








































D Y N A M I C  E C O N O M E T R I C  M O D E L S  
DOI: http://dx.doi.org/10.12775/DEM.2016.002  Vol. 16 (2016) 21−35 

Submitted October 20, 2016  ISSN (online) 2450-7067 

Accepted December 10, 2016 ISSN (print) 1234-3862 

Marcin Fałdziński, Magdalena Osińska
*
 

Volatility Estimators in Econometric Analysis of Risk 

Transfer on Capital Markets 

A b s t r a c t. The purpose of the research is to compare the performance of different volatili-

ty measures while used in testing for causality in risk between several emerging and mature 

capital markets. The following volatility estimators are considered: Parkinson, Garman-Klass, 

Rogers-Satchell, Garman-Klass-Yang-Zhang and Yang-Zhang and the AR-GARCH(1,1)-t 

model. Additionally, the extreme value theory is also applied. Several emerging capital mar-

kets are checked for being the source of the risk for both emerging and developed markets. 

The group of emerging markets includes the most intensively  growing economies in the 

world. The final results are such as the number of relationships between the markets is con-

siderably lower when the methods taken from the extreme value theory are used. 

K e y w o r d s: causality in risk, extreme value theory, growing emerging economies, risk 

transfer, volatility 

J E L Classification: G15; Q47. 

Introduction 

 The purpose of the research is to compare the performance of different 

volatility measures while used in testing for causality in risk between several 

emerging and mature capital markets. The problem considered in the report 

                                                 
* Correspondence to: Marcin Fałdziński, Nicolaus Copernicus University, Faculty of Eco-

nomic Sciences and Management, 13A Gagarina Street, 87-100 Toruń, Poland, e-mail: 

marf@umk.pl; Magdalena Osińska, Nicolaus Copernicus University, Faculty of Economic 

Sciences and Management, 13A Gagarina Street, 87-100 Toruń, e-mail: emo@umk.pl. 
 Financial support of the National Science Centre in Poland (UMO-

2015/17/B/HS4/01000) is gratefully acknowledged. 



Marcin Fałdziński, Magdalena Osińska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

22 

is rather complex from methodological perspective because it includes: 

