A Very Fast and Accurate Boundary Element Method for Options with Moving Barrier and Time-Dependent Rebate

40 Pages Posted: 23 Oct 2009

Date Written: March 12, 2009

Abstract

A numerical method to price options with moving barrier and time-dependent rebate is proposed. In particular, using the so-called Boundary Element Method, an integral representation of the barrier option price is derived in which one of the integrand function is not given explicitly but must be obtained solving a Volterra integral equation of the first kind. This equation is affected by several kinds of singularities, some of which are removed using a suitable change of variables. Then the transformed equation is solved using a low-order finite element method based on product integration. Several numerical experiments are carried out showing that the method proposed is extraordinarily fast and accurate. In particular a high level of accuracy is achieved also when the initial price of the underlying asset is close to the barrier, when the barrier and the rebate are not differentiable functions, or when the option's maturity is particularly long. Finally the numerical method proposed in this paper performs significantly better than binomial and trinomial lattices that are commonly employed in barrier option pricing.

Keywords: Barrier Option, Time-Dependent Barrier, Boundary Element Method, Volterra Integral Equation

JEL Classification: C02, C63, G13

Suggested Citation

Ballestra, Luca Vincenzo and Pacelli, Graziella, A Very Fast and Accurate Boundary Element Method for Options with Moving Barrier and Time-Dependent Rebate (March 12, 2009). Available at SSRN: https://ssrn.com/abstract=1492667 or http://dx.doi.org/10.2139/ssrn.1492667

Luca Vincenzo Ballestra

University of Bologna ( email )

Piazza Scaravilli 2
Bologna, 40100
Italy

Graziella Pacelli (Contact Author)

Polytechnic University of Marche ( email )

Piazzale Martelli 8
Ancona, 18039
Italy
+39(0)2207050 (Phone)

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