This paper provides an optimal filtering methodology in discretely observed continuous-time jump-diffusion models. Although the filtering problem has received little attention, it is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as...

The paper develops a simulation-based approach to sequential parameter learning and filtering in general state space models. Our approach is based on approximating the target posterior by a mixture of fixed lag smoothing distributions. Parameter inference exploits a sufficient statistic...