PROPN
ejpam-5107	168	1	+	+	CCONJ
ejpam-5107	168	2	[	[	PUNCT
ejpam-5107	168	3	1	1	NUM
ejpam-5107	168	4	2	2	NUM
ejpam-5107	168	5	(	(	PUNCT
ejpam-5107	168	6	dt)2h−1σ̃2	dt)2h−1σ̃2	NOUN
ejpam-5107	168	7	+	+	CCONJ
ejpam-5107	168	8	c(dt)h−1	c(dt)h−1	NOUN
ejpam-5107	168	9	√	√	NOUN
ejpam-5107	168	10	2	2	NUM
ejpam-5107	168	11	π	π	X
ejpam-5107	168	12	]	]	X
ejpam-5107	168	13	×	×	PROPN
ejpam-5107	168	14	(	(	PUNCT
ejpam-5107	168	15	∂2v̂	∂2v̂	PROPN
ejpam-5107	168	16	∂z2	∂z2	PROPN
ejpam-5107	168	17	−	−	PROPN
ejpam-5107	168	18	∂v̂	∂v̂	NOUN
ejpam-5107	168	19	∂z	∂z	PROPN
ejpam-5107	168	20	)	)	PUNCT
ejpam-5107	169	1	=	=	SYM
ejpam-5107	169	2	0	0	PROPN
ejpam-5107	169	3	f.	f.	PROPN
ejpam-5107	169	4	sumalpong	sumalpong	PROPN
ejpam-5107	169	5	,	,	PUNCT
ejpam-5107	169	6	e.	e.	PROPN
ejpam-5107	169	7	lauron	lauron	PROPN
ejpam-5107	169	8	/	/	SYM
ejpam-5107	169	9	eur	eur	PROPN
ejpam-5107	169	10	.	.	PUNCT
ejpam-5107	170	1	j.	j.	PROPN
ejpam-5107	170	2	pure	pure	PROPN
ejpam-5107	170	3	appl	appl	PROPN
ejpam-5107	170	4	.	.	PROPN
ejpam-5107	170	5	math	math	PROPN
ejpam-5107	170	6	,	,	PUNCT
ejpam-5107	170	7	17	17	NUM
ejpam-5107	170	8	(	(	PUNCT
ejpam-5107	170	9	3	3	NUM
ejpam-5107	170	10	)	)	PUNCT
ejpam-5107	170	11	(	(	PUNCT
ejpam-5107	170	12	2024	2024	NUM
ejpam-5107	170	13	)	)	PUNCT
ejpam-5107	170	14	,	,	PUNCT
ejpam-5107	170	15	2299	2299	NUM
ejpam-5107	170	16	-	-	SYM
ejpam-5107	170	17	2310	2310	NUM
ejpam-5107	170	18	2308	2308	NUM
ejpam-5107	171	1	finally	finally	ADV
ejpam-5107	171	2	we	we	PRON
ejpam-5107	171	3	take	take	VERB
ejpam-5107	171	4	the	the	DET
ejpam-5107	171	5	following	following	ADJ
ejpam-5107	171	6	transformation	transformation	NOUN
ejpam-5107	171	7	.	.	PUNCT
ejpam-5107	172	1	let	let	VERB
ejpam-5107	172	2	v̂	v̂	PRON
ejpam-5107	172	3	(	(	PUNCT
ejpam-5107	172	4	z	z	NOUN
ejpam-5107	172	5	,	,	PUNCT
ejpam-5107	172	6	t	t	PROPN
ejpam-5107	172	7	)	)	PUNCT
ejpam-5107	172	8	=	=	SYM
ejpam-5107	172	9	µ(η	µ(η	NOUN
ejpam-5107	172	10	,	,	PUNCT
ejpam-5107	172	11	τ	τ	PROPN
ejpam-5107	172	12	)	)	PUNCT
ejpam-5107	172	13	,	,	PUNCT
ejpam-5107	172	14	where	where	SCONJ
ejpam-5107	172	15	η	η	X
ejpam-5107	172	16	=	=	PROPN
ejpam-5107	172	17	z	z	PROPN
ejpam-5107	172	18	+	+	NUM
ejpam-5107	172	19	α(t	α(t	NOUN
ejpam-5107	172	20	)	)	PUNCT
ejpam-5107	172	21	and	and	CCONJ
ejpam-5107	172	22	τ	τ	PROPN
ejpam-5107	172	23	=	=	PUNCT
ejpam-5107	172	24	γ(t	γ(t	NOUN
ejpam-5107	172	25	)	)	PUNCT
ejpam-5107	172	26	.	.	PUNCT
ejpam-5107	173	1	at	at	ADP
ejpam-5107	173	2	the	the	DET
ejpam-5107	173	3	expiry	expiry	NOUN
ejpam-5107	173	4	date	date	NOUN
ejpam-5107	173	5	t	t	PROPN
ejpam-5107	173	6	of	of	ADP
ejpam-5107	173	7	the	the	DET
ejpam-5107	173	8	contract	contract	NOUN
ejpam-5107	173	9	,	,	PUNCT
ejpam-5107	173	10	α(t	α(t	PROPN
ejpam-5107	173	11	)	)	PUNCT
ejpam-5107	174	1	=	=	PUNCT
ejpam-5107	174	2	γ(t	γ(t	NOUN
ejpam-5107	174	3	)	)	PUNCT
ejpam-5107	174	4	=	=	PUNCT
ejpam-5107	174	5	0	0	X
ejpam-5107	174	6	.	.	PUNCT
ejpam-5107	175	1	so	so	ADV
ejpam-5107	175	2	we	we	PRON
ejpam-5107	175	3	have	have	VERB
ejpam-5107	175	4	the	the	DET
ejpam-5107	175	5	following	following	ADJ
ejpam-5107	175	6	calculations	calculation	NOUN
ejpam-5107	175	7	,	,	PUNCT
ejpam-5107	175	8	∂v̂	∂v̂	VERB
ejpam-5107	175	9	∂t	∂t	PROPN
