Stochastic Volatility and Riccati Equation
Document ID: 2010-1988
Published on: 1st October 2010
Author: Graeme Lawson
In this technical note we use the backward Kolmogorov equation1 to derive a partial differential equation (PDE) for the characteristic function of a stochastic volatility diffusion process. In order to find a solution to the PDE, we need to solve Riccati-Type equations. To this end, we principally follow Brigo & Mercurio2, by considering a more general stochastic volatility process and proceeding to find the joint characteristic function of the coupled system.
