Abstract: A system of coupled free boundary problems describing American put option pricing under regime switching is considered. In order to build numerical solution firstly a front-fixing transformation is applied. Transformed problem is posed on multidimensional fixed domain and is solved by explicit finite difference method. The numerical scheme is conditionally stable and is consistent with the first order in time and second order in space. The proposed approach allows the computation not only of the option price but also of the optimal stopping boundary. Numerical examples demonstrate efficiency and accuracy of the proposed method. The results are compared with other known approaches to show its competitiveness.

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