a comparison of several estimators of volatility such as Parkinson (1980), 

Garman and Klass (1980), Rogers and Satchell (1991), Garman, Klass, Yang 

and Zhang (1991) and Yang and Zhang (2000) while Value at Risk is calcu-

lated, a comparison of the mentioned estimators when extreme value theory 

(McNeil and Frey, 2000; Fałdziński, 2014) was added and testing for causal-

ity in risk using Hong et al. (2009) procedure as well as Candelon, Joëts and 

Tokpavi (2013) procedure. The GARCH(1,1) model with t-Student error 

distribution is considered as the benchmark for all the comparisons. The 

wide empirical analysis is also provided in the paper. The two groups of 

markets represented by main indices are considered, i.e. emerging ones, such 

as: Brazil (BOVESPA), Russia (RTS, MICEX), China (SSE), India (BSE), 

Turkey (XU 100), Indonesia (JCI) and Mexico (IPC) and mature ones, such 

as: USA (S&P 500, Great Britain (FTSE 100), Germany (DAX), France 

(CAC 40), Japan (NIKKEI 225), Switzerland (SSMI), Hong Kong (HSI), 

South Korea (KOSPI) and Australia (AOR). The group of emerging markets 

includes the most likely intense growth economies that determine the state of 

the market, capital flows and global relationships. We try to establish the 

source and the effect of risk in most important capital markets in the era of 

globalization as well as to determine the most likely time periods for risk 

transferring. This paper develops and continues the research reported in our 

previous publications (Fałdziński et al., 2012, Osińska et al., 2012), in which 

GARCH-POT methodology has been applied. In this paper we not only 

compare different volatility measures but also use them for causality in risk 

testing and find them useful in certain cases. These findings are of methodo-

logical and practical nature. The paper can be included into spillover analy-

sis, which can be examined in many ways. One of the results of spillover 

effect can be contagion. Contagion is defined as a significant increase in 

market co-movement after a shock to one country. The paper by Forbes and 

Rigobon (2002) defines and illustrates this problem while a wide survey of 

methods of its analysis can be found in Burzała (2014). In our publication 

we demonstrate that thanks to the extreme value theory only big shocks on 

financial markets, that may or may not cause contagion, are considered. Risk 

transfer from one market to another, examined in this report, can be consid-

ered as an incentive for contagion but it is not a sufficient condition. 

1. The Methodology 

 In our previous research (Fałdziński et al., 2012, Osińska et al. 2012) we 

applied Granger causality in risk definition that was formulated by Hong 



Volatility Estimators in Econometric Analysis of Risk Transfer on Capital Markets 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

23 

(2001) and testing idea that was derived by Hong (2001) and further modi-

fied by Hong et al. (2009). It was based on spectral representation of time 

series. In this paper Candelon et al. (2013) test is applied. It differs from 

Hong’s test in two ways. Firstly, a multivariate linear regression is used to 

calculate the LR-type test and secondly, the breaks in Value at Risk (VaR) at 

different probability levels are considered. According to the definition of 

Granger causality in risk 
1 2{ , }t tY Y  is a bivariate not necessarily stationary 

stochastic time series and   1lt lt l t
A A I


  1,2l   is the VaR at level 

(0,1)  for 
ltY  predicted using the information set 

   ( 1) ( 2) 11
, ,l t l t ll t

I Y Y Y 
  available at time 1t  . 

ltA  satisfies

  , 1
|lt lt l t

P Y A I 


  . We define  lt lt ltV I Y A   1,2l   which denotes 

the VaR break indicator. The break indicator takes on the value of 1 when 

VaR is exceeded by loss and takes on the value of 0 otherwise. Let assume 

that
1{ ,..., }mA    is the set of m  different probability levels. Next, we 

consider a vector , , 1 ,( ) [ ( ),..., ( )]  1,2i t i t i t mZ A V V i    comprising of m  dif-

ferent variables at time t  respective to the assumed set of probability levels. 

In the case of the Granger non-causality the null hypothesis is: 

0 1, 1 1, 1, 1: ( ) | ( ) |t t t tH E Z A I E Z A I 
       ,   (1) 

where 1, 1,{ ( ), }t sI Z A s t    and 1, 2,{ ( ), ( ), }t s sI Z A Z A s t   with the alterna-

tive 

1 1, 1 1, 1, 1: ( ) | ( ) |t t t tH E Z A I E Z A I 
       . (2) 

The null hypothesis says that the process  2tY  does not Granger-cause the 

process  1tY  in risk at the set of different levels   with respect to 
1tI 
. 

Candelon et al. (2013) have shown that the test statistic can be formulated 

using multivariate linear regression of the form 

1, 0 1 2, 1 2, 1( ) ( ) ... ( )t t L t L tZ A Z A Z A          (3) 

where 
0  is the (m,1) dimensions vector of constants, , 1,...,s s L   are the 

( , )m m  dimensions matrices of parameters and 
1t  is ( ,1)m  dimensions re-

sidual process.  



Marcin Fałdziński, Magdalena Osińska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

24 

The null hypothesis corresponds to the situation when 
0 1: ... 0LH      

which is fulfilled for 1, 0 2( )t tZ A    . The multivariate test statistic is de-

fined as follows: 

     ' '

2 2 1 1( 1) log logLR T mL          
   

 (4) 

where T is the number of observations of time series m  is the number of 

different probability levels assumed, L  is the number of lags in the regres-

sion. It informs about the time delay since the beginning till the end of the 

risk transfer.  