ejpam-5107	175	10	=	=	PUNCT
ejpam-5107	175	11	∂µ	∂µ	PROPN
ejpam-5107	175	12	∂η	∂η	PROPN
ejpam-5107	175	13	α′(t	α′(t	NOUN
ejpam-5107	175	14	)	)	PUNCT
ejpam-5107	176	1	+	+	CCONJ
ejpam-5107	176	2	∂µ	∂µ	PROPN
ejpam-5107	176	3	∂τ	∂τ	PROPN
ejpam-5107	176	4	γ′(t	γ′(t	NOUN
ejpam-5107	176	5	)	)	PUNCT
ejpam-5107	176	6	(	(	PUNCT
ejpam-5107	176	7	30	30	NUM
ejpam-5107	176	8	)	)	PUNCT
ejpam-5107	176	9	and	and	CCONJ
ejpam-5107	176	10	∂v̂	∂v̂	VERB
ejpam-5107	176	11	∂z	∂z	PROPN
ejpam-5107	177	1	=	=	PUNCT
ejpam-5107	177	2	∂µ	∂µ	PROPN
ejpam-5107	177	3	∂η	∂η	PROPN
ejpam-5107	177	4	,	,	PUNCT
ejpam-5107	177	5	(	(	PUNCT
ejpam-5107	177	6	31	31	NUM
ejpam-5107	177	7	)	)	PUNCT
ejpam-5107	177	8	∂2v̂	∂2v̂	PROPN
ejpam-5107	177	9	∂z2	∂z2	NOUN
ejpam-5107	177	10	=	=	SYM
ejpam-5107	177	11	∂2µ	∂2µ	PROPN
ejpam-5107	177	12	∂η2	∂η2	VERB
ejpam-5107	177	13	.	.	PUNCT
ejpam-5107	178	1	(	(	PUNCT
ejpam-5107	178	2	32	32	NUM
ejpam-5107	178	3	)	)	PUNCT
ejpam-5107	178	4	we	we	PRON
ejpam-5107	178	5	let	let	VERB
ejpam-5107	178	6	α′(t	α′(t	X
ejpam-5107	178	7	)	)	PUNCT
ejpam-5107	178	8	=	=	SYM
ejpam-5107	178	9	1	1	NUM
ejpam-5107	178	10	2	2	NUM
ejpam-5107	178	11	(	(	PUNCT
ejpam-5107	178	12	dt)2h−1σ̃2	dt)2h−1σ̃2	NOUN
ejpam-5107	178	13	+	+	CCONJ
ejpam-5107	178	14	c(dt)h−1	c(dt)h−1	NOUN
ejpam-5107	178	15	√	√	NUM
ejpam-5107	178	16	(	(	PUNCT
ejpam-5107	178	17	2	2	NUM
ejpam-5107	178	18	/	/	SYM
ejpam-5107	178	19	π)σ̃	π)σ̃	NOUN
ejpam-5107	178	20	and	and	CCONJ
ejpam-5107	178	21	γ′(t	γ′(t	NOUN
ejpam-5107	178	22	)	)	PUNCT
ejpam-5107	178	23	=	=	SYM
ejpam-5107	179	1	−	−	PROPN
ejpam-5107	179	2	[	[	PUNCT
ejpam-5107	179	3	1	1	NUM
ejpam-5107	179	4	2	2	NUM
ejpam-5107	179	5	(	(	PUNCT
ejpam-5107	179	6	dt)2h−1σ̃2	dt)2h−1σ̃2	NOUN
ejpam-5107	179	7	+	+	CCONJ
ejpam-5107	179	8	c(dt)h−1	c(dt)h−1	NOUN
ejpam-5107	179	9	√	√	NUM
ejpam-5107	179	10	(	(	PUNCT
ejpam-5107	179	11	2	2	NUM
ejpam-5107	179	12	/	/	SYM
ejpam-5107	179	13	π)σ̃	π)σ̃	NOUN
ejpam-5107	179	14	]	]	PUNCT
ejpam-5107	179	15	.	.	PUNCT
ejpam-5107	180	1	substituting	substitute	VERB
ejpam-5107	180	2	these	these	PRON
ejpam-5107	180	3	,	,	PUNCT
ejpam-5107	180	4	we	we	PRON
ejpam-5107	180	5	have	have	VERB
ejpam-5107	180	6	∂µ	∂µ	PROPN
ejpam-5107	180	7	∂η	∂η	PROPN
ejpam-5107	180	8	α′(t	α′(t	NOUN
ejpam-5107	180	9	)	)	PUNCT
ejpam-5107	181	1	+	+	CCONJ
ejpam-5107	181	2	∂µ	∂µ	PROPN
ejpam-5107	181	3	∂τ	∂τ	PROPN
ejpam-5107	181	4	(	(	PUNCT
ejpam-5107	181	5	−α′(t	−α′(t	PROPN
ejpam-5107	181	6	)	)	PUNCT
ejpam-5107	181	7	)	)	PUNCT
ejpam-5107	182	1	+	+	PUNCT
ejpam-5107	182	2	α′(t	α′(t	X
ejpam-5107	182	3	)	)	PUNCT
ejpam-5107	182	4	[	[	PUNCT
ejpam-5107	182	5	∂2µ	∂2µ	NOUN
ejpam-5107	182	6	∂η2	∂η2	VERB
ejpam-5107	182	7	−	−	PROPN
ejpam-5107	182	8	∂µ	∂µ	PROPN
ejpam-5107	182	9	∂η	∂η	PROPN
ejpam-5107	182	10	]	]	PUNCT
ejpam-5107	183	1	=	=	PUNCT
ejpam-5107	183	2	0	0	X
ejpam-5107	183	3	.	.	PUNCT
ejpam-5107	184	1	hence	hence	ADV
ejpam-5107	184	2	,	,	PUNCT
ejpam-5107	184	3	this	this	PRON
ejpam-5107	184	4	can	can	AUX
ejpam-5107	184	5	be	be	AUX
ejpam-5107	184	6	reduced	reduce	VERB
ejpam-5107	184	7	further	far	ADV
ejpam-5107	184	8	to	to	ADP
ejpam-5107	184	9	∂µ	∂µ	PROPN
ejpam-5107	184	10	∂τ	∂τ	PROPN
ejpam-5107	184	11	−	−	PROPN
ejpam-5107	184	12	∂2µ	∂2µ	NOUN
ejpam-5107	184	13	∂η2	∂η2	VERB
