A Boundary Element Formulation for the Pricing of Barrier Options

Shih-Yu  Shen; Yi-Long  Hsiao

doi:10.4236/ojmsi.2013.13006

Shih-Yu Shen^*, Yi-Long Hsiao

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

Cite this paper: Shen, S. and Hsiao, Y. (2013) A Boundary Element Formulation for the Pricing of Barrier Options. Open Journal of Modelling and Simulation, 1, 30-35. doi: 10.4236/ojmsi.2013.13006.

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