Abstract
In this paper we introduce a new numerical method for the linear complementarity problems (LCPs) arising from two-asset Black–Scholes and Heston's stochastic volatility American options pricing. Based on barycenter dual mesh, a class of finite volume method (FVM) is proposed for the spatial discretization, coupled with the backward Euler and Crank–Nicolson schemes are employed for time stepping of the partial differential equations (PDEs). Then, for the resulting time-dependent LCPs are solved by using an efficient modulus-based successive overrelaxation (MSOR) iteration method. Numerical experiments are carried out to verify the efficiency and usefulness of the proposed method.
Funding Statement
This work was supported by the National Natural Science
Foundation of China (Nos. 61463002, 62062005), the Special Basic Cooperative Research Programs
of Yunnan Provincial Undergraduate Universities' Association (Nos. 2019FH001-079,
2017FH001-124), the Scientific Research Fund of Yunnan Provincial Education Department
(No. 2019J0396) and the Guizhou Provincial Science and Technology Planning Project
(No. Qiankehejichu-ZK[2021]-yiban322).
Citation
Xiaoting Gan. Xiaolin Chen. Dengguo Xu. "Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization." Taiwanese J. Math. 26 (1) 69 - 101, February, 2022. https://doi.org/10.11650/tjm/210803
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