Luca Gonzato: Controlled Sequential Monte Carlo Methods for Continuous-Time Diffusion Models

Abstract: In this paper, we propose a general econometric approach to the estimation of continuous-time diffusion models. The combined usage of data augmentation and controlled Sequential Monte Carlo (SMC) methods allows to control discretization bias and provides efficient likelihood estimators, necessary for Bayesian inference. We test our methodology by considering a multifactor option pricing model where the latent volatility is a continuous-time matrix-valued Wishart process. To deal with the highly informative content of options data, we propose a likelihood tempering procedure to gradually introduce information from observations and construct optimal proposal distributions that deliver zero variance likelihood estimators. Numerical experiments on simulated data illustrate that our approach yields excellent tracking of the latent states and outperforms standard particle filtering techniques in terms of marginal likelihood estimation.