A Fixed Point Method for the Linear Complementarity Problem Arising from American Option Pricing

For American option pricing, the Black-Scholes-Merton model can be discretized as a linear comple- mentarity problem （LCP） by using some finite difference schemes. It is well known that the Projected Successive Over Relaxation （PSOR） has been widely applied to solve the resulted LCP. In this paper,...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2016-10, Vol.32 (4), p.921-932
Main Authors: Shi, Xian-Jun, Yang, Lei, Huang, Zheng-Hai
Format: Article
Language:English
Subjects:
Applications of Mathematics
Finite difference method
Iterative methods
LCP
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Pricing
Theoretical
不动点方法
全局收敛
分离技术
有限差分格式
期权定价
线性互补问题
美式
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Summary:For American option pricing, the Black-Scholes-Merton model can be discretized as a linear comple- mentarity problem （LCP） by using some finite difference schemes. It is well known that the Projected Successive Over Relaxation （PSOR） has been widely applied to solve the resulted LCP. In this paper, we propose a fixed point iterative method to solve this type of LCPs, where the splitting technique of the matrix is used. We show that the proposed method is globally convergent under mild assumptions. The preliminary numerical results are reported, which demonstrate that the proposed method is more accurate than the PSOR for the problems we tested.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-016-0613-6