Laplace Transform Methods for a Free Boundary Problem of Time-Fractional Partial Differential Equation System - Zhiqiang Zhou; Xuemei Gao (Discrete Dynamics in Nature and Society)
We study the pricing of the American options with fractal transmission system under two-state regime switching models. This pricing problem can be formulated as a free boundary problem of time-fractional partial differential equation (FPDE) system. Firstly, applying Laplace transform to the governing FPDEs with respect to the time variable results in second-order ordinary differential equations (ODEs) with two free boundaries. Then, the solutions of ODEs are expressed in an explicit form. Consequently the early exercise boundaries and the values for the American option are recovered using the Gaver-Stehfest formula. Numerical comparisons of the methods with the finite difference methods are carried out to verify the efficiency of the methods.