Pricing jump risk with utility indifference

Abstract

This paper is concerned with option pricing in an incomplete market driven by a jump-diffusion process. We price options according to the principle of utility indifference. Our main contribution is an efficient multi-nomial tree method for computing the utility indifference prices for both European and American options. Moreover, we conduct an extensive numerical study to examine how the indifference prices vary in response to changes in the major model parameters. It is shown that the model reproduces ‘crash-o-phobia’ and other features of market prices of options. In addition, we find that the volatility smile generated by the model corresponds to a zero mean jump size, while the volatility skew corresponds to a negative mean jump size.