The test statistic follows 
2  distribution with 2Lm  degrees of freedom. Due 

to the parameter uncertainty Dufour (2006) proposes a Monte Carlo method 

to obtain p-values. In order to check the hypothesis of spillovers in financial 

markets different volatility measures have been used. These measures de-

termine the empirical results and therefore are worth comparing. They do not 

affect the characteristics of the Candelon et al. test because it operates on 

breaks of VaR which can be defined at different levels. To estimate Value at 

Risk the following methods have been applied: 

1. Volatility estimators such as:  

a) Parkinson (1980) (P) 
2

1

1
ln

4ln(2)

N
i

P

i i

h

l




  
    

  
 ,  

b) Garman and Klass (1980) (GK) 

2 2

1

1
ln (2ln(2) 1) ln

2

N
i i

GK

i i i

h c

l o




      
           

      
 ,  

c) Rogers and Satchell (1991) (RS) 

1

ln ln ln ln
N

i i i i
RS

i i i i i

h h l l

c o c o




       
        

       
 ,  

d) Garman, Klass, Yang and Zhang (1991) (GKYZ) 

2 2 2

1 1

1
ln ln (2ln(2)) ln

2

N
i i i

GKYZ

i i i i

o h c

c l o


 

          
                 

          
  

e) Yang and Zhang (2000) (YZ) 

2 2 2

   (1 )YZ overnight volatility open to close RSk k        



Volatility Estimators in Econometric Analysis of Risk Transfer on Capital Markets 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

25 

0,34

1
1,34

1

k
N

N







, 

2

2

   

1

1
ln ln

1

N
i i

opent to close volatility

i i i

c c

N o o




    
     

      
 , 

2

2

 

1 1 1

1
ln ln

1

N
i i

overnight volatility

i i i

o o

N c c


  

    
     

      
 , 

where N  is the number of days taken into estimation, 
ih  is the highest 

price, 
il  is the lowest price, 

io  is the open price and 
ic  is the close 

price at day i . 

2. Conditional volatility models (AR(p)-GARCH(1,1) and AR(p)-

TARCH(1,1) both with Student error distribution (Zakoian, 1994)  

3. Conditional volatility models with the extreme value theory (AR(p)-

GARCH(1,1) with Student error distribution and Peaks over Threshold 

(POT) approach (McNeil and Frey, 2000; Fałdziński, 2014). 

4. Volatility estimators described in 1 with Peaks over Threshold (POT) 

approach. 

It is worth mentioning that using the extreme value theory represented by 

Peaks over Threshold (POT) enables identifying shocks (extreme changes) 

in some financial markets that affect other markets. Thus finding the break in 

VaR when POT approach is applied is a strong argument for the spillover 

effect.  

 The Peaks over Threshold method was described in Fałdziński (2014). 

To explain it briefly let us assume that a given sequence of i.i.d. observations 

1, , nX X  comes from unknown distribution function F , where we are in-

terested in excesses over a high threshold value u . Conditional excess distri-

bution function (cedf) 
uF  is defined as  ( ) | ,uF y P X u y X u     

0 Fy x u   , where X  is a random variable, u  is a given threshold, and 

y x u   is the excess (McNeil and Frey, 2000). The distribution 
uF  can be 

written as: 

( ) ( ) ( ) ( )
( )

1 ( ) 1 ( )
u

F u y F u F x F u
F y

F u F u

  
 

 
 (5) 

The realizations of the random variable X  lie between 0 and u , therefore 

the estimation of F in this interval generally poses no problems. According 

to the Pickands-Balkema-de Haan   (Pickands (1975), Balkema, de Haan 

(1974)) theorem, for x u , we can use the tail estimate 



Marcin Fałdziński, Magdalena Osińska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

26 

  , ,
ˆ ( ) 1 ( ) ( ) ( )n nF x F u G x F u     , where  , , ( )G x    is the generalized 

Pareto distribution (GDP), to approximate the distribution function ( )F x . 

