Utility indifference valuation for non-smooth payoffs with an application to power derivatives

Abstract

We consider the problem of exponential utility indifference valuation under the simplified framework where traded and nontraded assets are uncorrelated but where the claim to be priced possibly depends on both. Traded asset prices follows a multivariate Black and Scholes model, while non traded asset prices evolve as generalized Ornstein-Uhlenbeck processes. We provide a BSDE characterization of the utility indifference price (UIP) for a large class of non-smooth payoffs depending simultaneously on both classes of assets. The markovian setting and the gaussian property of non traded assets allow us to combine techniques coming from BSDEs and PDEs to characterize the UIP for possibly discontinuous European payoffs as the unique viscosity solution of a suitable PDE and the optimal hedging strategy as essentially the delta hedging strategy corresponding to the UIP. Moreover, we obtain asymptotic expansions for prices and hedging strategies when the risk aversion parameter is small. Finally, our results are applied to pricing and hedging power derivatives in various structural models for energy markets. This is a joint paper with G. Benedetti (University Paris-Dauphine and CREST).