不确定环境下再装股票期权的稳健定价模型

中国管理科学 ›› 2008, Vol. 16 ›› Issue (1): 25-31.

不确定环境下再装股票期权的稳健定价模型

张慧^1,2, 陈晓兰², 聂秀山³

1. 山东大学经济学院山东济南250100;
2. 山东财政学院统计与数理学院山东济南250014;
3. 山东财政学院计算机信息工程学院山东济南250014

收稿日期:2007-02-05 修回日期:2007-12-29 出版日期:2008-02-28 发布日期:2008-02-28
作者简介:张慧(1973),女(汉族),山东新泰市人,山东大学经济学院博士后,山东财政学院统计与数理学院副教授,研究方向:金融工程与风险管理.
基金资助:
国家自然科学基金资助项目(10671205);山东大学博士后基金资助项目(BSH05019)

Robust Pricing Model of Reload Stock Option under Uncertainty

ZHANG Hui^1,2, CHEN Xiao-lan², NIE Xiu-shan³

1.School of Economics, Shandong University, Jinan 250100, China;
2. School of Mathematics and Sciences, Shandong Finance University, Jinan 250014, China;
3. School of Computer & Information Engineering, Shandong Finance University, Jinan 250014, China

Received:2007-02-05 Revised:2007-12-29 Online:2008-02-28 Published:2008-02-28

摘要/Abstract

摘要： 研究具有Knight不确定性的金融市场,假定标的资产(股票)价格过程服从几何布朗运动,建立了再装股票期权在一个概率测度集合上的最大、最小定价模型。并借助于倒向随机微分方程(BSDE)以及偏微分方程(PDE)的重要理论完成了对模型的转化。最后利用随机过程的有关知识求出了该模型的显示表达式,并通过具体的数值分析揭示了Knight不确定性对再装股票期权定价的重要影响。

关键词: Knight不确定性, 再装股票期权, 稳健定价, BSDE

Abstract: The financial market with Knight uncertainty is studied.Assuming the underly ing stock asset follows geometric Brownian motion,the models of maximal and minimal pricing of reload stock option are built.Moreover,applying the theories of backw ard stochastic differential equation and partial differential equation,the models have been converted.At last the explicit solutions of the models have been given by using the theory of stochastic processes.And this paper depicts the important impact of Knight uncer tainty on the pricing of reload stock option through numerical analysis.

Key words: Knight uncertainty, reload stock option, robust pricing, BSDE

中图分类号:

F272

张慧, 陈晓兰, 聂秀山. 不确定环境下再装股票期权的稳健定价模型[J]. 中国管理科学, 2008, 16(1): 25-31.

ZHANG Hui, CHEN Xiao-lan, NIE Xiu-shan. Robust Pricing Model of Reload Stock Option under Uncertainty[J]. Chinese Journal of Management Science, 2008, 16(1): 25-31.