It can be shown that ˆ ( )F x  is also generalized Pareto distribution, with the 

same shape parameter  , but with scale and location parameters, corre-

spondingly equal:  1 ( )nF u


    and   1 ( ) 1 /nF u


   


    . 

Thus, the POT estimator of px  is obtained by inverting the formula for ˆ ( )F x  

Then substituting unknown parameters of the GPD by estimates ˆ ˆ( , )  , we 

get: 

ˆ

1

ˆ ˆ, ,

ˆ( ) 1ˆˆ ( ) 1
ˆ1 ( ) 1 ( )

n
p u

n n

p F u p
x F p G u

F u F u



 







 
     
        
      

. (6) 

If 
uN  is the number of exceedances of the threshold u  and n  is the total 

number of realizations that we have from the distribution F , Value-at-Risk 

in the Peaks over Threshold method equals: 

ˆ

ˆ
( ) 1

ˆ
u

n
VaR u

N




 



  
    
   

, (7) 

where   is a tolerance level.  

2. Characteristics of the Data 

 According to World Economic Outlook released in 20161 the potential 

for economic growth in China is projected to decrease from 7.3 in 2014 to 

6.0 in 2017 although it will still remain a very important country. The most 

prospective growth is projected in India: from 7.3 in 2014 to 7.5 in 2017 and 

in Mexico: from 2.3 in 2014 to 2.9 in 2017. Other countries like Russia and 

Brazil are expected to lose their growth rate and reach negative values. As 

concerns Turkey, its growth rate in 2015 was quite high. It amounted to 4% 

with decreasing perspective. There are also other very fast developing 

emerging economies like Kenya or Nigeria but we excluded them from the 

study because of relative smaller liquidity in financial markets. Another very 

fast developing economy is Indonesia, which yearly growth rate in 2015 was 

5.5%. Among these countries there is a competition to be not only the best 

                                                 
1 http://www.imf.org/external/pubs/ft/weo/2016/update/01/pdf/0116.pdf 

http://www.imf.org/external/pubs/ft/weo/2016/update/01/pdf/0116.pdf


Volatility Estimators in Econometric Analysis of Risk Transfer on Capital Markets 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

27 

emerging economy in the world but also a very important investment mar-

ket. In sequent years one may observe and predict development of new im-

portant economic areas. In Fig. 1 the annual growth rate of mentioned econ-

omies in 2006–2015 has been shown.  

 
 Figure 1. Annual growth rate in emerging economies over 2006–2015 [in %]

2
 

The dynamics of Chinese economy is still dominating although it started to 

decline after 2012. The opposite tendency can be noticed for India. Indone-

sia’s growth seems to be stable over the decade. Mexico, Turkey, Brazil and 

Russia suffered hard from the recession in 2009, but Mexico seems to be the 

most promising for the future. The data suggest that so called “BRIC group” 

that was considered a new economic body at the beginning of XXI century is 

no longer the case and other developing countries try to move from peripher-

ies to the center.  

 On the opposite side – developed financial markets are represented by 

traditional markets such as the USA, the Great Britain, Germany, France, 

Switzerland and Australia that was completed by relatively new but mature 

markets from Far East Asia such as Hong Kong and South Korea. In the 

paper we took into account the linkages between stock markets from differ-

ent continents so North and Latin Americas, Asia, Australia and Europe are 

                                                 
 2 Source: based on International Monetary Fund data. 

-10 

-5 

0 

5 

10 

15 

20 

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 

China India Indonesia Turkey 

Russia Mexico Brazil 



Marcin Fałdziński, Magdalena Osińska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

28 

represented. Such a selection does not cover all possible linkages but allows 

answering the question of direction of capital transfers in both periods: the 

bullish and the bearish markets. Big (and often negative) shocks in the finan-

cial market are usually perceived negatively by all groups of investors, mar-

ket makers and supervisors. They may be due to: huge market uncertainty, 

policy changes, unpredicted information, speculative attacks, and transfers 

from other markets. Sometime many causes may act simultaneously. Some 

of them may cause extreme changes in values of losses (and/or profits). 

