Two Splitting Methods for a Fixed Strike Asian Option

The valuation of Asian Options can often be reduced to the study of initial boundary problems for ultra-parabolic equations. Two splitting methods are used to transform the whole time-dependent problem of a fixed strike Asian option into two unsteady subproblems of a smaller complexity. The first subproblem is a time-dependent convection-diffusion and the finite volume difference method of S. Wang [6] is applied for its discretization. The second one is a transport problem and is approximated by monotone weighted difference schemes. The positivity property of the numerical methods is established. Numerical experiments are discussed.