A primal-dual active set approach to the valuation of American options in regime-switching models: numerical solutions and convergence analysis

• Published in: Computational & applied mathematics Vol. 43; no. 6
• Main Authors: Wen, Xin, Song, Haiming, Li, Yutian, Gao, Zihan
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.09.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Boundary conditions; Complex systems; Computational Mathematics and Numerical Analysis; Convergence; Error analysis; Finite difference method; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Truncation errors; Primal-dual active set method; Regime switching; 35A35; 90A09; 65K10; American options; 65M60; 65M12; Finite difference method
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-024-02862-9

In this study, we explore the valuation challenge posed by American options subject to regime switching, utilizing a model defined by a complex system of parabolic variational inequalities within an infinite domain. The initial pricing model is transformed into a linear complementarity problem (LCP) in a bounded rectangular domain, achieved through the application of a priori estimations and the introduction of an appropriate artificial boundary condition. To discretize the LCP, we employ a finite difference method (FDM), and address the resulting discretized system using a primal-dual active set (PDAS) strategy. The PDAS approach is particularly advantageous for its ability to concurrently determine the option’s price and the optimal exercise boundary. This paper conducts an extensive convergence analysis, evaluating both the truncation error associated with the FDM and the iteration error of the PDAS. Comprehensive numerical simulations are performed to validate the method’s accuracy and efficiency, underscoring its significant potential for application in the field of financial mathematics.