In general the process of globalization caused that the financial markets 

seem to act in the same way; they are linked. It is interesting that little atten-

tion is paid to the big and positive changes in financial markets.  

 However in the literature one can find several individual cases of little 

linkages between different markets. For example China during Asian crisis 

1997–1998 was an example of completely separated market that was ana-

lyzed by Lardy (1998). On the other hand, when markets are related it can be 

expected to transfer from one market to another like in the period 2007–2009 

between USA and Europe. Risk can be generated locally or take the specific 

form like it was in 1997 between Japan and USA (see: Peek and Rosengren, 

1997).  

 To answer the question of risk transfer between emerging and mature 

markets we used daily data from the period 03.01.2010–02.01.2015 (T=1260 

observations). The log returns has been used for calculations in the form: 

 1100 ln( ) ln( )t t tr P P  , while testing for Granger causality in risk we have 

used different lags 5,10,15,25L   and we obtained p-values using Monte 

Carlo simulations (Dufour, 2006), having assuming 1000 repetitions. In fig-

ure 2 the comparison of VaR breaks’ computed with different volatility es-

timators basing on DAX returns is shown. One can notice that the highest 

values are indicated by Garman, Klass, Yang and Zhang estimator. In figure 

3 the results of the latter are compared with the AR(1)-GARCH(1,1) with 

POT model. In the cases of shocks the AR(1)-GARCH(1,1) with POT seem 

to perform better. 

 

 

 

 

 

 

 

 



Volatility Estimators in Econometric Analysis of Risk Transfer on Capital Markets 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

29 

 
 Figure 2. VaRs computed with different volatility estimators basing on DAX re-

turns  

 
 Figure 3. VaRs computed with GARCH-POT method and Garman-Klass-Yang-

Zhang volatility estimator basing on DAX returns 

-6 

-4 

-2 

0 

2 

4 

6 

10
-1

5-
20

10
 

11
-1

5-
20

10
 

12
-1

5-
20

10
 

1-
15

-2
01

1 

2-
15

-2
01

1 

3-
15

-2
01

1 

4-
15

-2
01

1 

5-
15

-2
01

1 

6-
15

-2
01

1 

7-
15

-2
01

1 

8-
15

-2
01

1 

9-
15

-2
01

1 

10
-1

5-
20

11
 

11
-1

5-
20

11
 

12
-1

5-
20

11
 

1-
15

-2
01

2 

2-
15

-2
01

2 

3-
15

-2
01

2 

4-
15

-2
01

2 

5-
15

-2
01

2 

6-
15

-2
01

2 

7-
15

-2
01

2 

8-
15

-2
01

2 

9-
15

-2
01

2 

10
-1

5-
20

12
 

11
-1

5-
20

12
 

12
-1

5-
20

12
 

DAX VaR (Parkinson) 
VaR (Garman-Klass) VaR (Rogers-Sachell) 
VaR (Garman-Klass-Yang-Zhang) VaR (Yang-Zhang) 

-8 

-6 

-4 

-2 

0 

2 

4 

6 

8 

1-
4-

20
10

 

3-
4-

20
10

 

5-
4-

20
10

 

7-
4-

20
10

 

9-
4-

20
10

 

11
-4

-2
01

0 

1-
4-

20
11

 

3-
4-

20
11

 

5-
4-

20
11

 

7-
4-

20
11

 

9-
4-

20
11

 

11
-4

-2
01

1 

1-
4-

20
12

 

3-
4-

20
12

 

5-
4-

20
12

 

7-
4-

20
12

 

9-
4-

20
12

 

11
-4

-2
01

2 

DAX VaR (GARCH-POT) VaR (Garman-Klass-Yang-Zhang) 



Marcin Fałdziński, Magdalena Osińska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

30 

A precise comparison of different estimators of volatility was presented in 

table 1. We compared the analyzed volatility estimators with AR-GARCH, 

AR-GARCH-POT and Garman-Klass-Yang-Zhang with POT using seven 

different loss functions (described below the table). The preferred model is 

AR-GARCH-POT which was indicated in 4 cases on 7. Twice the Garman-

Klass-Yang-Zhang with POT was indicated and once the Rogers-Satchell 

estimator. 

