




































© 2017 Nicolaus Copernicus University. All rights reserved.  

http://www.dem.umk.pl/dem 

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.2017.008  Vol. 17 (2017) 129−145 

Submitted November 28, 2017  ISSN (online) 2450-7067 

Accepted December 28, 2017 ISSN (print) 1234-3862 

Aneta Włodarczyk
*
 

Regime-dependent Assessment of the European  

Union Aviation Allowances Price Risk 

A b s t r a c t. In this article the European Union Aviation Allowances (EUAA) price risk, 

associated with the activity of aircraft operators within the European Economic Area (EEA), 

has been evaluated across the low and high volatility periods occurring on the carbon permits 

market. It is found that Markov-switching heteroscedasticity models distinguish well between 

two volatility regimes, as well as three volatility regimes on the EUAA futures market, and 

that the assessments of EUAA price risk are clearly different in the regimes. These findings 

may be explained by the European Union Emission Trading Scheme (EU ETS) design and the 

changes in both the EU climate policy rules and global regulations in the scope of CO2 emis-

sions by international aviation. 

K e y w o r d s: European Union Aviation Allowances; EU Emission Trading Scheme; Mar-

kov-switching model; risk. 

J E L Classification: C40; G32; L93; Q53. 

Introduction  

Worrying statistics concerning the over 3% share of CO2 emission from 

international aviation bunkers in the total carbon dioxide emission in the EU 

countries in 2004 and the forecasts concerning an increase in greenhouse 

gases emission in international aviation by about 70% in 2020 compared 

with 2005 led the international community to take interest in the issues of 

                                                 
* Correspondence to: Aneta Włodarczyk, Czestochowa University of Technology, Faculty 

of Management, 19B Armii Krajowej Street, 42-200 Częstochowa, Poland, e-mail: 

aneta.w@interia.pl. 
 This work was financed by Czestochowa University of Technology.  



Aneta Włodarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

130 

limiting the negative impact of air transport on the natural environment. In 

2008 the European Commission adopted the directive on including civil 

aviation into the EU Emission Trading Scheme (EU ETS), which refers to 

the EU’s long-term policy aimed at limiting the greenhouse effect, im-

provement in the environment quality, increased energy efficiency and 

growth of renewable energy sources share in the energy consumption struc-

ture (Directive 2008/101/WE). Aircraft operators that in the given year carry 

out aviation operations covered by the Attachment 1 to the Directive 

2003/87/WE in the territory of European Economic Area have been included 

into the EU ETS.  

The period of civil aviation participation in the EU ETS has been divided 

into the two settlement periods: the first one of them comprising only the 

year 2012, the aim of which was to adjust the aircraft operators functioning 

to the functioning scheme of the remaining sectors in the allowances trading 

system, and the second one (common for all the sectors covered by the EU 

ETS) for the years 2013-2020. The EU ETS system operates according to the 

“cap and trade” principle. A permissible limit of CO2 emissions in the given 

period (“cap”) has been determined for all aircraft operators included into 

the system, which is gradually decreased over time. In order to asses this 

limit, data on average annual CO2 emission in aviation was used, which cov-

ered the reference period of 2004-2006 and came from the European Organi-

sation for the Safety of Air Navigation (Eurocontrol). In the first settlement 

period the total amount of European Union Aviation Allowances (EUAAs) 

to be allocated for aircraft operators was 97% of the average calculated from 

historical aviation emissions in the reference period. In the second settlement 

period the joint annual number of allowances granted to the aviation sector 

decreased to 95% of the same average emission. Within the established limit, 

in the first settlement period 85% of allowances allocated to cover the annual 

CO2 emission of civil aviation will be granted to aircraft operators free of 

charge, and 15% of aviation allowances will be sold in the auctioning sys-

tem. In the period from 1
st
 January 2013 to 31

st
 December 2020 in turn, 82% 

of aviation allowances will be allocated free of charge, 15% will constitute 

allowances purchased at auctions, and 3% will be moved to a special reserve 

for new aircraft operators. Chin and Zhang (2013) presented mathematical 

formulas and described in detail the method of emission allowances alloca-

tion consistent with the Directive 2008/101/EC and proposed an alternative 

method of allowances allocation (the Augmented EU ETS), which considers 

energy efficiency of aircraft operators (Chin and Zhang, 2013). The Euro-

pean Commission Regulation No 601/2012 imposes on aircraft operators the 

following duties, which result from their participation in the EU ETS sys-



Regime-dependent Assessment of the EUAA Price Risk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

