Numerical method for pricing discretely monitored double barrier option by orthogonal projection method

Abstract

In this paper, we consider discretely monitored double barrier option based on the Black-Scholes partial differential equation. In this scenario, the option price can be computed recursively upon the heat equation solution. Thus we propose a numerical solution by projection method. We implement this method by considering the Chebyshev polynomials of the second kind. Finally, numerical examples are carried out to show accuracy of the presented method and demonstrate acceptable accordance of our method with other benchmark methods.

Keywords

• double barrier option
• orthogonal projection
• chebyshev polynomial
• black-scholes model