A hybrid finite difference scheme for pricing Asian options

In this paper we apply a hybrid finite difference scheme to evaluate the prices of Asian call options with fixed strike price. We use the Crank–Nicolson method to discretize the time variable and a hybrid finite difference scheme to discretize the spatial variable. The hybrid difference scheme uses the central difference approximation whenever the mesh points are sufficiently away from the left-hand side of the domain to ensure the stability of the scheme; otherwise a midpoint upwind difference scheme is used. The matrix associated with the discrete operator is an M-matrix, which ensures that the spatial discretization scheme is maximum-norm stable. It is proved that the scheme is second-order convergent with respect to both time and spatial variables. Numerical experiments support these theoretical results.