Gradient-based simulated maximum likelihood estimation for stochastic volatility models using characteristic functions

Parameter estimation and statistical inference are challenging problems for stochastic volatility (SV) models, especially those driven by pure jump Lévy processes. Maximum likelihood estimation (MLE) is usually preferred when a parametric statistical model is correctly specified, but traditional MLE implementation for SV models is computationally infeasible due to high dimensionality of the integral involved. To overcome this difficulty, we propose a gradient-based simulated MLE method under the hidden Markov structure for SV models, which covers those driven by pure jump Lévy processes. Gradient estimation using characteristic functions and sequential Monte Carlo in the simulation of the hidden states are implemented. Numerical experiments illustrate the efficiency of the proposed method.