| 微分对策在期权定价中的应用:数值分析 |
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| 引用本文： | 郑立辉,冯珊,张兢田,王安兴.微分对策在期权定价中的应用:数值分析[J].华中科技大学学报(自然科学版),1998(11). |
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| 作者姓名： | 郑立辉 冯珊 张兢田 王安兴 |
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| 作者单位： | 华中理工大学系统工程研究所，华中理工大学经济学院 |
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| 摘 要： | 研究了期权定价的微分对策方法中得到的偏微分方程的数值解法．通过微分对策的离散化，并运用离散时间动态规划原则得到了原偏微分方程的有限差分逼近．基于粘性解的概念证明了有限差分方程的解一致收敛于原偏微分方程的解．给出了计算机仿真结果，并讨论了期权价格的性质．
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| 关 键 词： | 期权定价 数值分析 偏微分方程 粘性解 |
A Differential Game Approach to the Option Pricing Problem: Numerical Analysis |
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| Zheng Lihui,Feng Shan,Zhang Jingtian,Wang Anxing.A Differential Game Approach to the Option Pricing Problem: Numerical Analysis[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,1998(11). |
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| Authors: | Zheng Lihui Feng Shan Zhang Jingtian Wang Anxing |
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| Institution: | Zheng Lihui Feng Shan Zhang Jingtian Wang Anxing |
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| Abstract: | The paper is concerned with numerical solution of the partial differential equation derived in the differential game approach to option pricing. A finite difference approximation to the original equation is obtained by discretizing the differential game and using the discrete time dynamic programming principle. Based on the theory of viscosity solution, it is proved that the solution to the difference equation converges to that of the partial differential equation. Computer simulations are carried out and the properties of the option price are analyzed. |
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| Keywords: | option pricing numerical analysis partial differential equation viscosity solution |
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