The rapid development of European carbon markets over the last decade motivates an analysis of the dynamics driving the world's newest asset class. This thesis examines a class of stochastic volatility, jump-diffusion specifications for modelling the return and volatility dynamics of European Union Allowances (EUAs), thereby constituting a basis for carbon derivative pricing and risk management.
The parameters of four models with Gaussian log-volatility and zero mean are estimated using Bayesian MCMC. The models, which increase in order of complexity, attempt to capture the observed leptokurtosis of EUA returns as well as the heteroskedasticity and clustering of EUA volatility. Each specification is evaluated in-sample using the Deviance Information Criteria (DIC) popularised by Berg et. al. (2004) for financial time series. The DIC, as an adequacy measure, combines goodness-of-fit with a penalty for model complexity. The analysis reveals that the stochastic volatility, jump diffusion model (SVJ) of Bates (1996) and the stochastic volatility variance- gamma model (SVVG) of Madan (1998) perform the best in-sample.
The gold standard of goodness-of-fit, however, is the out-of-sample performance of a model as the risks financial practitioners face lie in future price and volatility uncertainty. Out-of-sample simulated kernel density estimates reveal that the models under consideration capture some, but not all of the unconditional leptokurtosis of the true EUA process. The DIC statistic is again used to assess out-of-sample model adequacy. Results indicate that the SVJ model ranks first amongst the alternative specifications - as it did in-sample.
The out-of-sample volatility forecasting performance of each model is also considered, motivated by the fact that volatility is of primary concern to derivative specialists and portfolio managers. The SVJ model achieves the smallest mean absolute error of the difference between one-period-ahead forecasts of daily volatility and realised volatility. This implies that the volatility forecasting accuracy of the SVJ model is optimal amongst the competing specifications.
Large, unforeseen losses in financial markets over the last two decades have prompted the need for forecasts of the entire density of risk parameters rather than point and interval forecasts only. Out-of-sample model performance is thus extended by applying a powerful technique for density forecast evaluation which relies on the probability integral transformation of observed data. The transformed series characterises correct specification of both the dynamics and the distributional form of the unobservable data generating process. Results indicate that the SVJ model is the only specification that estimates an out-of-sample density with sufficient weight in the tails of the distribution. The model also delivers consistent estimates of the conditional variance parameters of the underlying price generating process. This implies that the SVJ specification is the best model amongst the four alternatives for calculating Value-at-Risk statistics, for stress testing carbon portfolios and for performing scenario analysis.
The findings of this thesis demonstrate that EUA return and volatility dynamics can be characterised by the SVJ model of Bates (1996) - a relatively parsimonious stochastic volatility specification that allows for compound Poisson-type jumps in returns. Once jumps in returns have been accounted for, jumps in volatility appear to be of less importance. In addition to the model's volatility forecasting accuracy and its goodness-offit both in and out-of-sample, it is economically appealing as it generates near closed-form option prices. These attributes render the SVJ model a natural choice for carbon derivative pricing and risk management.