跳扩散模型下永久美式看跌期权定价  

Pricing perpetual options with jump diffusion

作　　者：姜礼尚[1] 罗俊[1] 

机构地区：[1]同济大学数学研究所,上海200092

出　　处：《系统工程理论与实践》2008年第2期10-18,共9页Systems Engineering-Theory & Practice

摘　　要：目的是针对现有方法不能处理的价格"向下跳空"给出一般跳扩散模型下永久美式看跌期权定价公式以及最佳实施边界的显式表达式."向下跳空"相比"向上跳空"的重要性在于,价格有可能从继续持有区域瞬时跳入停止实施区域,强烈影响到美式期权持有者的投资决策.文章强调跳量的概率密度函数p(y)是一般形式的,通过偏微分方程方法引入格林函数,给出永久美式看跌期权的价格,并通过自由边界条件(smooth junction condition)给出最佳实施边界的显式表达式.This paper gives the pricing of the perpetual American put options in jump-diffusion model.We focus on how to deal with the general downward jumps. The downward jumps are quite different to the upward jumps because the stock price may jump from the continuation region of the option to the stopping region instantly. In our model the probability density function of the jump size p （y） is general. A closed series formula of the price is given by introducing some kind of Green function and the optimal exercise boundary of the perpetual put option is given by the smooth junction condition.

关 键 词：永久美式期权 跳扩散模型 向上跳空和向下跳空 最佳实施边界 自由边界一阶导数连续条件 

分 类 号：F830.572[经济管理—金融学] F830.91