tau method for pricing american options under complex models

In this paper, we will study the numerical solutions of a class of complex partial differential equations (pde) systems with free boundary conditions. this kind of problems arise naturally in pricing (finite-maturity) american options, which is applies to a wide variety of asset price models including the constant elasticity of variance (cev), hyper-exponential jump-diffusion (hejd) and the finite moment log stable (fmls) models. developing efficient numerical schemes will have significant applications in finance computation. these equations have already been solved by the hybrid laplace transform-finite difference methods and the laplace transform method(ltm). in this paper we will introduce a method to solve these equations by tau method. also, we will show that using this method will end up to a faster convergence. numerical examples demonstrate the accuracy and velocity of the method in cev models.