Analysis of filtering and smoothing algorithms for Lévy-driven stochastic volatility models

Filtering and smoothing algorithms that estimate the integrated variance in Lévy-driven stochastic volatility models are analyzed. Particle filters are algorithms designed for nonlinear, non-Gaussian models while the Kalman filter remains the best linear predictor if the model is linear but non-Gaussian. Monte Carlo experiments are performed to compare these algorithms across different specifications of the model including different marginal distributions and degrees of persistence for the instantaneous variance. The use of realized variance as an observed variable in the state space model is also evaluated. Finally, the particle filter's ability to identify the timing and size of jumps is assessed relative to popular nonparametric estimators.