快扩散过程下永久美式看跌期权的定价

数学物理学报 ›› 2012, Vol. 32 ›› Issue (6): 1056-1062.

快扩散过程下永久美式看跌期权的定价

彭大衡

广东商学院金融学院广州 510320

收稿日期:2011-12-22 修回日期:2012-10-22 出版日期:2012-12-25 发布日期:2012-12-25
基金资助:
教育部人文社会科学研究规划基金(10YJA630122)资助

Pricing of Perpetual American Put with Fast Diffusion Process

PENG Da-Heng

School of Finance, Guangdong University of Business Studies, Guangzhou |510320

Received:2011-12-22 Revised:2012-10-22 Online:2012-12-25 Published:2012-12-25
Supported by:
教育部人文社会科学研究规划基金(10YJA630122)资助

摘要/Abstract

摘要：

研究标的资产价格服从快扩散过程的永久美式看跌期权定价问题. 首先, 借助文献[3]给出标的资产价格服从快扩散过程的欧式看跌期权定价公式,
然后, 通过求解一个自由边界问题并利用二次逼近方法, 对标的资产价格服从快扩散过程的永久美式看跌期权的价格以及实施该期权时的临界标的资产价格给出了显式解. 所得结论是Black-Scholes市场中关于永久美式看跌期权定价的推广.

关键词: 快扩散, 永久美式看跌期权, 二次逼近

Abstract:

This paper studies the price of perpetual American put with fast diffusion process. Firstly, using literature [3], the price of European put option is given when the underlying asset follows fast diffusion process, then the closed-form solutions for pricing of perpetual American put and the critical asset price when the underlying asset's price follows fast diffusion process are obtained by solving a free boundary
value problem. Results obtained here are the extension of the corresponding one in the Black-Scholes market.

Key words: Fast diffusion, Perpetual American put, Quadratic approximation

中图分类号:

91B28

彭大衡. 快扩散过程下永久美式看跌期权的定价[J]. 数学物理学报, 2012, 32(6): 1056-1062.

PENG Da-Heng. Pricing of Perpetual American Put with Fast Diffusion Process[J]. Acta mathematica scientia,Series A, 2012, 32(6): 1056-1062.