Document Type : Research Article


Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran


The European option can be exercised only at the expiration date while an American option can be exercised on or at any time before the expiration date.
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 solve by the Hybrid Laplace transformfinite 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.