ejpam-5107	184	14	=	=	SYM
ejpam-5107	184	15	0	0	NUM
ejpam-5107	184	16	(	(	PUNCT
ejpam-5107	184	17	33	33	NUM
ejpam-5107	184	18	)	)	PUNCT
ejpam-5107	184	19	with	with	ADP
ejpam-5107	184	20	the	the	DET
ejpam-5107	184	21	initial	initial	ADJ
ejpam-5107	184	22	condition	condition	NOUN
ejpam-5107	184	23	µ(η	µ(η	NOUN
ejpam-5107	184	24	,	,	PUNCT
ejpam-5107	184	25	t	t	NOUN
ejpam-5107	184	26	)	)	PUNCT
ejpam-5107	185	1	=	=	SYM
ejpam-5107	185	2	(	(	PUNCT
ejpam-5107	185	3	eη	eη	NOUN
ejpam-5107	185	4	−k)+	−k)+	PROPN
ejpam-5107	185	5	.	.	PUNCT
ejpam-5107	186	1	(	(	PUNCT
ejpam-5107	186	2	34	34	NUM
ejpam-5107	186	3	)	)	PUNCT
ejpam-5107	186	4	the	the	DET
ejpam-5107	186	5	solution	solution	NOUN
ejpam-5107	186	6	for	for	ADP
ejpam-5107	186	7	this	this	DET
ejpam-5107	186	8	equation	equation	NOUN
ejpam-5107	186	9	is	be	AUX
ejpam-5107	186	10	µ(η	µ(η	NOUN
ejpam-5107	186	11	,	,	PUNCT
ejpam-5107	186	12	τ	τ	X
ejpam-5107	186	13	)	)	PUNCT
ejpam-5107	186	14	=	=	SYM
ejpam-5107	186	15	1	1	NUM
ejpam-5107	186	16	2	2	NUM
ejpam-5107	186	17	√	√	NUM
ejpam-5107	186	18	πτ	πτ	ADP
ejpam-5107	186	19	∫	∫	PROPN
ejpam-5107	187	1	+	+	PROPN
ejpam-5107	187	2	∞	∞	PROPN
ejpam-5107	187	3	−∞	−∞	ADP
ejpam-5107	187	4	µ0(ξ)e	µ0(ξ)e	CCONJ
ejpam-5107	187	5	−(η−ξ)2/4τdξ	−(η−ξ)2/4τdξ	PROPN
ejpam-5107	187	6	(	(	PUNCT
ejpam-5107	187	7	35	35	NUM
ejpam-5107	187	8	)	)	PUNCT
ejpam-5107	187	9	now	now	ADV
ejpam-5107	187	10	for	for	ADP
ejpam-5107	187	11	eξ	eξ	PROPN
ejpam-5107	187	12	−k	−k	PROPN
ejpam-5107	187	13	≥	≥	NUM
ejpam-5107	187	14	0	0	NUM
ejpam-5107	187	15	,	,	PUNCT
ejpam-5107	187	16	ξ	ξ	PRON
ejpam-5107	187	17	≥	≥	NOUN
ejpam-5107	187	18	lnk	lnk	NOUN
ejpam-5107	187	19	.	.	PUNCT
ejpam-5107	188	1	(	(	PUNCT
ejpam-5107	188	2	36	36	NUM
ejpam-5107	188	3	)	)	PUNCT
ejpam-5107	188	4	hence	hence	ADV
ejpam-5107	188	5	,	,	PUNCT
ejpam-5107	188	6	the	the	DET
ejpam-5107	188	7	integration	integration	NOUN
ejpam-5107	188	8	domain	domain	NOUN
ejpam-5107	188	9	can	can	AUX
ejpam-5107	188	10	be	be	AUX
ejpam-5107	188	11	equivalently	equivalently	ADV
ejpam-5107	188	12	[	[	X
ejpam-5107	188	13	−∞	−∞	NOUN
ejpam-5107	188	14	,	,	PUNCT
ejpam-5107	188	15	lnk	lnk	NOUN
ejpam-5107	188	16	]	]	PUNCT
ejpam-5107	188	17	.	.	PUNCT
ejpam-5107	189	1	hence	hence	ADV
ejpam-5107	189	2	,	,	PUNCT
ejpam-5107	189	3	we	we	PRON
ejpam-5107	189	4	can	can	AUX
ejpam-5107	189	5	write	write	VERB
ejpam-5107	189	6	the	the	DET
ejpam-5107	189	7	solution	solution	NOUN
ejpam-5107	189	8	as	as	ADP
ejpam-5107	189	9	µ(η	µ(η	NOUN
ejpam-5107	189	10	,	,	PUNCT
ejpam-5107	189	11	τ	τ	X
ejpam-5107	189	12	)	)	PUNCT
ejpam-5107	189	13	=	=	SYM
ejpam-5107	189	14	1	1	NUM
ejpam-5107	189	15	2	2	NUM
ejpam-5107	189	16	√	√	NUM
ejpam-5107	189	17	πτ	πτ	ADP
ejpam-5107	189	18	∫	∫	PROPN
ejpam-5107	190	1	+	+	CCONJ
ejpam-5107	190	2	∞	∞	PROPN
ejpam-5107	190	3	lnk	lnk	NOUN
ejpam-5107	190	4	(	(	PUNCT
ejpam-5107	190	5	eξ	eξ	NOUN
ejpam-5107	190	6	−k)e−(η−ξ)2/4τdξ	−k)e−(η−ξ)2/4τdξ	NOUN
ejpam-5107	190	7	=	=	NOUN
ejpam-5107	190	8	1	1	NUM
ejpam-5107	190	9	2	2	NUM
ejpam-5107	190	10	√	√	NUM
ejpam-5107	190	11	πτ	πτ	ADP
ejpam-5107	190	12	∫	∫	PROPN
ejpam-5107	191	1	+	+	CCONJ
ejpam-5107	191	2	∞	∞	PROPN
ejpam-5107	191	3	lnk	lnk	NOUN
ejpam-5107	191	4	eξe−(η−ξ)2/4τdξ	eξe−(η−ξ)2/4τdξ	PROPN
