Application of Laplace-Fourier Inversion to Option Pricing

Christophe Bahadoran and B. Leblanc
Centre de Mathématiques Appliquées, Palaiseau
mata@cmapx.polytechnique.fr

Abstract

In recent financial literature, several situations have emerged where the price of an option could be determined via its Laplace or Fourier transform. This method is computationally more efficient than a PDE approach, when the latter is available. Numerical inversion of transforms is a crucial but delicate matter which has no universal solution (cf. Davies and Martin (1979): Laplace transform inversion is still an art more than a science). Thus it is necessary to test and compare several algorithms. An extensive choice of methods is provided in Davies and Martin (1979) and Abate and Whitt (1991). In this paper, we provide effective numerical solutions for some significant cases where theory is available.