Gradient-based simulated maximum likelihood estimation for Lévy-driven Ornstein-Uhlenbeck stochastic volatility models

This paper studies the parameter estimation problem for Ornstein-Uhlenbeck stochastic volatility models driven by Lévy processes. Estimation is regarded as the principal challenge in applying these models since they were proposed by Barndorff-Nielsen and Shephard [<italic>J. R. Stat. Soc. Ser. B</italic>, 2001, <bold>63</bold>(2), 167-241]. Most previous work has used a Bayesian paradigm, whereas we treat the problem in the framework of maximum likelihood estimation, applying gradient-based simulation optimization. A hidden Markov model is introduced to formulate the likelihood of observations; sequential Monte Carlo is applied to sample the hidden states from the posterior distribution; smooth perturbation analysis is used to deal with the discontinuities introduced by jumps in estimating the gradient. Numerical experiments indicate that the proposed gradient-based simulated maximum likelihood estimation approach provides an efficient alternative to current estimation methods.