ejpam-5107	191	5	−	−	PROPN
ejpam-5107	191	6	1	1	NUM
ejpam-5107	191	7	2	2	NUM
ejpam-5107	191	8	√	√	NUM
ejpam-5107	191	9	πτ	πτ	ADP
ejpam-5107	191	10	∫	∫	PROPN
ejpam-5107	192	1	+	+	CCONJ
ejpam-5107	192	2	∞	∞	PROPN
ejpam-5107	192	3	lnk	lnk	ADJ
ejpam-5107	192	4	ke−(η−ξ)2/4τdξ	ke−(η−ξ)2/4τdξ	PROPN
ejpam-5107	192	5	f.	f.	PROPN
ejpam-5107	192	6	sumalpong	sumalpong	PROPN
ejpam-5107	192	7	,	,	PUNCT
ejpam-5107	192	8	e.	e.	PROPN
ejpam-5107	192	9	lauron	lauron	PROPN
ejpam-5107	192	10	/	/	SYM
ejpam-5107	192	11	eur	eur	PROPN
ejpam-5107	192	12	.	.	PUNCT
ejpam-5107	193	1	j.	j.	PROPN
ejpam-5107	193	2	pure	pure	PROPN
ejpam-5107	193	3	appl	appl	PROPN
ejpam-5107	193	4	.	.	PROPN
ejpam-5107	193	5	math	math	PROPN
ejpam-5107	193	6	,	,	PUNCT
ejpam-5107	193	7	17	17	NUM
ejpam-5107	193	8	(	(	PUNCT
ejpam-5107	193	9	3	3	NUM
ejpam-5107	193	10	)	)	PUNCT
ejpam-5107	193	11	(	(	PUNCT
ejpam-5107	193	12	2024	2024	NUM
ejpam-5107	193	13	)	)	PUNCT
ejpam-5107	193	14	,	,	PUNCT
ejpam-5107	193	15	2299	2299	NUM
ejpam-5107	193	16	-	-	SYM
ejpam-5107	193	17	2310	2310	NUM
ejpam-5107	193	18	2309	2309	NUM
ejpam-5107	193	19	let	let	VERB
ejpam-5107	193	20	ξ	ξ	PROPN
ejpam-5107	193	21	=	=	SYM
ejpam-5107	193	22	η	η	PROPN
ejpam-5107	193	23	+	+	PROPN
ejpam-5107	193	24	√	√	PROPN
ejpam-5107	193	25	2τω	2τω	NOUN
ejpam-5107	193	26	,	,	PUNCT
ejpam-5107	193	27	then	then	ADV
ejpam-5107	193	28	we	we	PRON
ejpam-5107	193	29	can	can	AUX
ejpam-5107	193	30	have	have	VERB
ejpam-5107	193	31	ω	ω	NOUN
ejpam-5107	193	32	=	=	SYM
ejpam-5107	194	1	ξ	ξ	PROPN
ejpam-5107	194	2	−	−	PROPN
ejpam-5107	194	3	η√	η√	PROPN
ejpam-5107	194	4	2τ	2τ	NUM
ejpam-5107	194	5	(	(	PUNCT
ejpam-5107	194	6	37	37	NUM
ejpam-5107	194	7	)	)	PUNCT
ejpam-5107	194	8	and	and	CCONJ
ejpam-5107	194	9	dξ	dξ	PROPN
ejpam-5107	194	10	=	=	NOUN
ejpam-5107	194	11	√	√	NUM
ejpam-5107	194	12	2τdω	2τdω	NUM
ejpam-5107	194	13	.	.	PUNCT
ejpam-5107	195	1	(	(	PUNCT
ejpam-5107	195	2	38	38	NUM
ejpam-5107	195	3	)	)	PUNCT
ejpam-5107	195	4	therefore	therefore	ADV
ejpam-5107	195	5	,	,	PUNCT
ejpam-5107	195	6	µ(η	µ(η	NOUN
ejpam-5107	195	7	,	,	PUNCT
ejpam-5107	195	8	τ	τ	X
ejpam-5107	195	9	)	)	PUNCT
ejpam-5107	195	10	=	=	SYM
ejpam-5107	195	11	1√	1√	NUM
ejpam-5107	195	12	2π	2π	PROPN
ejpam-5107	195	13	eη+τ	eη+τ	PROPN
ejpam-5107	195	14	∫	∫	PROPN
ejpam-5107	196	1	η−lnk+2τ√	η−lnk+2τ√	ADJ
ejpam-5107	196	2	2τ	2τ	NOUN
ejpam-5107	197	1	−∞	−∞	ADP
ejpam-5107	197	2	e−	e−	PROPN
ejpam-5107	197	3	ζ2	ζ2	NOUN
ejpam-5107	197	4	2	2	NUM
ejpam-5107	197	5	dζ	dζ	PROPN
ejpam-5107	197	6	−	−	PROPN
ejpam-5107	197	7	1√	1√	PROPN
ejpam-5107	197	8	2π	2π	NOUN
ejpam-5107	197	9	k	k	PROPN
ejpam-5107	197	10	∫	∫	PROPN
ejpam-5107	197	11	η−lnk√	η−lnk√	NOUN
ejpam-5107	197	12	2τ	2τ	NOUN
ejpam-5107	197	13	−∞	−∞	ADP
ejpam-5107	197	14	e−ω2/2dω	e−ω2/2dω	PROPN
ejpam-5107	197	15	.	.	PUNCT
ejpam-5107	198	1	this	this	PRON
ejpam-5107	198	2	can	can	AUX
ejpam-5107	198	3	be	be	AUX
ejpam-5107	198	4	written	write	VERB
ejpam-5107	198	5	as	as	ADP
ejpam-5107	198	6	µ(η	µ(η	NOUN
ejpam-5107	198	7	,	,	PUNCT
ejpam-5107	198	8	τ	τ	X
ejpam-5107	198	9	)	)	PUNCT
ejpam-5107	198	10	=	=	SYM
ejpam-5107	198	11	eη+τn	eη+τn	PROPN
ejpam-5107	198	12	(	(	PUNCT
ejpam-5107	198	13	d1)−kn	d1)−kn	INTJ
ejpam-5107	198	14	(	(	PUNCT
ejpam-5107	198	15	d2	d2	PROPN
