Author(s)

A.J. Davies, M.E. Honnor, C.H. Lai, A.K. Parrott & S. Rout

Abstract

A distributed algorithm is developed to solve the Black-Scholes equation in the hedging of portfolios. The Black-Scholes equation is parabolic in time and such problems have been shown to be ideally suited to the use of the Laplace transform rather than a finite difference time-stepping method. The application of the Laplace transform to the Black-Scholes equation gives rise to an elliptic problem and any suitable solver may be used in the transform space. We shall use the finite volume method. The numerical inversion of the Laplace transform is effected by Stehfest’s method which requires a solution for each transform parameter. Since these solutions are obtained independently the method is an excellent candidate for an implementation in a distributed com

Keywords