An Implicit Scheme for American Put Options

被引：0
作者：
Xinfu Chen
Zhengyang Lu
Jingtang Ma
Jinye Shen
机构：
[1] Southwestern University of Finance and Economics,School of Mathematics
来源：
Journal of Scientific Computing | 2023年 / 97卷
关键词：
American put options; Implicit finite difference methods; Parabolic variational inequalities; Free boundary problems; 65C20; 65C40; 65M06; 91G20; 91G60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, an implicit scheme is proposed to solve a parabolic variational inequality arising from the American put options. The discretization leads to a class of discrete elliptic variational inequalities. Well-posedness, including existence, uniqueness, comparison principle, and stability of the discrete elliptic variational inequality is established. A simple and efficient algorithm to solve the implicit discretized variational inequality is discovered. The novelty here is an explicit formula for the optimal exercise boundary. An improved algorithm is also presented to eliminate the singularity near the time to expiry. Numerical examples are carried out to show the accuracy and efficiency of the proposed algorithms.
引用
收藏
相关论文
共 68 条
[1]  
Allegretto W(2001)Finite element error estimates for a nonlocal problem in American option valuation SIAM J. Numer. Anal. 39 834-857
[2]  
Lin Y(1996)American option valuation: new bounds, approximations, and a comparison of existing methods Rev. Financ. Stud. 9 1211-1250
[3]  
Yang H(1997)Pricing american-style securities using simulation J. Econ. Dyn. Control 21 1323-1352
[4]  
Broadie M(1998)Randomization and the American put Rev. Financ. Stud. 11 597-626
[5]  
Detemple J(1992)Alternative characterizations of American put options Math. Financ. 2 87-106
[6]  
Broadie M(2019)A HODIE finite difference scheme for pricing American options Adv. Difference Equ. 67 1-17
[7]  
Glasserman P(2010)A robust finite difference scheme for pricing American put options with singularity-separating method Numer. Algorithms 53 497-510
[8]  
Carr P(2020)Stability and error analysis of operator splitting methods for American options under the Black-Scholes model J. Sci. Comput. 82 1-17
[9]  
Carr P(2006)A mathematical analysis of the optimal exercise boundary for American put options SIAM J. Math. Anal. 38 1613-1641
[10]  
Jarrow R(2016)Convergence rate of free boundary of numerical scheme for American option Discrete Contin. Dyn. Syst. Ser. B 21 1435-1444
1234567