ejpam-5107	198	16	)	)	PUNCT
ejpam-5107	198	17	(	(	PUNCT
ejpam-5107	198	18	39	39	NUM
ejpam-5107	198	19	)	)	PUNCT
ejpam-5107	198	20	where	where	SCONJ
ejpam-5107	198	21	d1	d1	PROPN
ejpam-5107	198	22	=	=	SYM
ejpam-5107	198	23	η	η	PROPN
ejpam-5107	198	24	−	−	PROPN
ejpam-5107	198	25	lnk	lnk	NOUN
ejpam-5107	198	26	+	+	NOUN
ejpam-5107	198	27	2τ√	2τ√	NUM
ejpam-5107	198	28	2τ	2τ	NUM
ejpam-5107	198	29	(	(	PUNCT
ejpam-5107	198	30	40	40	NUM
ejpam-5107	198	31	)	)	PUNCT
ejpam-5107	198	32	d2	d2	PROPN
ejpam-5107	198	33	=	=	SYM
ejpam-5107	198	34	η	η	PROPN
ejpam-5107	198	35	−	−	PROPN
ejpam-5107	198	36	lnk√	lnk√	NOUN
ejpam-5107	198	37	2τ	2τ	NUM
ejpam-5107	198	38	(	(	PUNCT
ejpam-5107	198	39	41	41	NUM
ejpam-5107	198	40	)	)	PUNCT
ejpam-5107	198	41	and	and	CCONJ
ejpam-5107	198	42	n(d1	n(d1	NOUN
ejpam-5107	198	43	)	)	PUNCT
ejpam-5107	198	44	=	=	SYM
ejpam-5107	199	1	1√	1√	NUM
ejpam-5107	199	2	2π	2π	NUM
ejpam-5107	199	3	∫	∫	NOUN
ejpam-5107	199	4	d1	d1	PROPN
ejpam-5107	199	5	−∞	−∞	ADP
ejpam-5107	199	6	e	e	NOUN
ejpam-5107	199	7	−1	−1	NOUN
ejpam-5107	199	8	2	2	NUM
ejpam-5107	199	9	ζ2dζ	ζ2dζ	X
ejpam-5107	199	10	(	(	PUNCT
ejpam-5107	199	11	42	42	NUM
ejpam-5107	199	12	)	)	PUNCT
ejpam-5107	199	13	n(d2	n(d2	NOUN
ejpam-5107	199	14	)	)	PUNCT
ejpam-5107	199	15	=	=	SYM
ejpam-5107	200	1	1√	1√	NUM
ejpam-5107	200	2	2π	2π	NUM
ejpam-5107	200	3	∫	∫	PROPN
ejpam-5107	200	4	d2	d2	PROPN
ejpam-5107	200	5	−∞	−∞	PROPN
ejpam-5107	200	6	e	e	PROPN
ejpam-5107	200	7	−1	−1	NOUN
ejpam-5107	200	8	2	2	NUM
ejpam-5107	200	9	ω2	ω2	NOUN
ejpam-5107	200	10	dω	dω	PROPN
ejpam-5107	200	11	.	.	PUNCT
ejpam-5107	201	1	(	(	PUNCT
ejpam-5107	201	2	43	43	NUM
ejpam-5107	201	3	)	)	PUNCT
ejpam-5107	201	4	by	by	ADP
ejpam-5107	201	5	inverse	inverse	NOUN
ejpam-5107	201	6	change	change	NOUN
ejpam-5107	201	7	of	of	ADP
ejpam-5107	201	8	variables	variable	NOUN
ejpam-5107	201	9	,	,	PUNCT
ejpam-5107	201	10	the	the	DET
ejpam-5107	201	11	formula	formula	NOUN
ejpam-5107	201	12	in	in	ADP
ejpam-5107	201	13	the	the	DET
ejpam-5107	201	14	theorem	theorem	NOUN
ejpam-5107	201	15	can	can	AUX
ejpam-5107	201	16	be	be	AUX
ejpam-5107	201	17	derived	derive	VERB
ejpam-5107	201	18	.	.	PUNCT
ejpam-5107	202	1	corollary	corollary	ADJ
ejpam-5107	202	2	5	5	NUM
ejpam-5107	202	3	.	.	PUNCT
ejpam-5107	203	1	without	without	ADP
ejpam-5107	203	2	the	the	DET
ejpam-5107	203	3	transaction	transaction	NOUN
ejpam-5107	203	4	cost	cost	NOUN
ejpam-5107	203	5	and	and	CCONJ
ejpam-5107	203	6	under	under	ADP
ejpam-5107	203	7	a	a	DET
ejpam-5107	203	8	fractional	fractional	ADJ
ejpam-5107	203	9	brownian	brownian	ADJ
ejpam-5107	203	10	motion	motion	NOUN
ejpam-5107	203	11	,	,	PUNCT
ejpam-5107	203	12	the	the	DET
ejpam-5107	203	13	closed	closed	ADJ
ejpam-5107	203	14	form	form	NOUN
ejpam-5107	203	15	formula	formula	NOUN
ejpam-5107	203	16	for	for	ADP
ejpam-5107	203	17	the	the	DET
ejpam-5107	203	18	european	european	ADJ
ejpam-5107	203	19	call	call	NOUN
ejpam-5107	203	20	option	option	NOUN
ejpam-5107	203	21	price	price	NOUN
ejpam-5107	203	22	vc(x	vc(x	NOUN
ejpam-5107	203	23	,	,	PUNCT
ejpam-5107	203	24	r	r	NOUN
ejpam-5107	203	25	,	,	PUNCT
ejpam-5107	203	26	t	t	PROPN
ejpam-5107	203	27	)	)	PUNCT
ejpam-5107	203	28	is	be	AUX
ejpam-5107	203	29	given	give	VERB
