A Multivariate Non-Gaussian Stochastic Volatility Model with Leverage for Energy Markets

Spot prices in energy markets exhibit special features like price spikes, mean-reversion inverse, stochastic volatility, inverse leverage effect and co-integration between the different commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. Second order structure and stationary issues of the model are analysed. Moreover the implied multivariate forward model is derived. Due to the flexibility of the model stylized facts of the forward curve as contango, backwardation and humps are explained. Moreover, a transformed-based method to price options on the forward is described, where fast and precise algorithms for price computations can be implemented. A simulation method for Monte Carlo generation of price paths is introduced