An analytic approximation of the likelihood function for the Heston model volatility estimation problem

Estimating the volatility from the underlying asset price history for the discrete observations case is a challenging inference problem. Yet it has attracted much research interest due to the key role of volatility in many areas of finance. In this paper we consider the Heston stochastic volatility model and propose an accurate analytic approximation for the volatility likelihood function. The model is based on considering the joint probability density of the asset and the volatility, and integrating out past volatility variables. The likelihood simplifies to a product of T terms, where T is the length of the past history considered. An extension to the problem of fixed parameter estimation is also presented. Simulation results indicate the effectiveness and accuracy of the proposed method.