Bayesian Estimation of Asymmetric Jump-Diffusion Processes

Abstract

The hypothesis that asset returns are log-normally distributed has been widely rejected. The extant literature has shown that empirical asset returns are highly skewed and leptokurtic (fat tails). The Affine Jump-Diffusion (AJD) model improves upon the log-normal specification by adding a jump component to the return process. The two-sided jump-diffusion (TSJD) model further improves upon the AJD specification by allowing for the tail behavior of the return distribution to be asymmetrical. The Pareto-Beta (Ramezani and Zeng, 1998) and the Double Exponential (Kou, 2002) models present two alternative TSJD specifications. Under the Pareto-Beta specification, two Poisson processes govern the arrival rate of good and bad news, leading to Pareto distributed up-jumps or Beta distributed down-jumps in prices. Under the Double Exponential specification, a single Poisson process generates jumps in returns but the up and down magnitudes are generated by two exponential distributions. Both specifications results in highly asymmetric jump diffusion processes with desirable empirical and theoretical features. Accordingly, these models have been widely adopted in the portfolio choice, option pricing, and other branches of the literature. The primary objective of this paper is to contribute to the econometric methods for estimating the parameters of the TSJD models. Relying on the Bayesian approach, we develop a Markov Chain Monte Carlo (MCMC) estimation technique that is appropriate to these specifications. We then provide an empirical assessment of these model using daily returns for the S&P-500 and the NASDAQ indexes, as well as individual stocks. We complete our analysis by providing a comparison of the estimated parameters under the MCMC and the MLE methodologies.