Efficient and fast numerical method for pricing discrete double barrier option by projection method

In this paper, we introduce a new and considerably fast numerical method based on projection method in pricing discrete double barrier option. According to the Black-Scholes framework, the price of option in each monitoring dates is the solution of well-known partial differential equation that can be expressed recursively upon the heat equation solution. These recursive solutions are approximated by projection method and expressed in operational matrix form. The most important advantage of this method is that its computational time is nearly fixed against monitoring dates increase. Afterward, in implementing projection method we use Legendre polynomials as an orthogonal basis. Finally, the numerical results show the validity and efficiency of presented method in comparison with some others.