Scientific stochastic volatility models for the European carbon markets: forecasting and extracting conditional moments

Abstract

This paper builds and implements a multifactor stochastic volatility model for the latent (and observable) volatility of the carbon front December forward contracts at the European Carbon Exchanges, applying Bayesian Markov chain Monte Carlo simulation methodologies for estimation, inference, and model adequacy assessment. Stochastic volatility is the main way time-varying volatility is modelled in financial markets. Our main objective is therefore to structure a scientific model specifying volatility as having its own stochastic process. Appropriate model descriptions broaden the applications into derivative pricing purposes, risk assessment and asset allocation and portfolio management. From an estimated optimal and appropriate stochastic volatility model, the paper reports risk and portfolio measures, extracts conditional one-step-ahead moments (smoothing), forecast one-step-ahead conditional volatility (filtering), evaluates shocks from conditional variance functions, analyses multi-step-ahead dynamics, and calculates conditional persistence measures. The analysis adds insight and enables forecasts to be made, building up the methodology for developing valid scientific commodity market models.