An Empirical Assessment of the Double Exponential Jump-Diffusion Process

Abstract

The double exponential jump-diffusion (DEJD) model, recently proposed by Kou (2002) and Ramezani & Zeng (1998), generates a highly skewed and leptokurtic distribution and is capable of matching key features of stock and index returns. Moreover, DEJD leads to tractable pricing formulas for exotic and path dependent options (Kou & Wang, 2004). Accordingly, the Double Exponential representation has gained wide acceptance. However, estimation and empirical assessment of this model has received little attention to date. The primary objective of this paper is to fill this gap. We use daily returns for NYSE and NASDAQ firms and daily and monthly returns for the S&P-500 and the NASDAQ indexes, in conjunction with maximum likelihood estimation to fit the DEJD model. We utilize the BIC criterion to assess the performance of DEJD relative to a number of alternatives. For individual stocks, based on data spanning the period 10/96-12/98, we find that relative to the Log-normal Jump-Diffusion (LJD), the DEJD provides a better fit for only 11% of the sampled firms. For these firms and the indexes, we compare DEJD to six popular versions of the ARCH specification using data for the period 1/1999 through 12/2003. The performance of DEJD for individual stocks is strong for this period: DEJD performs better than LJD and ARCH for majority of cases. For indexes the ARCH alternatives dominate, but the DEJD provides a better fit than LJD. Overall the empirical evidence in support of DEJD is mixed.