Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions

• 成果类型: Article
• 署名作者: Fu, Michael C.; Li, Bingqing; Li, Guozhen; Wu, Rongwen
• 署名单位: University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; Nankai University; Capital One Financial Corporation
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2016.2522
• 发表日期: 2017
• 页码: 3961-3977
• 关键词: jump-diffusion process; option pricing; European option; generating function; lattice path

摘要

We obtain a closed-form solution for pricing European options under a general jump-diffusion model that can incorporate arbitrary discrete jump-size distributions, including nonparametric distributions such as an empirical distribution. The flexibility in the jump-size distribution allows the model to better capture leptokurtic features found in real-world data. The model uses a discrete-time framework and leads to a pricing formula that is provably convergent to the continuous-time price as the discretization is increased. The solution is easy to implement with fast convergence properties. Numerical results illustrate the efficiency and accuracy of the proposed model and highlight its robustness and flexibility.