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美式期权定价问题的变网格差分方法

张铁,祝丹梅   

  1. 东北大学数学系,信息科学与工程学院, 沈阳, 110004
  • 出版日期:2008-11-14 发布日期:2009-02-05
  • 基金资助:

    国家自然科学基金资助项目(No.10771031).

张铁,祝丹梅. 美式期权定价问题的变网格差分方法[J]. 计算数学, 2008, 30(4): 379-387.

Zhang Tie, Zhu Danmei. THE DIFFERENCE METHODS WITH VARIABLE MESH FOR AMERICAN OPTION PRICING[J]. Mathematica Numerica Sinica, 2008, 30(4): 379-387.

THE DIFFERENCE METHODS WITH VARIABLE MESH FOR AMERICAN OPTION PRICING

Zhang Tie,  Zhu Danmei   

  1. Department of Mathematics, College of Information Science and Engineering,  Northeastern University, Shenyang 110004, China
  • Online:2008-11-14 Published:2009-02-05

本文提出一种求解美式期权定价自由边值问题的变网格差分方法. 通过建立一个自由边界所满足的方程, 利用变网格技术可同时求出期权的差分解和最佳执行边界. 本文分别讨论了显式和隐式变网格差分格式, 并给出了差分解的收敛性和稳定性分析. 数值实验表明本文算法是一个非常有效的期权定价算法.

In this paper, the difference methods with variable meshes are proposed for the American option pricing problems in the free boundary value form.
By means of an equation derived for the free boundary, the option values and the optimal exercise boundary can be computed simultaneously by using the variable mesh technique. Both explicit and implicit difference schemes are discussed, and the stability and convergence are analyzed. Numerical experiments show that the new algorithm is very efficient for option pricing problems.

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