Asset price jumps, Bayesian estimation, Particle filters, Self-exciting jumps, SVJD.
Non-parametric approach to financial time series jump estimation, using the L-Estimator, is compared with the parametric approach utilizing Stochastic-Volatility-Jump-Diffusion (SVJD) models, estimated with Markov-Chain Monte-Carlo (MCMC) and Particle Filters. The comparison is performed on simulated time series with different kinds of dynamics, including Poisson jumps, self-exciting Hawkes jumps and co-jumps. Additional comparison is performed on the real-world daily time series of 4 major currency exchange rates. The results from the simulation study show that in the in-sample period, the parametric approach, using SVJD models, significantly outperforms the non-parametric L-Estimator based approach. In the out-sample period, the parametric approach achieves similar accuracy as the non-parametric approach in the case of Poisson jumps that are large, and it outperforms the nonparametric approach in the case of Hawkes jumps that are large. The L-Estimator provides better results in the cases when the simulated jumps are small, regardless of the dynamics of the jump process. Application of the methods to real-world foreign exchange rate time series further shows that the parametric jump estimates may be biased in the case when overly large jumps occur or when the stochastic volatility grows too high.