A numerical study of Asian option with high-order compact finite difference scheme

In this paper, an unconditionally stable compact finite difference scheme is proposed for the solution of Asian option partial differential equation. Second derivative approximations of the unknowns are eliminated with the unknowns itself and their first derivative approximations while retaining the fourth order accuracy and tri-diagonal nature of the scheme. Proposed compact finite difference scheme is fourth order accurate in spatial variable and second order accurate in temporal variable. Moreover, consistency, stability and convergence of the proposed compact finite difference scheme is proved and it is shown that proposed compact finite difference scheme is unconditionally stable. It is shown that for a given accuracy, proposed compact finite difference scheme is significantly efficient as compared to the central difference scheme. Numerical results are given to validate the theoretical results.