ejpam-5107	203	30	by	by	ADP
ejpam-5107	203	31	vc(x	vc(x	NOUN
ejpam-5107	203	32	,	,	PUNCT
ejpam-5107	203	33	r	r	NOUN
ejpam-5107	203	34	,	,	PUNCT
ejpam-5107	203	35	t	t	PROPN
ejpam-5107	203	36	)	)	PUNCT
ejpam-5107	203	37	=	=	SYM
ejpam-5107	204	1	x(t)n(d1)−kp	x(t)n(d1)−kp	X
ejpam-5107	204	2	(	(	PUNCT
ejpam-5107	204	3	r	r	NOUN
ejpam-5107	204	4	,	,	PUNCT
ejpam-5107	204	5	t	t	PROPN
ejpam-5107	204	6	,	,	PUNCT
ejpam-5107	204	7	t	t	NOUN
ejpam-5107	204	8	)	)	PUNCT
ejpam-5107	204	9	n(d2	n(d2	PROPN
ejpam-5107	204	10	)	)	PUNCT
ejpam-5107	204	11	(	(	PUNCT
ejpam-5107	204	12	44	44	NUM
ejpam-5107	204	13	)	)	PUNCT
ejpam-5107	204	14	where	where	SCONJ
ejpam-5107	204	15	d1	d1	PROPN
ejpam-5107	204	16	=	=	SYM
ejpam-5107	204	17	d2	d2	PROPN
ejpam-5107	204	18	+	+	CCONJ
ejpam-5107	204	19	√	√	ADJ
ejpam-5107	204	20	σ̃2	σ̃2	PROPN
ejpam-5107	204	21	∫	∫	PROPN
ejpam-5107	204	22	t	t	PROPN
ejpam-5107	204	23	t	t	PROPN
ejpam-5107	204	24	(	(	PUNCT
ejpam-5107	204	25	ds)2h	ds)2h	NOUN
ejpam-5107	204	26	,	,	PUNCT
ejpam-5107	204	27	d2	d2	PROPN
ejpam-5107	204	28	=	=	SYM
ejpam-5107	204	29	ln	ln	PROPN
ejpam-5107	204	30	x	x	PUNCT
ejpam-5107	204	31	kp	kp	X
ejpam-5107	204	32	(	(	PUNCT
ejpam-5107	204	33	r	r	NOUN
ejpam-5107	204	34	,	,	PUNCT
ejpam-5107	204	35	t;t	t;t	NOUN
ejpam-5107	204	36	)	)	PUNCT
ejpam-5107	204	37	−	−	NOUN
ejpam-5107	205	1	1	1	NUM
ejpam-5107	205	2	2	2	NUM
ejpam-5107	205	3	σ̃	σ̃	PROPN
ejpam-5107	205	4	2	2	NUM
ejpam-5107	205	5	∫	∫	NOUN
ejpam-5107	205	6	t	t	PROPN
ejpam-5107	205	7	t	t	PROPN
ejpam-5107	205	8	(	(	PUNCT
ejpam-5107	205	9	ds)2h√	ds)2h√	PROPN
ejpam-5107	205	10	σ̃2	σ̃2	PROPN
ejpam-5107	205	11	∫	∫	PROPN
ejpam-5107	205	12	t	t	PROPN
ejpam-5107	205	13	t	t	PROPN
ejpam-5107	205	14	(	(	PUNCT
ejpam-5107	205	15	ds)2h	ds)2h	NOUN
ejpam-5107	205	16	,	,	PUNCT
ejpam-5107	205	17	σ̃2	σ̃2	PROPN
ejpam-5107	205	18	=	=	SYM
ejpam-5107	205	19	σ2x	σ2x	NOUN
ejpam-5107	205	20	+	+	CCONJ
ejpam-5107	205	21	σ22b	σ22b	NOUN
ejpam-5107	205	22	2	2	NUM
ejpam-5107	205	23	+	+	SYM
ejpam-5107	205	24	2ρσxσ2b	2ρσxσ2b	NUM
ejpam-5107	205	25	,	,	PUNCT
ejpam-5107	205	26	b	b	X
ejpam-5107	205	27	=	=	SYM
ejpam-5107	205	28	1	1	NUM
ejpam-5107	205	29	p	p	NOUN
ejpam-5107	205	30	∂p	∂p	PROPN
ejpam-5107	205	31	∂r	∂r	PROPN
ejpam-5107	205	32	,	,	PUNCT
ejpam-5107	205	33	references	reference	NOUN
ejpam-5107	205	34	2310	2310	NUM
ejpam-5107	205	35	n(d	n(d	NOUN
ejpam-5107	205	36	)	)	PUNCT
ejpam-5107	205	37	=	=	SYM
ejpam-5107	206	1	1√	1√	NUM
ejpam-5107	206	2	2π	2π	NUM
ejpam-5107	206	3	∫	∫	X
ejpam-5107	207	1	d	d	X
ejpam-5107	207	2	−∞	−∞	X
ejpam-5107	207	3	e	e	PROPN
ejpam-5107	207	4	−1	−1	NOUN
ejpam-5107	207	5	2	2	NUM
ejpam-5107	207	6	y2dy	y2dy	X
ejpam-5107	207	7	.	.	PROPN
ejpam-5107	208	1	4	4	NUM
ejpam-5107	208	2	.	.	X
ejpam-5107	208	3	conclusion	conclusion	NOUN
ejpam-5107	208	4	and	and	CCONJ
ejpam-5107	208	5	recommendations	recommendation	NOUN
ejpam-5107	208	6	this	this	DET
ejpam-5107	208	7	paper	paper	NOUN
ejpam-5107	208	8	presents	present	VERB
ejpam-5107	208	9	an	an	DET
ejpam-5107	208	10	extension	extension	NOUN
ejpam-5107	208	11	of	of	ADP
ejpam-5107	208	12	the	the	DET
ejpam-5107	208	13	bsmmodel	bsmmodel	NOUN
ejpam-5107	208	14	for	for	ADP
ejpam-5107	208	15	european	european	ADJ
ejpam-5107	208	16	call	call	NOUN
