Simulated likelihood approximations for stochastic volatility models

Abstract

This paper deals with parametric inference for continuous-time stochastic volatility models observed at discrete points in time. We consider approximate maximum likelihood estimation: for the kth-order approximation, we pretend that the observations form a kth-order Markov chain, find the corresponding approximate log-likelihood function, and maximize it with respect to θ. The approximate log-likelihood function is not known analytically, but can easily be calculated by simulation. For each k, the method yields consistent and asymptotically normal estimators. Simulations from a model based on the Cox-Ingersoll-Ross model are used for illustration.