不确定环境下障碍再装期权的动态定价模型
——基于BSDE解的期权定价方法

J4 ›› 2011, Vol. 46 ›› Issue (3): 52-57.

不确定环境下障碍再装期权的动态定价模型
——基于BSDE解的期权定价方法

张慧^1,2,孟纹羽¹,来翔³

1.山东财政学院统计与数理学院, 山东济南 250014; 2.山东大学经济学院, 山东济南 250100;
3.山东大学数学学院, 山东济南 250100

收稿日期:2010-05-10 发布日期:2011-04-21
作者简介:张慧(1973- ),女,副教授,博士研究生,研究方向为金融工程与风险管理. Email: ly19323@sohu.com
基金资助:
国家自然科学基金资助项目10671205); 山东省自然科学基金青年项目 (Q2007A03);山东省社会科学规划研究项目（10DJGJ07）;山东省统计局重点课题项目(KT1052)

Dynamic pricing model of the reload stock option with two barriers under Knightian uncertainty
— the method of option pricing based on the solution of BSDE

ZHANG Hui^{1, 2}, MENG Wen-yu¹, LAI Xiang³

1. School of Statistics ＆ Mathematics, Shandong University of Finance, Jinan, 250014, Shandong, China;
2. School of Economics, Shandong University, Jinan 250100, Shandong, China;
3. School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2010-05-10 Published:2011-04-21

摘要/Abstract

摘要：

研究了Knight不确定环境下的金融市场,利用倒向随机微分方程(backward stochastic differential equation,BSDE)的解以及时间-风险折现方法,提出了障碍再装股票期权的动态定价模型,并求出了模型的显式解,得到了障碍再装股票期权的动态定价区间,这与Epstein的基础资产结果在形式上是一致的。最后通过具体的数值分析揭示了投资者个体对Knight 不确定性的主观情绪以及上下障碍价格对障碍再装股票期权定价的重要影响。

关键词: Knight不确定性;期权定价;倒向随机微分方程;时间-风险折现;再装股票期权

Abstract:

The financial market with Knightian uncertainty is studied. Using the solution of BSDE and the method of time-risk discount, the dynamic pricing model of the reload stock option with two barriers is proposed. Also, the explicit solution of the model is derived. And obtaining the dynamic pricing interval of the reload stock option with two barriers is in accordance with Epstein′s conclusion. Finally, a numerical analysis is applied to depict the important impacts of the investors′ subjective sentimens to Knightian uncertainty and the up and down barrier prices on the pricing of the reload stock option with two barriers.

Key words: Knightian uncertainty; option pricing; backward stochastic differential equation; time-risk discount; reload stock option

张慧1,2,孟纹羽1,来翔3. 不确定环境下障碍再装期权的动态定价模型
——基于BSDE解的期权定价方法[J]. J4, 2011, 46(3): 52-57.

ZHANG Hui1, 2, MENG Wen-yu1, LAI Xiang3. Dynamic pricing model of the reload stock option with two barriers under Knightian uncertainty
— the method of option pricing based on the solution of BSDE[J]. J4, 2011, 46(3): 52-57.

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