ejpam-5107	208	17	option	option	NOUN
ejpam-5107	208	18	introduced	introduce	VERB
ejpam-5107	208	19	by	by	ADP
ejpam-5107	208	20	black	black	ADJ
ejpam-5107	208	21	,	,	PUNCT
ejpam-5107	208	22	scholes	schole	NOUN
ejpam-5107	208	23	and	and	CCONJ
ejpam-5107	208	24	merton	merton	NOUN
ejpam-5107	208	25	by	by	ADP
ejpam-5107	208	26	considering	consider	VERB
ejpam-5107	208	27	a	a	DET
ejpam-5107	208	28	stochastic	stochastic	ADJ
ejpam-5107	208	29	rate	rate	NOUN
ejpam-5107	208	30	under	under	ADP
ejpam-5107	208	31	a	a	DET
ejpam-5107	208	32	fractional	fractional	ADJ
ejpam-5107	208	33	brownian	brownian	ADJ
ejpam-5107	208	34	motion	motion	NOUN
ejpam-5107	208	35	instead	instead	ADV
ejpam-5107	208	36	of	of	ADP
ejpam-5107	208	37	a	a	DET
ejpam-5107	208	38	constant	constant	ADJ
ejpam-5107	208	39	rate	rate	NOUN
ejpam-5107	208	40	and	and	CCONJ
ejpam-5107	208	41	adding	add	VERB
ejpam-5107	208	42	a	a	DET
ejpam-5107	208	43	transaction	transaction	NOUN
ejpam-5107	208	44	cost	cost	NOUN
ejpam-5107	208	45	.	.	PUNCT
ejpam-5107	209	1	a	a	DET
ejpam-5107	209	2	closed	close	VERB
ejpam-5107	209	3	-	-	PUNCT
ejpam-5107	209	4	form	form	NOUN
ejpam-5107	209	5	formula	formula	NOUN
ejpam-5107	209	6	for	for	ADP
ejpam-5107	209	7	european	european	ADJ
ejpam-5107	209	8	call	call	NOUN
ejpam-5107	209	9	option	option	NOUN
ejpam-5107	209	10	is	be	AUX
ejpam-5107	209	11	derived	derive	VERB
ejpam-5107	209	12	under	under	ADP
ejpam-5107	209	13	risk	risk	NOUN
ejpam-5107	209	14	-	-	PUNCT
ejpam-5107	209	15	neutral	neutral	ADJ
ejpam-5107	209	16	measure	measure	NOUN
ejpam-5107	209	17	using	use	VERB
ejpam-5107	209	18	replication	replication	NOUN
ejpam-5107	209	19	techniques	technique	NOUN
ejpam-5107	209	20	.	.	PUNCT
ejpam-5107	210	1	also	also	ADV
ejpam-5107	210	2	,	,	PUNCT
ejpam-5107	210	3	the	the	DET
ejpam-5107	210	4	fractional	fractional	ADJ
ejpam-5107	210	5	brownian	brownian	ADJ
ejpam-5107	210	6	motion	motion	NOUN
ejpam-5107	210	7	employs	employ	VERB
ejpam-5107	210	8	the	the	DET
ejpam-5107	210	9	flexible	flexible	ADJ
ejpam-5107	210	10	dependence	dependence	NOUN
ejpam-5107	210	11	of	of	ADP
ejpam-5107	210	12	the	the	DET
ejpam-5107	210	13	increments	increment	NOUN
ejpam-5107	210	14	of	of	ADP
ejpam-5107	210	15	the	the	DET
ejpam-5107	210	16	evolution	evolution	NOUN
ejpam-5107	210	17	of	of	ADP
ejpam-5107	210	18	the	the	DET
ejpam-5107	210	19	prices	price	NOUN
ejpam-5107	210	20	making	make	VERB
ejpam-5107	210	21	it	it	PRON
ejpam-5107	210	22	more	more	ADV
ejpam-5107	210	23	closer	close	ADJ
ejpam-5107	210	24	to	to	ADP
ejpam-5107	210	25	the	the	DET
ejpam-5107	210	26	real	real	ADJ
ejpam-5107	210	27	world	world	NOUN
ejpam-5107	210	28	scenario	scenario	NOUN
ejpam-5107	210	29	.	.	PUNCT
ejpam-5107	211	1	for	for	ADP
ejpam-5107	211	2	further	further	ADJ
ejpam-5107	211	3	studies	study	NOUN
ejpam-5107	211	4	,	,	PUNCT
ejpam-5107	211	5	a	a	DET
ejpam-5107	211	6	similar	similar	ADJ
ejpam-5107	211	7	formula	formula	NOUN
ejpam-5107	211	8	can	can	AUX
ejpam-5107	211	9	be	be	AUX
ejpam-5107	211	10	derived	derive	VERB
ejpam-5107	211	11	also	also	ADV
ejpam-5107	211	12	that	that	PRON
ejpam-5107	211	13	employs	employ	VERB
ejpam-5107	211	14	stochastic	stochastic	ADJ
ejpam-5107	211	15	volatilities	volatility	NOUN
