MCMC Analysis of Diffusion Models With Application to Finance

Abstract

This article proposes a new method for estimation of parameters in diffusion processes from discrete observations. The method is based on Markov-chain Monte Carlo methodology and applies to a wide class of models including systems with unobservable state variables and nonlinearities. The method is applied to the estimation of parameters in one-factor (CEV) interest-rate models and a two-factor model with a latent stochastic volatility component (SV). The CEV model is found to do a poor job in capturing the time-varying volatility interest-rate data. The SV model provides vastly superior fit to that of the CEV model. The article also presents a simulation study that demonstrates that the method provides accurate parameter estimates of the SV model at moderate sample sizes.