Bayesian Estimation of Volatility with Moment-Based Nonlinear Stochastic Filters

This article adresses parameter estimation with moment-based stochastic filters that only heed the first two moments of the state densities. This approximation provides good results in numerous cases. However, due to missing linear correlation between diffusion parameters and expected states, Bayesian estimation of diffusion parameters such as volatility is not possible. While other filters overcome this problem by simulations, we present a deterministic algorithm for Bayesian estimation of the diffusion coefficient based on sigma points which can be applied to all moment-based filters. To show the validity of the algorithm we use the continuous-discrete unscented Kalman filter proposed by Singer [18].