The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps
- Cite this article as:
- Benth, F.E. & Meyer-Brandis, T. Finance Stochast. (2005) 9: 563. doi:10.1007/s00780-005-0161-z
We derive the density process of the minimal entropy martingale measure in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard . 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. The dynamics of the processes determining the price and volatility are explicitly given under the minimal entropy martingale measure, and we derive a Black & Scholes equation with integral term for the price dynamics of derivatives. It turns out that the minimal entropy price of a derivative is given by the solution of a coupled system of two integro-partial differential equations.