A jump-diffusion model for option pricing

• 成果类型: Article
• 署名作者: Kou, SG
• 署名单位: Columbia University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.48.8.1086.166
• 发表日期: 2002
• 页码: 1086-1101
• 关键词: CONTINGENT CLAIMS; high peak; Heavy Tails; interest rate models; rational expectations; overreaction and underreaction

摘要

Brownian motion and normal distribution have been widely used in the Black-Scholes option-pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called volatility smile in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jump-diffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path-dependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.