Simulated Likelihood Approximations for Stochastic Volatility Models

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 "k"th-order approximation, we pretend that the observations form a "k"th-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. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..