On convergence of the utility indifference pricing in the model preserving the CGMY minimal entropy martingale measure

Abstract

Motivated by financial instrument for pricing and hedging and also by the field of risk management, we consider measure changes for CGMY Levy processes which stay in the CGMY class. Within this two-parametric Esscher class of measure changes, we focus on the martingale measure with minimal relative entropy, called 'model preserving minimal entropy martingale measure' (MPMEMM). We link this measure to the utility-based indifference pricing. We precisely show that for bounded payoffs, the (exponential) utility indifference price goes to the option's price evaluated under the MPMEMM as the Arrow-Pratt measure of absolute risk aversion goes to zero. We also show that the class of Esscher martingale measures preserving the CGMY character is reduced to a single measure, described in full detail. Our results are new and contribute to the theory of option pricing under Levy models.