We give a short introduction to energy markets, describing how they function and what products are traded. Next we survey some of the popular models that have been proposed in the literature. We extend the analysis of one of these models to include for stochastic volatility effects. In particular, we analyse a mean reverting stochastic spot price dynamics with a stochastic mean level modelled as an Ornstein–Uhlenbeck process. We include in this dynamics a stochastic volatility model of the Barndorff-Nielsen and Shephard type. Some properties of the dynamics are derived and discussed in relation to energy markets. Moreover, we derive a semi-analytical expression for the forward price based on such a spot dynamics. In the last part of these lecture notes we consider a cross-commodity spot price model including jumps. A Margrabe formula for options on the spread is derived, along with an analysis of the dependency risk under an Esscher measure transform. An empirical example demonstrates that the Esscher transform may increase the tail dependency in the bivariate jump part of the spot model.
The final publication is available at Springer