Utility indifference pricing and hedging for structured contracts in energy markets

TL;DR

This paper develops a utility indifference pricing framework for structured energy contracts, using nonlinear PDEs and stochastic models, providing new insights into optimal exercise and hedging strategies with numerical validation.

Contribution

It introduces a comprehensive utility indifference pricing method for structured energy products in incomplete markets, incorporating stochastic factors and hedging strategies.

Findings

Characterization of prices via nonlinear PDEs.

Representation of prices as auxiliary optimization problems.

Numerical results demonstrating practical applicability.

Abstract

In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyer's utility indifference price of a given product in terms of continuous viscosity solutions of suitable nonlinear PDEs. This gives a way to identify reasonable candidates for the optimal exercise strategy for the structured product as well as for the corresponding hedging strategy. Moreover, in a model with two correlated assets, one traded and one nontraded, 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.