Estimating volatility and model parameters of stochastic volatility models with jumps using particle filter

Abstract

Despite the success of particle filter, there are two factors which cause difficulties in its implementation. The first one is the choice of importance functions commonly used in the literature which are far from being optimal. The second one is the combined state and parameter estimation problem. In a widely used Heston model on stochastic volatility in financial literature, we are able to circumvent both these problems. To reflect the most realistic situation, we also include jump in the stochastic volatility model. Numerical results show the effectiveness of the algorithms.