Fast Filtering in Switching Approximations of Nonlinear Markov Systems With Applications to Stochastic Volatility
This paper develops an efficient approach to analytical learning of Asymmetric Stochastic Volatility (ASV) models through nonlinear filtering, and shows that they are useful for practical risk management. This involves the derivation of a Nonlinear Quadrature Filter (NQF) that operates directly on the nonlinear ASV model. The NQF filter makes Gaussian approximations to the prior and posterior density of the latent volatility, but not in the observation space which makes possible easy handling of heavy-tailed data. Experiments in Value-at-Risk (VaR) assessment via an original bootsrtapping methodology are conducted with NQF and several ASV learning algorithms. The results indicate that our approach yields models with better statistical characteristics than the considered competitors, and slightly improved VaR forecasts.