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.
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.
 F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-659. doi:10.1086/260062
 R. C. Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, Vol. 4, No. 1, 1973, pp. 141-183. doi:10.2307/3003143
 J. C. Cox, S. A. Ross and M. Rubinstein, “Option Pricing: A Simplified Approach,” Journal of Financial Economics, Vol. 7, 1979, pp. 229-264.
 N. Kunitomo and M. Ikeda, “Pricing Options with Curved Boundaries,” Mathematical Finance, Vol. 2, No. 4, 1992, pp. 275-298. doi:10.1111/j.1467-9965.1992.tb00033.x
 H. Geman and M. Yor, “Pricing and Hedging Double-Barrier Options: A Probabilistic Approach,” Mathematical Finance, Vol. 6, No. 4, 1996, pp. 365-378.
 A. Pelsser, “Pricing Double Barrier Options Using Laplace Transforms,” Finance and Stochastics, Vol. 4, No. 1, 2000, pp. 95-104. doi:10.1007/s007800050005
 R. Zvan, K. R. Vetzal and P. A. Forsyth, “PDE Methods for Pricing Barrier Options,” Journal of Economics Dynamics & Control, Vol. 24, No. 11, 2000, pp. 1563-1590.
 S. Sanfelici, “Galerkin Infinite Element Approximation for Pricing Barrier Options and Options with Discontinuous Payoff,” Decisions in Economics and Finance, Vol. 27, No. 2, 2004, pp. 125-151.
 A. M. L. Wang, Y. H. Liu and Y. L. Hsiao, “Barrier Option Pricing: A Hybrid Method Approach,” Quantitative Finance, Vol. 9, No. 3, 2009, pp. 341-352.
 S. Y. Shen and A. M. L. Wang, “On Stop-Loss Strategies for Stock Investments,” Applied Mathematics and Computation, Vol. 119, 2001, pp. 317-337.