Bayesian Analysis of Stochastic Volatility Models with Levy Jumps: Application to Value at Risk

In this paper we analyze asset returns models with diffusion part and jumps in returns with stochastic volatility either from diffusion or pure jump part. We consider different specifications for the pure jump part including compound Poisson, Variance Gamma and Levy α-stable jumps. Monte Carlo Markov chain algorithm is constructed to estimate models with latent Variance Gamma and Levy α−stable jumps. Our construction corrects for separability problems in the state space of the MCMC for Levy α−stable jumps. We apply our model specifications for analysis of S&P500 daily returns. We find, that models with infinite activity jumps and stochastic volatility from diffusion perform well in capturing S&P500 returns characteristics. Models with stochastic volatility from jumps cannot represent excess kurtosis and tails of returns distributions. One-day and one-week ahead prediction and VaR performance characterizing conditional returns distribution rejects Variance Gamma jumps in favor of Levy α−stable jumps in returns. JEL classification: C1; C11; G1; G12