Filtering a nonlinear stochastic volatility model

Abstract

We introduce a class of stochastic volatility models whose parameters are modulated by a hidden nonlinear dynamical system. Our aim is to incorporate the impact of economic cycles, or business cycles, into the long-term behavior of volatility dynamics. We develop a discrete-time nonlinear filter for the estimation of the hidden volatility and the nonlinear dynamical system based on return observations. By exploiting the technique of a reference probability measure we derive filters for the hidden volatility and the nonlinear dynamical system.