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

Abstract

In this paper I analyze a broad class of continuous-time jump diffusion models of asset returns. In the models, stochastic volatility can arise either from a diffusion part, or a jump part, or both. The jump component includes either compound Poisson or Lévy [alpha]-stable jumps. To be able to estimate the models with latent Lévy [alpha]-stable jumps, I construct a new Markov chain Monte Carlo algorithm. I estimate all model specifications with S&P500 daily returns. I find that models with Lévy [alpha]-stable jumps perform well in capturing return characteristics if diffusion is a source of stochastic volatility. Models with stochastic volatility from jumps and models with Poisson jumps cannot represent excess kurtosis and tails of return distribution. In density forecast and VaR analysis, the model with Lévy [alpha]-stable jumps and joint stochastic volatility performs the best among all other specifications, since both diffusion and infinite activity jump part provide information about latent volatility.