A generalized integral equation formulation for pricing American options under regime-switching model (Q6591516)

In this article, a generalized and highly efficient integral equation formulation for the price of American put options under regime-switching model with a goal of improving computational efficiency in mind, particularly when the number of regimes is large is presented. The main contributions of this paper are of two folds. Firstly, the integral equation method proposed by \textit{S.-P. Zhu} and \textit{Y. Zheng} [Int. J. Comput. Math. 100, No. 7, 1454--1479 (2023; Zbl 1515.91163)] is extended to the regime-switching model, in which any finite number of the regimes can be efficiently dealt with. In order to extend and implement the method, the authors first need to translate the regime-switching model into a new system governing the option's Theta. One of the parameters is the corresponding optimal exercise price from the fixed regime, while the others are the remaining option prices tangled in the function. Secondly, the authors present a newly proved theorem that facilitates the decoupling of the unknown coefficients involved in the system of \(n\) PDEs, so that they can be solved recursively. The original system of PDEs under \(n\)-state regime-switching model is explored in Section 2. A new system governing the option's Theta is detailed in Section 3. In Section 4, a newly proved theorem is presented.