131 

tem: the necessity to monitor carbon dioxide emission in each year, submit-

ting a verified report on historical carbon dioxide emission to the proper 

body and its settlement through redemption of a proper amount of emission 

allowances in the EU Redemption Registry. Aircraft operators may settle 

their own CO2 emissions by means of emission allowances assigned to sta-

tionary installations (European Union Allowances - EUAs) or aviation al-

lowances (EUAAs). Moreover, aircraft operators should possess a plan to 

monitor annual emissions, approved by the appointed in the given member 

country competent body. There are sanctions foreseen that can be applied to 

operators that fail to settle their CO2 emissions in the given year, including 

a prohibition on flights to the European Union. Aircraft operators also has 

a possibility to apply for allocation of free CO2 emission allowances for the 

years 2013–2020 from a special reserve, provided that they complied with 

the obligation to monitor tonne-kilometres throughout 2014. Such a system 

of CO2 emission allowances allocation was supposed to be an incentive to 

invest in environmentally-friendly technologies and modernise the air fleet 

against an alternative to incur additional costs of purchasing allowances. The 

emission allowances trading system was considered by the European Com-

mission to be the most effective and least expensive instrument to limit the 

emission of greenhouse gases in aviation in the territory of the EU member 

states, yet, it encountered criticism. This concerned additional costs gener-

ated by the EU ETS for the aircraft operators participating in it, which was 

connected with, among others, purchases of missing EUAAs, new environ-

mentally-friendly investments, administrative costs. The growing fears of 

aircraft operators included into the EU ETS concerned the loss of their com-

petitive position due to their lower market share, change of entry barriers or 

lower profits margin (Meleo et al., 2016). The most severe objection con-

cerned imposing additional charges on aircraft operators from outside the 

EU. The charges resulted from participation in the EU ETS and were im-

posed without any prior agreements, which was treated as a breach of the 

Chicago Convention on International Civil Aviation (1944). In response to 

this the European Commission introduced derogating mechanisms: „stop the 

clock” derogation (Decision 2013/337/EU), the exclusions mechanism in the 

scope of aviation operations covered by the EU ETS system (Regulation 

2014/421). The abovementioned legislative regulations in the scope of obli-

gations concerning reporting the emission from aviation operations within 

the EU ETS in the years 2013–2014, postponing the deadline to settle these 

emissions for 2013 and 2014, delayed the launch of aviation allowances 



Aneta Włodarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

132 

trading in the auctioning system.
1
 In addition, they influenced the volatility 

of EUAAs prices and the volume of EUAAs derivatives trading, as well as 

the interest of aircraft operators in the use of this type instruments to manage 

the CO2 emission risk. 

The inclusion of international aviation into the EU Emission Trading 

Scheme causes that the management of the EUAA price risk is becoming 

increasingly important for companies covered by the EU ETS. The increase 

in the price allowances volatility in the secondary market and the reduction 

of free allowances, which are granted to companies, cause the increase in 

their exposure to price risk. The aim of this article is to evaluate the EUAA 

price risk connected with the activity of aircraft operators within the Europe-

an Economic Area, distinguishing between low and high volatility periods 

occurring on the carbon permits market. Volatility and downside risk 

measures are used to assess this type of risk across different regimes of the 

EUAAs' future prices, which are identified by means of Markov-switching 

models. 

