Option Pricing Under a Mixed-Exponential Jump Diffusion Model

• 成果类型: Article
• 署名作者: Cai, Ning; Kou, S. G.
• 署名单位: Hong Kong University of Science & Technology; Columbia University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1110.1393
• 发表日期: 2011
• 页码: 2067-2081
• 关键词: jump diffusion; mixed-exponential distributions; lookback options; barrier options; Merton's normal jump diffusion model; first passage times

摘要

This paper aims to extend the analytical tractability of the Black-Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing models, such as hyperexponential and double-exponential jump diffusion models, because the mixed-exponential distribution can approximate any distribution as closely as possible, including the normal distribution and various heavy-tailed distributions. The mixed-exponential jump diffusion model can lead to analytical solutions for Laplace transforms of prices and sensitivity parameters for path-dependent options such as lookback and barrier options. The Laplace transforms can be inverted via the Euler inversion algorithm. Numerical experiments indicate that the formulae are easy to implement and accurate. The analytical solutions are made possible mainly because we solve a high-order integro-differential equation explicitly. A calibration example for SPY options shows that the model can provide a reasonable fit even for options with very short maturity, such as one day.