Parameter Estimation for Discretely Observed Stochastic Volatility Models

Abstract

This paper deals with parameter estimation for stochastic volatility models. We consider a two-dimensional diffusion process (Y-t, V-t). Only (Y-t) is observed at n discrete times with a regular sampling interval. The unobserved coordinate (V-t) rules the diffusion coefficient (volatility) of (Y-t) and is an ergodic diffusion depending on unknown parameters. We build estimators of the parameters present in the stationary distribution of (V-t), based on appropriate functions of the observations. Consistency is proved under the asymptotic framework that the sampling interval tends to 0, while the number of observations and the length of the observation time tend to infinity. Asymptotic normality is obtained under an additional condition on the rate of convergence of the sampling interval. Examples of models from finance are treated, and numerical simulation results are given.