1. Research Methodology  

The CO2 emission allowances price risk from the aircraft operators point 

of view may result in a danger of not achieving by them the expected returns 

due to a sale of excessive or purchase of insufficient aviation allowances on 

the secondary market (neutral risk concept). The aviation allowances price 

risk may be perceived as a danger of sustaining a loss, which can have sig-

nificant impact on financial results of the aircraft operator (negative risk 

concept). Volatility measures are the tools which are most frequently used to 

measure risk according to the neutral risk concept, while risk measurement 

in the negative meaning are conducted according to the downside risk meas-

ure (Jajuga, 2007). The most frequently determined by practitioners volatil-

ity measures include: standard deviation, interquartile range and absolute 

median deviation. The downside risk measure, which exposes only unfa-

vourable situations for the aircraft operator when the real returns on sale or 

purchase of aviation allowances was below the average, is semi-standard 

deviation. 

The first volatility measures, which have been estimated on the basis of 

settlement prices of EUAAs futures contracts, is standard deviation (Kuziak, 

2011): 

                                                 
1
 Aviation auctions have been conducted since 1st January 2015. 



Regime-dependent Assessment of the EUAA Price Risk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

133 








T

t

t RR
T 2

2)(
1

1
 , (1) 

where: %100*)/ln( 1 ttt PPR – return on sale/purchase of aviation allow-

ance on the secondary market in t period; Pt – settlement price of EUAA in t 

period; Pt–1 – settlement price of EUAA in the period t–1(t = 2,.., T);   – 

standard deviation; tR  – expected value of EUAA returns. 

Coefficient of variation is also used in order to assess how much risk accom-

panies one unit of profit from the investment in the EUAA futures market. 

The lower the value of this measure is, the higher the expected profit on 

sale/purchase of aviation allowances is at the defined risk level or lower risk 

at the defined level of profit:   

%100
R

Vs


  (2) 

where sV is coefficient of variation. 

Asymmetric risk measure is semi-standard deviation, which can be defined 

in the following way (Booth et al., 2005):  





T

t

td
T

SV
2

2

1

1
, (3) 

for 










RRR

R
d

t

t

t

t

Rfor             

Rfor                     0
, (4) 

where SV – semi-standard deviation. 

This measure reflects an unfavourable for aircraft operators situation, where 

the returns on sale/purchase of EUAAs on the secondary market were below 

their expectations. 

Robust volatility estimators in turn are characterized by the fact that pre-

sent in the sample outliers have little impact on the estimation results 

(Trzpiot, 2010). This is a very important property for EUAAs return series, 

where single outliers occur, which confirms extremely high change of avia-

tion allowances price form period to period. The most frequently applied 

robust volatility estimator is absolute median deviation, which can be de-

scribed by means of the following relation (Trzpiot, 2010): 



Aneta Włodarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

134 

}}{{)( i
i

t
t

t RmedianRmedianRMAD  , (5) 

where MAD(Rt) – absolute median deviation of EUAA returns.  

One of the simplest robust volatility estimators is interquartile range (IQR), 

which ignores up to 25% of lowest and largest returns (Trzpiot, 2010): 

)()( 13 tt RQRQIQR  , (6) 

where )(1 tRQ  and )(3 tRQ  – respectively the first and third quartile of 

EUAA returns empirical distribution.  

It is worth stressing that risk has been most often measured under the as-

sumption of the worst- scenario in the market, what has been derived from 

the negative concept of risk and has contributed to the popularization of the 

downside risk measures. However, this approach may not reflect the change 

of uncertainty sets with respect to different market environments (e.g. calm 

and turbulent periods). Following Liu and Chen (2014), in this article 

Markov regime switching models are used to describe the time-varying un-

certainty set of the first and second order moments, which are related to two 

main characteristics of investments in the EUAA futures, namely expected 

profits and risk. 

As a result, Markov-switching dynamic regression models with N-

regimes (MS(N)-DR(p)) have been used to describe the different dynamism 

of the EUAAs returns series, generated by changing risk factors on the mar-

ket of CO2 emission allowances (Hamilton, 1990; Doornik, 2013):  

)),(,0(~

   ,)(...)()()(

2
t

22110

t

tpttptttttt

sN

RsRsRssR



  
  (7) 

where: i(st) – the parameter describing the influence of delayed by i-periods 

EUAA returns per the current returns (i=1,2,…,p), t  – the error term, 

)(2
ts - residual variance dependent on the valid at the given moment re-

gime, st – non-observable variable modelled as homogeneous Markov chain 

of N regimes and the transition probabilities matrix  
}1,...,1,0{,| 


NjijipP . 