ejpam-5107	211	16	for	for	ADP
ejpam-5107	211	17	both	both	PRON
ejpam-5107	211	18	asset	asset	NOUN
ejpam-5107	211	19	value	value	NOUN
ejpam-5107	211	20	and	and	CCONJ
ejpam-5107	211	21	interest	interest	NOUN
ejpam-5107	211	22	rate	rate	NOUN
ejpam-5107	211	23	.	.	PUNCT
ejpam-5107	212	1	moreover	moreover	ADV
ejpam-5107	212	2	,	,	PUNCT
ejpam-5107	212	3	this	this	DET
ejpam-5107	212	4	pricing	pricing	NOUN
ejpam-5107	212	5	can	can	AUX
ejpam-5107	212	6	be	be	AUX
ejpam-5107	212	7	extended	extend	VERB
ejpam-5107	212	8	further	far	ADV
ejpam-5107	212	9	by	by	ADP
ejpam-5107	212	10	considering	consider	VERB
ejpam-5107	212	11	geometric	geometric	ADJ
ejpam-5107	212	12	fractional	fractional	ADJ
ejpam-5107	212	13	brownian	brownian	ADJ
ejpam-5107	212	14	motion	motion	NOUN
ejpam-5107	212	15	.	.	PUNCT
ejpam-5107	213	1	references	reference	NOUN
ejpam-5107	213	2	[	[	X
ejpam-5107	213	3	1	1	NUM
ejpam-5107	213	4	]	]	X
ejpam-5107	213	5	f	f	PROPN
ejpam-5107	213	6	black	black	ADJ
ejpam-5107	213	7	and	and	CCONJ
ejpam-5107	213	8	m	m	PROPN
ejpam-5107	213	9	scholes	schole	NOUN
ejpam-5107	213	10	.	.	PUNCT
ejpam-5107	214	1	the	the	DET
ejpam-5107	214	2	pricing	pricing	NOUN
ejpam-5107	214	3	of	of	ADP
ejpam-5107	214	4	options	option	NOUN
ejpam-5107	214	5	and	and	CCONJ
ejpam-5107	214	6	corporate	corporate	ADJ
ejpam-5107	214	7	liabilities	liability	NOUN
ejpam-5107	214	8	.	.	PUNCT
ejpam-5107	215	1	journal	journal	NOUN
ejpam-5107	215	2	of	of	ADP
ejpam-5107	215	3	political	political	ADJ
ejpam-5107	215	4	economy	economy	NOUN
ejpam-5107	215	5	,	,	PUNCT
ejpam-5107	215	6	81:637–654	81:637–654	NUM
ejpam-5107	215	7	,	,	PUNCT
ejpam-5107	215	8	1973	1973	NUM
ejpam-5107	215	9	.	.	PUNCT
ejpam-5107	216	1	[	[	X
ejpam-5107	216	2	2	2	NUM
ejpam-5107	216	3	]	]	X
ejpam-5107	216	4	r	r	NOUN
ejpam-5107	216	5	merton	merton	NOUN
ejpam-5107	216	6	.	.	PUNCT
ejpam-5107	217	1	theory	theory	NOUN
ejpam-5107	217	2	of	of	ADP
ejpam-5107	217	3	rational	rational	ADJ
ejpam-5107	217	4	option	option	NOUN
ejpam-5107	217	5	pricing	pricing	NOUN
ejpam-5107	217	6	.	.	PUNCT
ejpam-5107	218	1	journal	journal	NOUN
ejpam-5107	218	2	of	of	ADP
ejpam-5107	218	3	economics	economic	NOUN
ejpam-5107	218	4	and	and	CCONJ
ejpam-5107	218	5	management	management	NOUN
ejpam-5107	218	6	science	science	NOUN
ejpam-5107	218	7	,	,	PUNCT
ejpam-5107	218	8	4:141–183	4:141–183	NUM
ejpam-5107	218	9	,	,	PUNCT
ejpam-5107	218	10	1973	1973	NUM
ejpam-5107	218	11	.	.	PUNCT
ejpam-5107	219	1	[	[	X
ejpam-5107	219	2	3	3	X
ejpam-5107	219	3	]	]	X
ejpam-5107	219	4	d	d	X
ejpam-5107	219	5	nualart	nualart	PROPN
ejpam-5107	219	6	.	.	PUNCT
ejpam-5107	219	7	fractional	fractional	ADJ
ejpam-5107	219	8	brownian	brownian	ADJ
ejpam-5107	219	9	motion	motion	NOUN
ejpam-5107	219	10	:	:	PUNCT
ejpam-5107	219	11	stochastic	stochastic	ADJ
ejpam-5107	219	12	calculus	calculus	NOUN
ejpam-5107	219	13	and	and	CCONJ
ejpam-5107	219	14	applications	application	NOUN
ejpam-5107	219	15	.	.	PUNCT
ejpam-5107	220	1	european	european	PROPN
ejpam-5107	220	2	mathematical	mathematical	PROPN
ejpam-5107	220	3	society	society	NOUN
ejpam-5107	220	4	,	,	PUNCT
ejpam-5107	220	5	3:141–162	3:141–162	NUM
ejpam-5107	220	6	,	,	PUNCT
ejpam-5107	220	7	2006	2006	NUM
ejpam-5107	220	8	.	.	PUNCT