Stochastic Volatility and Jumps: Exponentially Affine Yes or No? An Empirical Analysis of S&P500 Dynamics
42 Pages Posted: 21 Mar 2009 Last revised: 28 May 2009
Date Written: March 18, 2009
This paper analyzes exponentially affine and non-affine stochastic volatility models with jumps in returns and volatility. Markov Chain Monte Carlo (MCMC) technique is applied within a Bayesian inference to estimate model parameters and latent variables using daily returns from the S&P 500 stock index. There are two approaches to overcome the problem of misspecification of the square root stochastic volatility model. The first approach proposed by Christoersen, Jacobs and Mimouni (2008) suggests to investigate some non-affine alternatives of the volatility process. The second approach consists in examining more heavily parametrized models by adding jumps to the return and possibly to the volatility process. The aim of this paper is to combine both model frameworks and to test whether the class of affine models is outperformed by the class of non-affine models if we include jumps into the stochastic processes. We conclude that the non-affine model structure have promising statistical properties and are worth further investigations. Further, we find affine models with jump components that perform similar to the non affine models without jump components. Since non affine models yield economically unrealistic parameter estimates, and research is rather developed for the affine model structures we have a tendency to prefer the affine jump diffusion models.
Keywords: Stochastic volatility, Markov Chain Monte Carlo (MCMC), Bayesian inference Deviance information criteria (DIC), Bayes factor
JEL Classification: G11, G12
Suggested Citation: Suggested Citation