The elements of stochastic matrix P, defining the process probability transi-

tion from j regime at t–1 moment to i regime at the t moment, satisfy the 

Markov property (Hamilton, 1990): 

)|(

),...,,|(

1

00221|

jsisP

isisjsisPp

tt

ttttji








, (8) 



Regime-dependent Assessment of the EUAA Price Risk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

135 

means that probability of moving to the next regime depends only on the 

current regime of a system and not on the previous regimes. 
Therefore, the transition probability matrix can be defined in the following 

way (Doornik, 2013): 












































111

1

1

0

110

1|11|10|11

1|11|10|11

1|01|00|01













NNNNt

Nt

Nt

ttt

pppNs

ppps

ppps

Nsss

P , (9) 

at the conditions that guarantee the stochastic structure of this matrix: 







1

0

j|i| .,for     0p           ,1
N

i

ji N-10,1,...i,j p  (10) 

Stawicki (2004) describing this class of econometric models introduced the 

concept of a dual stochastic process to emphasize the existence of an unob-

servable variable that has controlled the changes of regimes in addition to 

the observable economic variable being the subject of modelling (Stawicki, 

2004). 

Moreover, on the basis of estimated transition probabilities (elements of 

stochastic matrix P), the further expected duration of the system in a given 

regime can be determined (Hamitlon, 1990): 

)(    
1

1

|

 N-1 0, 1,...,i 
p

D
ii

i 


 , (11) 

where: Di – average duration of EUAAs returns in i-th regime.   

It is also worth stressing that the model (7) considers the heteroscedasticity 

characteristic for the EUAAs returns through introduction of Markov switch-

ing also in the residual variance. 

The most frequently applied parameter estimation method of Markov 

switching model is the maximum likelihood method (ML), which makes use 

of FSQP algorithm (Feasible Sequential Quadratic Programming) (Law-

rence and Tits, 2001; Psaradakis and Sola, 1998). A by-product of the 

Markov-switching model parameter estimation is a sequence of smoothed 

probabilities )|( Tt jsP  which make it possible to identify the moment of 

process switching between the particular volatility regimes. These probabil-



Aneta Włodarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

136 

ity inferences allow to draw conclusions about the EUAA returns process 

being in a particular regime, although the regime variable st is unobserved. 

On this basis, the time series of the EUAAs returns have been divided into 

observations generated in different volatility regimes, and then risk measures 

(1)–(6) have been estimated for each sub-sample.  

Additionally, regime classification measure (RCM) has been used to de-

termine the number of regimes in Markov switching models (Ang and 

Bekaert, 2002): 

 







T

t

N

i

tt isP
T

NNRCM
1

1

0

1
2 ))|((

1
100)( , (12) 

where: )|( 1 tt isP – filter regime probabilities series (i= 0,1,…,N–1 and 

t= 1,2,…,T), 1t  – information set available up to time t–1.  

Alternatively, Ang and Bekaert (2002) suggested to replace the filter regime 

probabilities by the smoothed probabilities over the entire sample  

( )|( Tt jsP  ) in (12). For the two-regime model the RCM statistics rang-

es from 0 to 100 and smaller value of this measure means better regime clas-

sification. High values of the RCM may indicate that the Markov switching 

model cannot successfully distinguish between regimes from the behavior of 

the data. It may point at misspecification of the number of regimes (Ang and 

Bekaert, 2002). 

