The model evaluates EUA prices has attracted some researcher’s attention. The review of their methodology frameworks underlines two main strands: the first one proposes numerous regression models to explain the allowance prices by different economic and financial determinants with differences in the data analysed (i.e. phases I, II and II).
These varying ways to explain the allowance prices can elucidate in part the different and, sometimes, contradictory results. In this sense, we find that the judgment of the authors can be related to the trading phase selected (Chevallier, 2012, Creti et al.
, 2012; Rickels et al., 2015, among others) and the factors which appear to drive the carbon price as well as the key determinants of the price of EUAs (Fezzi and Bunn, 2009; Hintermann, 2010; Maydybura, 2011; Bredin and Muckley, 2011, among others).
Being aware of the problems of assuming the EUA price formation in terms of a set of exogenous determinants, an alternative line of research (i.e. second strand) has focused on the stochastic properties of daily EUA spot prices and the application of models from financial econometrics to EUA data.
Seifert et al. (2008), Daskalakis et al. (2009), Benz and Tr?ck (2009) and Hitzemann and Uhrig-Homburg (2013) which focus on the stochastic properties of daily price data and provide, amongst other things, evidence for conditional heteroskedasticity.
Paolella and Taschini (2008) propose mixed GARCH models which allowed for the unconditional tail behaviour and heteroskedasticity in the EUA price series. According to their results, they have reported the validity of these models in capturing the price volatility at the end of Phase I.
Seifert et al. (2008) use a stochastic equilibrium model to analyse the dynamics of EUA spot prices.
Their main conclusion is that an EUAs pricing model exhibits a time- and price volatility structure. Daskalakis et al. (2009) model the effects of abolishing banking on futures prices during Phase I and develop a framework for pricing and hedging of intra-phase and inter-phase futures and options on futures. Benz and Tr?ck (2009) advocate the use of Markov switching and GARCH models for the volatility analysis of the EUA spot prices in Phase I.
Their results support the strength of both models to emphasis the specific characteristics of the EUA time series, such as cyclic phases, volatility clustering, skewness, and excess kurtosis. Bao (2013) analyses the EUA end-of-day spot price and real-time price using the change point analysis.
A key result is that the EUAs spot price can be decomposed into two parts: a diffusion part which resembles white noise, and a jump part which can be linked to influential political news in the market. It’s important to note that these studies that addressing the stochastic properties of EUAs prices are limited to data from Phase I.
It is possible that the results of the first phase are not fully generalizable to other phases. In this context, Benschop et al. (2014) support the performance of Markov Switching GARCH models to predict EUA log returns during the second trading phase.
Recall that these models are developed to capture some characteristics of data such as the volatility clustering, breaks in the volatility process and heavy-tailed distributions. Recently, Gil-Alana (2016) re-examines the behaviour of persistence in carbon emission allowance prices.
For this purpose, they use daily data for the period between 2007-2014 and techniques based on the concept of long memory accounting for structural breaks and non-linearities in the data.
Results indicate that, while there is no evidence of non-linearity, when allowing for structural breaks, the persistence of shocks to the carbon emission allowance is markedly reduced, with the same being transitory for recent sub-samples. Similarly, M?lar et al. (2017) study structural breaks in the emission allowance price process of the European Union Trading System but during Phase ? and Phase III. There is indeed a structural break between Phase II and Phase III.
However, there are several regimes within each of these phases. Moreover, the findings suggest that the high-volatility regimes are usually the regimes with negative average returns, whereas low-volatility regimes usually exhibit zero or positive average returns.
Yang et al. (2015) are the first who introduce the jump effects in modelling CO2 emission allowance prices. In particular, they demonstrate that the dynamic jump ARMA-GARCH model can provide more accurate valuations of the CO2 emission allowance options on futures than other models in terms of a pricing error.
More recently, Daskalakis et al. (2019) investigate various popular diffusion and jump-diffusion processes used to describe commodity prices. The study covers data of three main markets for emission allowances within the EU ETS: Powernext, Nord Pool and European Climate Exchange (ECX).
Their analysis suggests that the prohibition of banking of emission allowances between distinct phases of the EU ETS has significant implications in terms of EUA futures pricing. Besides, the non-mean reverting models proposed by Merton (1976) are the more appropriate process.
Despite the result of these studies, it is important to note that this second strand of research focusing on financial econometric statistics may need to be more extended to cover the modern models that reflected the properties and data of EUAs. This present research is entered into this aim.