Table 1. Mean value of the loss functions for VaR(0.95)  

Method QPS I QPS II QPS III RLF FLF LF OLF 

AR-GARCH 0.0988 5.0516 0.0360 0.0778 0.1669 0.1168 7.4261 
AR-GARCH-

POT 
0.0940 4.8277 0.0337 0.0730 0.1647 0.1094 7.7466 

Parkinson 0.1619 4.6296 0.0698 0.1028 0.1719 0.1642 5.7280 
Rogers-Satchell 0.1770 6.0812 0.1020 0.1218 0.1877 0.1916 5.4615 
Garman-Klass 0.1738 5.5389 0.0893 0.1159 0.1822 0.1834 5.4851 
Garman-Klass 
Yang-Zhang 

0.1323 4.5242 0.0499 0.0852 0.1638 0.1341 6.5845 

Yang-Zhang 0.1979 6.7888 0.1331 0.1386 0.1991 0.2180 5.0100 
Garman-Klass-

Yang-Zhang 
POT 

0.1303 4.3008 0.0500 0.0812 0.1615 0.1283 6.8112 

 Note: QPS I means Quadratic Probability Score function with binary loss function (Lopez, 1998), QPS II 

means Quadratic Probability Score function with size-adjusted loss function (Lopez, 1998), QPS III 
means Quadratic Probability Score function with size loss function (Blanco and Ihle, 1998), RLF means 

Regulatory Loss Function (Sarma et al., 2003), FLF means Firm's Loss Function (Sarma et al., 2003) with 

opportunity cost of capital equals 0.05, LF means Loss Function (Angelidis and Degiannakis, 2006) and 
OLF means Overestimation Loss Function (Fałdziński, 2011). The lowest (best) values of measures are in 

bold.  

3. Causality in Risk between Emerging and Developed Markets 

 In this section we show the results of Hong et al. (2009) and Candelon et 

al. (2013) tests for Granger causality in risk when emerging markets are 

indicated to be a source of risk transfer. Having in mind the results shown in 

table 1 the following methods of volatility analysis were used: AR(p)-

GARCH(1,1)-POT with t-distribution and Garman-Klass-Yang-Zhang vola-

tility estimator.  The results are presented in tables 2–5.  
  



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31 

Table 2. Granger causality in risk for long position where AR-GARCH-POT with  

t-distribution was applied (5 up to 25 lags, Hong et al. test) 

BOVESP
A 

→ 

AOR, BSE, CAC40, DAX, HSI, JCI, KOSPI, MICEX, NIKKEI225, RTS, SSE, 
SSMI, XU100 

BSE AOR, JCI, KOSPI, MICEX, NASDAQ, SP500 

IPC AOR, DAX, HSI, KOSPI, MICEX, NIKKEI225, RTS, S&P 500 

JCI KOSPI 

MICEX AOR, BSE, HSI, KOSPI, NASDAQ, NIKKEI225, XU100 

RTS AOR, BSE, HSI, KOSPI, NASDAQ, NIKKEI225 

SSE FTSE100, KOSPI, NASDAQ 

XU100 HSI, KOSPI 

Note: “→” shows direction of causality.  