2. Data and Empirical Results  

Intercontinental Exchange Futures Europe in London (ICE Futures 

Europe), adjusting itself to the changing regulations in the scope of the EU 

climate policy, introduced into trade the EUAA futures contracts in February 

2012. This product was dedicated primarily to aircraft operators as an in-

strument of CO2 emission risk management, due to a significant increase in 

their exposition to this type of risk after civil aviation had been included into 

the EU ETS. Hedging operations with the use of aviation allowances futures 

should gain in popularity as the international law provisions are being tight-

ened in the scope of carbon dioxide emission in civil aviation and the princi-

ples of the EU ETS functioning towards introducing an auctioning system as 

a basic form of acquiring emission allowances by aircraft operators. An im-

portant stage of CO2 emission risk management process in the civil aviation 

sector is the measuring price risk of EUAA futures contracts. In the empiri-

cal research two types of risk measures have been used for this purpose: 

volatility risk measure and downside risk measure, which have been esti-



Regime-dependent Assessment of the EUAA Price Risk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

137 

mated on the basis of weekly returns of EUAAs futures prices listed on the 

ICE Futures in the period from 04.03.2012 to 01.10.2017.
2
 The shaping of 

weekly settlement prices and returns for constructed benchmark series for 

EUAAs futures have been presented in Fig. 1. 

 

Figure 1. Weekly prices of the EUAA futures [EUR/tCO2] (upper panel) and their 

returns [%] (lower panel) quoted in the ICE Futures Europe in the period 

4.03.2012 – 01.10.2017 

Table 1. MS( N)-AR(4) models for the EUAAs returns 

Parameter MS(2)-DR(4) MS(3)-DR(4) 

Regime 0 Regime 1 Regime 0 Regime 1 Regime 2 

Constant 0.696 
[0.049] 

–1.104 
[0.350] 

0.726 
[0.045] 

–20.529 
[0.002] 

0.358 
[0.654] 

AR-4 –0.179 
[0.019] 

–0.129 
[0.234] 

–0.212 
[0.013] 

–2.288 
[0.001] 

–0.050 
[0.546] 

sigma 4.113 
(0.420) 

11.356 
(1.090) 

3.820 
(0.357) 

11.089 
(3.919) 

8.393 
(0.808) 

Matrix P R(0, t) R(1, t) R(0, t) R(1, t) R(2, t) 
R(0, t+1) 0.9349 0.1077 0.9314 0.0000 0.0739 
R(1, t+1) 0.0651 0.8923 0.0000 0.2092 0.0470 
R(2, t+1) – – 0.0686 0.7908 0.8791 

Di (in weeks) 22.38 15.43 22.43 1.40 9.46 
Returns assigned 

to regime 
62.37% 

(179returns) 
37.63% 

(108returns) 
54.70% 

(157returns) 
2.44% 

(7 returns) 
42.86% 

(123returns) 

Note:  P – transition probabilities matrix, standard errors of parameter estimates in parenthesis, p-value in 

brackets.  

Markov switching heteroscedastisity models (MS(N)-DR(p) for N = 2,3 and 

p = 1, 2, 3, 4) (7) were estimated to describe the dynamism of the EUAAs 

                                                 
2 The research uses the December prices of EUAA futures quoted on the ICE Futures 

Europe, presented on the website https://www.quandl.com (access 18.10.2017).  



Aneta Włodarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

138 

returns series in various volatility regimes. The best results have been pre-

sented in Table 1.
3
  

Two regimes have been distinguished in the first approach: the low vola-

tility regime (regime 0) that describes the period of calm on the EUAAs 

futures market and the high volatility regime (regime 1) characterized by 

turbulent changes on this market, which are generated mainly by changes to 

the regulations concerning CO2 emission in the aviation sector. The volatility 

parameter estimated for the regime 1 (11.356) is almost three times higher 

than the parameter describing the volatility in regime 0 (4.113). The differ-

ences between the regimes can be observed also for the parameter describing 

the expected profit from the EUAAs futures transactions, which in the low 

volatility regime is positive and in the high volatility regime negative. More-

over, each of the regimes is rather stable, as the estimated transition prob-

abilities of indicating a chance of EUAAs returns process to remain in the 

given regime in the next period are relatively high (they amount respectively 

0.9349 and 0.8923). Therefore, the low volatility regime on the EUAAs fu-

tures market lasts for about 22 weeks, while the high volatility regime lasts 

on average for over15 weeks.  

