Abstract: American put option pricing under regime switching is modelled by a system of coupled partial differential equations. The proposed model combines better the reality of the market by incorporating the regime switching jointly with the emotional behaviour of traders using the rationality parameter approach recently introduced by Tågholt Gad and Lund Petersen to cope with possible irrational exercise policy. The classical rational exercise is recovered as a limit case of the rational parameter. The resulting nonlinear system of PDEs is solved by a weighted finite difference method, also known as -method. In order to avoid the need of an iterative method for nonlinear system, the term with rationality parameter and the coupling term are treated explicitly. Next, the resulting linear system is solved by Thomas algorithm. Stability conditions for the numerical scheme are studied by using von Neumann approach. Numerical examples illustrate the efficiency and accuracy of the proposed method.

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