Joachim Priou: GARCH models with Generalized Hyperbolic innovations with application to carbon derivative pricing

The aim of this work is to use a new modelling technique for CO2 emission quotas (EUA), in order to calculate the price of structured products, in particular options on the CO2 allowances. After a short discussion about the specificities of this market, we investigate several GARCH-filtering processes for CO2 emission permits prices. We take interest, in particular, in GARCH models with fractional powers in the autoregressive process of the volatility (the APARCH), and in GARCH models with regime switching (RS-GARCH). Calibration of GARCH, conducted using the CO2 European Union Allowances (EUA) daily prices from 2005 to 2009, is carried out maximizing likelihood as well as using Bayesian inference in models with too high complexity for relying upon numerical optimization.

We use these modellings under the historical measure to derive a model for options pricing under the risk neutral measure. We compare both approaches, one following the work of Gerber and Siu (1994) using a stochastic discount factor exponential affine, the other one using the recent method developed by Chorro, Guégan and Ielpo (2010) and considering an empirical martingale correction technique.

Interestingly, we notice that the GARCH processes with fat-tailed distributions (such as Student or Normal Inverse Gaussian ones) fit better CO2 market data. Option prices calculation still gives evidence to the fact that normal innovations are not satisfactory, but may conduct to rather different conclusions from the fitting study, showing the importance to distinguish historic and risk neutral probabilities.