In the second approach three regimes have been distinguished: the low 

volatility regime (regime 0), the high volatility regime (regime 2) and 

„spiky” regime (regime 1) for which the standard deviation of the error term 

took the highest value (11.089) compared to the low and high volatility re-

gimes (respectively 3.82 and 8.393). The average profit from EUAAs futures 

transaction is highest in the low volatility regime. The spiky regime is a tran-

sitional one, which means that there is a great chance (0.7908) that in the 

next period it will be replaced by the high volatility regime. Only single 

EUAAs returns have been assigned to this regime, which indicate extreme 

changes of EUAAs futures prices connected with the structural changes in 

the system of aviation allowances trade.  

Table 2 shows the results of diagnostic tests on standardised residuals 

from each model, which allow for positive verification of white noise prop-

erties for residuals series. The Akaike information criterion demonstrates the 

model of three regimes to be better adjusted to the EUAAs returns series, 

                                                 
3 Basic descriptive statistics and diagnostic tests verifying the presence of structural break 

occurrence, autocorrelation, volatility clustering, leptokurtosis effects have been determined 

for both presented in Figure 1 variables. The results of conducted diagnostic tests justify the 

use of Markov switching heteroscedastisity models (7) to describe the dynamism of the 

EUAAs returns series in various volatility regimes.  Their results are available upon request 

from author. 



Regime-dependent Assessment of the EUAA Price Risk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

139 

while the Schwarz criterion reaches the lowest value for models of two re-

gimes. 

Table 2. Diagnostic tests for scaled residuals from MS( N)-AR(4) models 

Test MS(2)-DR(4) MS(3)-DR(4) 

AIC 
SC 

6.707 
 6.809 

6.675 
6.841 

B-P(20) 21.120 
[0.390] 

18.492 
[0.555] 

ARCH(1–5) 0.970  
[0.437] 

1.695  
[0.136] 

J-B 5.614 
 [0.061] 

4.009  
[0.135] 

LR 80.132  
[0.000] 

99.299 
[0.000] 

RCM 33.547 0.350 

Note:  B-P(k) – Box-Pierce test of serial correlation up to order k, ARCH(1-q) – Engle’s ARCH test for 

heteroscedasticity up to lag q, J-B – Jarque-Bera test for normality, LR – likelihood ratio test for non-
linearity, RCM – regime classification measure, AIC – Akaike Information Criterion, SC – Schwarz 

Information Criterion, p-value in brackets.  

It is worth stressing that for both Markov-switching heteroscedasticity mod-

els, the Davies (1987) upperbound for the p-value of the LR test of linearity 

strongly rejects the linear model (Doornik, 2013). The calculated values of 

the RCM statistics are rather low in the case of each specification of Markov 

switching model, what indicates the correct classification of regimes in the 

estimated models. 

 
Figure 2. Weekly EUAAs returns (upper panel), smoothed probabilities for regime 0 

(middle panel) and smoothed probabilities for regime 1 (lower panel) in 

the period 4.03.2012 – 01.10.2017 



Aneta Włodarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

140 

 

Figure 3. Weekly EUAAs returns and smoothed probabilities for regime 0 (upper 

panel), smoothed probabilities for regime 1 and regime 2 (lower panel) in 

the period 4.03.2012 – 01.10.2017 

On the basis of obtained in the estimation procedure values of smoothed 

probabilities, the moments of process switching between particular volatility 

regimes were estimated. Then, the EUAAs returns series was divided into 

two sub-samples generated by the low and high volatility regimes (see Fig. 

2) or three sub-samples generated by the regimes of low and high volatility 

and the spiky regime (see Fig. 3). One can observe that in each case the ma-

jority of EUAAs returns have been assigned to the low volatility regime 

(respectively: 62.37% and 54.70%). However, the sub-sample connected 

with the high volatility regime is relatively numerous, which is a characteris-

tic phenomenon on the CO2 emission allowance market (Sanin et al., 2015). 

