The density process of the minimal entropy martingale measure in a stochastic volatility market. A PDE Approach

Abstract

In a stochastic volatility market the Radon-Nikodym density of the minimal entropy martingale measure can be expressed in terms of the solution of a semilinear partial differential equation (PDE). This fact has been explored and illustrated for the time-homogeneous case in a recent paper by Benth and Karlsen [3]. However, there are some cases which time-dependent parameters are required such as when it comes to calibration. This paper generalizes their model to the time-inhomogeneous case.