Table 3. Granger causality in risk for long position where Garman-Klass-Yang-

Zhang volatility estimator was applied (5 up to 25 lags, Hong et al. test) 

BOVESPA 

 
 

→ 
 
 
 
 

BSE, FTSE100, JCI, SSMI 

BSE 
AOR, BOVESPA, CAC40, DAX, FTSE100, HSI, IPC, KOSPI, NASDAQ, S&P 500, 

SSMI 

IPC AOR, BOVESPA, HSI 

JCI 
AOR, BOVESPA, BSE, CAC40, DAX, FTSE100, HSI, IPC, KOSPI, MICEX, 

NASDAQ, RTS, S&P 500, SSMI, XU100 

MICEX AOR, BOVESPA, BSE, DAX, NASDAQ, S&P 500 

RTS AOR, BOVESPA, BSE, DAX, FTSE100, NASDAQ, S&P 500 

SSE BOVESPA, DAX, FTSE100, MICEX, NASDAQ, RTS, S&P 500 

XU100 
AOR, BOVESPA, BSE, CAC40, DAX, FTSE 100, JCI, KOSPI, NASDAQ, RTS, 

S&P 500, SSMI 

 Note: “→” shows direction of causality. 

Table 4. Granger causality in risk for long position where AR-GARCH-POT with  

t-distribution was applied (5 up to 25 lags, Candelon et al. test) 

BOVESPA 

→ 

AOR, BSE, DAX, HSI, IPC, KOSPI, NIKKEI 225 

BSE IPC, KOSPI 

IPC BSE, CAC 40, FTSE 100, IPC, KOSPI, MICEX, NIKKEI 225, RTS, SSE 

JCI FTSE 100, KOSPI 

MICEX CAC40, FTSE 100, JCI, MICEX, SSE 

RTS BSE, CAC40, FTSE 100, IPC, JCI, MICEX, SSE 

SSE CAC40, JCI, MICEX 

XU 100 CAC40, FTSE 100, JCI, MICEX 

Note: “→” shows direction of causality. 

  



Marcin Fałdziński, Magdalena Osińska 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

32 

Table 5. Granger causality in risk for long position where Garman-Klass-Yang-

Zhang volatility estimator was applied (5 up to 25 lags, Candelon et al. 

test) 

BOVESPA 

 
 

→ 
 
 
 
 

AOR, BSE, CAC40, DAX, FTSE100, HSI, IPC, JCI, KOSPI, NASDAQ, 
NIKKEI225, SSE, SSMI 

BSE AOR, CAC40, DAX, HSI, IPC, KOSPI NASDAQ, NIKKEI225, SSE 

IPC 
AOR, BSE, CAC40, DAX, HSI, JCI, KOSPI, NASDAQ, NIKKEI225, SSE, S&P 

500, SSMI 

JCI BOVESPA, BSE, CAC40, DAX, IPC, KOSPI, NASDAQ, NIKKEI225, SSE 

MICEX BSE, CAC40, DAX, HSI, IPC, KOSPI, NASDAQ, NIKKEI225, S&P 500, SSMI 

RTS 
BOVESPA, AOR, BSE, CAC40, DAX, FTSE100, HSI, IPC, KOSPI, NASDAQ, 

NIKKEI225, S&P 500, SSMI 

SSE BOVESPA, BSE, CAC40, DAX, HSI, IPC, KOSPI, NASDAQ, NIKKEI225 

XU100 BSE, CAC40, DAX, HSI, IPC, KOSPI, NASDAQ, NIKKEI225, S&P 500, SSMI 

 Note: “→” shows direction of causality. 

In the tables 2–5 the results of testing for Granger causality in risk for long 

positions (losses) are presented. Computing results for short positions (prof-

its) we can observe lower number of relationships between the markets. 

