MCMC analysis of diffusion models with application to finance

Abstract

In this paper a new method is proposed for estimation of parameters in diffusion processes from discrete observations. The proposed simulation based MCMC methodology applies to a wide class of models including systems with unobservable state variables and non-linearities. We apply the method to the estimation of parameters in one-factor interest rate models of the CEV class and to a generalization of this model to a two-factor model with a stochastic volatility component. The small sample properties of the estimator are studied through sampling experiments for the stochastic volatility model and the results indicate that the method provides accurate estimates at moderate sample sizes.