A Boundary Element Formulation for the Pricing of Barrier Options

Shih-Yu Shen^2*, Yi-Long Hsiao¹

¹Department of Finance, National Dong Hwa University, Taiwan, China.
²Institute of Applied Mathematics, National Cheng-Kung University, Taiwan, China.

DOI: 10.4236/ojmsi.2013.13006                

Abstract

In this article, we derive a boundary element formulation for the pricing of barrier option. The price of a barrier option is modeled as the solution of Black-Scholes’ equation. Then the problem is transformed to a boundary value problem of heat equation with a moving boundary. The boundary integral representation and integral equation are derived. A boundary element method is designed to solve the integral equation. Special quadrature rules for the singular integral are used. A numerical example is also demonstrated. This boundary element formulation is correct.

Keywords

Boundary Element Method; Black-Scholes Equation; Moving Boundary; Option Pricing; Barrier Option

Conflicts of Interest

The authors declare no conflicts of interest.

References

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