INDIFFERENCE PRICING AND THE MINIMAL ENTROPY MARTINGALE MEASURE IN A STOCHASTIC VOLATILITY MODEL WITH JUMPS

Abstract

We use the dynamic programming approach to derive an equation for the utility indifference price of Markovian claims in a stochastic volatility model proposed by Barndorff-Nielsen and Shephard (2001). The pricing equation is a Black & Scholes equation with a nonlinear integral term involving the risk preferences of the investor. Passing to the zero risk aversion limit, we present a Feynman-Kac representation of the minimal entropy price. The density of the minimal entropy martingale measure is found via the Girsanov transform of the Brownian motion and a subordinator process controlling the jumps in the volatility model. The density is represented by the logarithm of the value function for an investor with exponential utility and no claim issued, and a Feynman-Kac representation of this function is provided. We calculate the function explicitly in a special case, and show some properties in the general case. Selve paperet i pdf-format er attached.