A fourth order numerical method based on B-spline functions for pricing Asian options

This paper is concerned with the construction of a higher order numerical method for pricing Asian options with fixed strike price. We first transform the two-dimensional partial differential equation governing the value of an Asian option into a one-dimensional partial differential equation. In this method, the temporal variable is discretized by means of Crank-Nicolson scheme and the spatial variable is discretized by means of quartic B-spline collocation approach. The discretization is based on uniform mesh. We prove that the method is fourth-order convergent with respect to space variable and second-order convergent with respect to time variable in the maximum norm. Stability of the method is analyzed. Numerical experiment is carried out to demonstrate the applicability and efficiency of the method. It is shown that the rates of convergence predicted theoretically are same as that obtained numerically and the method is unconditionally stable. The approximate solution corresponding to the present method has been compared with the analytical result. Moreover, our results have been compared with those obtained by other methods. The option and delta values for various values of volatilities and interest rates are computed. (C) 2020 Elsevier Ltd. All rights reserved.