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An Empirical Assessment of the Double Exponential Jump-Diffusion Process

33 Pages Posted: 18 Oct 2004  

Cyrus A. Ramezani

California Polytechnic State University, San Luis Obispo

Yong Zeng

University of Missouri at Kansas City - Department of Mathematics and Statistics

Date Written: October 15, 2004

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.

Keywords: Asset Price Processes, Double Exponential Jump-Diffusion, Pareto-Beta Jump Diffusion, Leptokurtic Distributions, Volatility Smile and Smirk, MLE

JEL Classification: C32, C52, G12, G13

Suggested Citation

Ramezani, Cyrus A. and Zeng, Yong, An Empirical Assessment of the Double Exponential Jump-Diffusion Process (October 15, 2004). Available at SSRN: https://ssrn.com/abstract=606101 or http://dx.doi.org/10.2139/ssrn.606101

Cyrus A. Ramezani (Contact Author)

California Polytechnic State University, San Luis Obispo ( email )

School of Business
San Luis Obispo, CA 93407
United States

Yong Zeng

University of Missouri at Kansas City - Department of Mathematics and Statistics ( email )

United States

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