Utility indifference pricing and hedging for structured contracts in energy markets

In this paper we focus on pricing of structured products in energy markets using utility indifference pricing approach. In particular, we compute the buyer's price of such derivatives for an agent investing in the forward market, whose preferences are described by an exponential utility function. Such a price is characterized in terms of continuous viscosity solutions of suitable non-linear PDEs. This provides an effective way to compute both an optimal exercise strategy for the structured product and a portfolio strategy to partially hedge the financial position. In the complete market case, the financial hedge turns out to be perfect and the PDE reduces to particular cases already treated in the literature. Moreover, in a model with two assets and constant correlation, we obtain a representation of the price as the value function of an auxiliary simpler optimization problem under a risk neutral probability, that can be viewed as a perturbation of the minimal entropy martingale measure. Finally, numerical results are provided.