American Option Valuation Under the Framework of CGMY Model with Regime-Switching Process

In this paper, the values and optimal exercise prices of American option under the CGMY model with regime-switching process are considered. For this case, the pricing mathematical model is a free boundary problem which includes d coupled fractional partial differential equations (PDEs) in one dimension with free boundary conditions, d denoting the number of regimes of financial market. The above problem is changed as a fixed one by adding a nonlinear penalty term to each fractional PDE. After the finite difference method is set to solve the transformed model, unlike the conventional method, the discretized coupling system is reformulated by expanding dimensions such that numerical results in all states can be calculated simultaneously. Finally, significant effects of the parameters in our model on the option exercise price are verified through our selected numerical results. Meanwhile, the curves of Delta and Gamma are reported to show feasibility of our model and the proposed numerical method.