In each sub-sample associated with the given volatility regime measures 

of profit and risk have been determined (1)–(6) (see Table 3). The regime 

comprising turbulent changes occurring on the market of CO2 emission al-

lowances in aviation, the source of which is primarily uncertainty accompa-

nying the changes of the EU climate policy and global regulations in the 

scope of pollutant emission by this sector, is characterized by much higher 

values of volatility and downside risk measures compared to regime 0. Fo-

cusing on the neutral concept of risk, one can see that the ratio between stan-

dard deviations estimated in regime 1 and 0 amounts to almost three. Having 

rejected the outliers in the process of risk measurement, the absolute median 

deviation in regime 1 is near three times higher than in regime 0. The same 

ratio is obtained when semi-standard deviations in high and low volatility  

regimes are compared, according to negative concept of risk. Aircraft opera-

tors securing themselves against the EUAAs price risk by means of futures 



Regime-dependent Assessment of the EUAA Price Risk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

141 

contracts in the high volatility periods could on average lose 0.995% per 

week, and in the low volatility periods they could on average earn 0.621%. 

Table 3. Risk measurement for the EUAAs futures transactions in particular regimes 

Statistic MS(2)-DR(4) MS(3)-DR(4) 

Regime 0 Regime 1 Regime 0 Regime 1 Regime 2 

Minimum –13.246 –48.791 –8.049 –48.791 –15.214 

Mean 0.621 –0.995 0.710 –22.166 0.421 

Median 0.589 –1.017 0.692 –22.816 0.248 

Maximum 10.828 23.660 8.701 20.516 23.660 

Standard deviation 4.189 11.708 3.995 21.907 8.573 

Absolute median deviation 2.701 7.835 2.556 5.776 6.322 

IQR 5.291 15.572 4.905 13.684 12.262 

Semi standard deviation 2.982 8.874 2.734 12.134 5.835 

Note:  IQR – Interquartile range, the coefficient of variation is not calculated because of negative values 

of expected return in some regimes.  

In the half of the weeks corresponding with the high volatility regime on the 

futures market, it was possible to lose at least 1.017%. In the half of the 

weeks assigned to the low volatility regime, EUAAs returns were not lower 

than 0.589%. Similar conclusions can be formulated for the 3-regime 

Markov switching model, when the estimated risk measures were compared 

for the high and low volatility regime. The risk accompanying the transac-

tions concluded on the derivatives market was very high in regime 1 

(21.907% according to the neutral risk concept, 12.134% according to the 

negative concept). In the spiky regime the volatility estimated with the 

means of the robust estimator which is absolute median deviation, amounts 

5.776% and is significantly lower than other volatility measures. Consider-

ing also the average value (–22.166%) and median (–22.816%) one can as-

sume that the majority of observations assigned to regime 1 constitute ex-

tremely large, negative EUAAs returns. The results presented in Table 3 

indicate significant differences in the level of risk accompanying the transac-

tions concluded on the EUAAs futures market, depending on the presence of 

the volatility regime in the given period. Therefore, Markov switching mod-

els may constitute a useful tool that allows to identify the moment of switch-

ing between regimes or determine the average lasting time of particular vola-

tility regimes on the aviation allowances secondary market. 

Conclusions 

Decisions concerning tightening the EU climate policy in the scope of 

greenhouse gases emission from aviation and modifying the principles of the 



Aneta Włodarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

142 

EU ETS functioning will affect competitiveness of aircraft operators per-

forming flights within the European Economic Area in the years 2012–2020. 