It may suggest that taking into account profits the markets are more inde-

pendent (they do not share profits) while in the case of losses otherwise situ-

ation takes place. The remained results are available on request. In general, 

we can say that the Garman-Klass-Yang-Zhang volatility estimator indicates 

the Granger causality in risk more frequently than the AR-GARCH-POT 

method. This was intuitively expected, because the latter method takes into 

account the extreme observations while the volatility estimators includes all 

observations corrected by the high, low minimum and maximum values. The 

results show that there is Granger causality in risk between emerging capital 

markets and highly developed ones. Some capital markets absorb risk more 

often than others. We can delineate the markets which absorb the risk (risk-

takers) most frequently when the risk transfer is from emerging markets: 

AOR, CAC 40, FTSE 100, HSI, NIKKEI 225 and KOSPI in the case of the 

GARCH-POT method. In the case of the volatility estimators the group of 

the risk-takers is: AOR, BOVESPA, BSE, CAC 40, DAX, NIKKEI 225, 

S&P 500 and NASDAQ. The latter group is larger which is not surprising 

due the fact that volatility estimators fit better to the ‘average values’ of the 

time series. The overlapping of two methods of estimating Value-at-Risk and 

testing for Granger causality in risk is rather easily visible. The difference 

between Hong et all test and Candelon et al. test is such that in case of AR-

GARCH-POT model the results are the same in 13 cases only. The causal 

impact of MICEX, RTS, SSE and XU 100 on other markets was found to be 



Volatility Estimators in Econometric Analysis of Risk Transfer on Capital Markets 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 21–35 

33 

quite different while the impact of BOVESPA, BSE IPC and JPC can be 

considered as similar.  

Conclusions 

 In the paper we extended our previous investigations using quite sophis-

ticated research methods and we concentrated on huge magnitude of changes 

(extreme values). Our findings should be considered when systemic risk in 

the global economy is analyzed. They are linked with the problem of spillo-

ver  in the sense that risk transfer from one market to another can be consid-

ered as an incentive for extending negative trends (contagion) but it is not 

a sufficient condition.  

 In the paper we analyze the linkages between capital markets located in 

both emerging and developed economies. The difference between emerging 

and mature markets lays in different types of institutions like financial su-

pervision, possibility of quoting the instruments from abroad, the number 

and type of listed instruments and, what is probably most important, in mar-

ket liquidity. The question whether less liquid market can ‘produce’ more 

risk due to the lack of many alternatives within the market and more loosely 

rules is very important in the era of globalization. The answer can have 

many practical implications including financial regulations.  

 In our research it was indicated that basing on volatility estimators it is 

possible to find more “causal” relationships than basing on AR-GARCH-

POT methods. It is due to the fact that volatility estimators are better fitted to 

the average volatility values than the methods based on the extreme value 

theory. We can observe risk transfer from emerging markets to the highly 

developed ones, so that the research helped to find the explanation of the 

problem put in the introduction. The markets which absorb risk transfers 

most frequently are: S&P500, CAC40, NIKKEI225, NASDAQ and 

FTSE100. The empirical results of Hong et al test and Candelon et al test are 

slightly different that results from different tolerance levels allowing in both 

testing procedures. 

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Estymatory zmienności w ekonometrycznej analizie transferu ryzyka 
na rynkach kapitałowych 

Z a r y s  t r e ś c i. Celem badania jest porównanie wykorzystania różnych estymatorów 

zmienności, zastosowanych do testowania przyczynowości w ryzyku, między kilkoma wy-

branymi rynkami wschodzącymi i rozwiniętymi. W pracy uwzględniono następujące estyma-

tory zmienności: Parkinsona, Garmana i Klassa, Rogersa i Satchella, Garmana, Klassa, Yanga 

i Zhanga, Yanga i Zhanga oraz model GARCH(1,1)-t. Dodatkowo wykorzystano narzędzia 

teorii wartości ekstremalnych. Kilka wybranych rynków wschodzących zostało przebadanych, 

czy są źródłem ryzyka dla rynków rozwijających i rozwiniętych. Wyniki pokazują, że przy-

czynowość w ryzyku występuje rzadziej w przypadku modeli z wykorzystaniem teorii warto-

ści ekstremalnych. 

S ł o w a  k l u c z o w e: przyczynowość w ryzyku, teoria wartości ekstremalnych, rozwój 

rynków wschodzących, transfer ryzyka, zmienność. 




