支付股利的跳跃-扩散过程下美式看涨期权定价  

Pricing American Call Option on Stocks with Known Dividends under the Jump-diffusion Process

作　　者：彭斌[1,2] 

机构地区：[1]北京建筑大学经济与管理工程学院,北京100044 [2]中国人民大学商学院,北京100872

出　　处：《数理统计与管理》2014年第4期734-743,共10页Journal of Applied Statistics and Management

基　　金：国家自然科学基金资助项目(71002098);北京市高校青年英才计划项目(YETP1652)

摘　　要：讨论了当基础资产遵循跳跃-扩散过程时支付股利美式看涨期权定价问题。在等价鞅测度下,导出在风险中性定价模型中,标的股票服从跳跃-扩散过程并且在期权有效期支付一次股利时美式看涨期权的解析定价公式,然后将其扩展到期权有效期多次支付股利的美式看涨期权,其价值在期权有效期等间隔支付股利次数趋于无穷时将收敛于连续支付股利的美式看涨期权,在此基础上,提供了便于实践应用的外推加速法以减少计算复杂性。This paper discusses the pricing of American call option on stocks with known dlvlclenas when the underlying asset follows a jump-diffusion process. Under the equivalent martingale measure and risk neutral pricing model, we derive analytical valuation formula for American call option on a stock that obeys a jump-diffusion process and pays only one dividend during the life of the option. We then generalize these results to many dividends during the life of the option. The value of American call option with equally spaced discrete dividend payouts will converge in the limit to the value of the American call option with continuous dividends as the number of dividend payouts increases to infinity. In order to minimize the impact of the computational complexity, A method of extrapolation acceleration is provided.

关 键 词：跳跃-扩散过程 支付股利美式看涨期权 外推加速法 

分 类 号：F832[经济管理—金融学] O212[理学—概率论与数理统计]