Therefore, it is important that the system of CO2 emission risk management 

is adjusted to individual needs of a given aircraft operator and targeted to 

implement eco-innovations, making it possible not only to comply with legal 

regulations concerning the size of CO2 emission but also to earn on the 

growth of fuel efficiency and transportation process optimization by the 

operator (Ko et al., 2017). Moreover, the constant control over the CO2 

emissions in order to the maintenance it below the upper allowed threshold 

and sale at an attractive price the surplus of CO2 emission allowances leads 

to strengthening the competitive advantage of aircraft operators. By includ-

ing civil aviation to the EU ETS system the legislators wanted to implement 

the principle “polluter pays”, yet, the economic practice has shown that simi-

larly to the energy sector, aircraft operators started gradually transfer the cost 

of participation in the EU ETS on the customers. Thanks to including the 

cost of CO2 emission into the price of tickets, despite received free of charge 

share of aviation allowances, the operators recorded windfall profit. Making 

use of this option depends on the elasticity of the demand for aviation ser-

vices, offers of competitive air carriers, state regulations of air transport 

market in the scope of access to both domestic transports as well as on inter-

national markets (concessions, certificates) (Tłoczyński, 2015; Dyduch, 

2013). Due to the fact that aircraft operators have to make decisions on the 

way they use aviation allowances, the measurement of EUAAs price risk on 

the secondary market is of vital importance in this decision-making process. 

If the marginal profit from the sale of aviation service is higher than the 

market value of EUAA allowances, the aviation allowances will be used to 

cover CO2 emissions derived from the air operations (Dyduch, 2013).  

The paper shows the changes in the EUAAs price risk level depending 

on the volatility regime in force on the aviation allowances secondary mar-

ket. On the basis of estimated Markov switching models the Author has 

identified two or three volatility regimes, for each different risk measures 

have been determined. The high volatility regime, in which the risk accom-

panying the sale and purchase transactions of EUAAs futures was several 

time higher than in the low volatility regime, has been assigned to the peri-

ods when important regulations in the aviation sector were introduced. The 

periods assigned to the high volatility regime corresponded with such events 

as: the end of the first settlement period for the aviation sector in the EU 

ETS (2012-11-25–2013-01-13), conducting the first settlement of historical 

CO2 emissions in civil aviation for the year 2012 and publishing the decision 

of the European Parliament and Council on implementing the „stop the 



Regime-dependent Assessment of the EUAA Price Risk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 129–145 

143 

clock” mechanism (2013-04-21, 2013-04-28–2013-06-23), publishing the 

Regulation 421/2014 on further derogation in aviation (2014-04-06–2014-

05-25), works on concluding a global agreement regarding implementation 

of the Carbon Offset and Reduction Scheme for International Aviation, 

CORSIA) (2016-06-19–2016-12-25). Such an approach makes it possible to 

measure more precisely the risk that accompanies the sale/purchase transac-

tions of aviation allowances on the secondary market. It also allows diversi-

fication of the adopted by aircraft operators strategies of securing themselves 

against the risk of CO2 emission allowances price depending on the price 

volatility regime in force. 

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145 

Reżimowo-zależna ocena ryzyka zmian cen unijnych  
uprawnień lotniczych do emisji CO2 

Z a r y s  t r e ś c i. W artykule oszacowano ryzyko zmian cen unijnych uprawnień lotniczych 

do emisji CO2, które towarzyszy działalności operatorów statków powietrznych wykonywanej 

w ramach Europejskiego Obszaru Gospodarczego, w okresach niskiej i wysokiej zmienności 

występujących na tym rynku. Pokazano, że reżimy zmienności na rynku kontraktów futures 

na uprawnienia lotnicze zostały prawidłowo zidentyfikowane, zarówno dla dwustanowego, 

jak i trzystanowego przełącznikowego modelu Markowa, a oszacowane miary ryzyka różnią 

się w reżimach. Występowanie różnych reżimów zmienności na tym rynku można wyjaśnić 

modyfikowaniem zasad funkcjonowania europejskiego systemu handlu emisjami oraz wpro-

wadzaniem zmian zarówno w polityce klimatycznej UE, jak i w globalnych regulacjach doty-

czących emisji CO2 przez lotnictwo międzynarodowe. 

S ł o w a  k l u c z o w e: europejski system handlu emisjami; przełącznikowe modele Mar-

kowa; ryzyko; unijne uprawnienia lotnicze do emisji CO2. 


