Shannon wavelets inverse Fourier technique for computacional finance

Abstract

[en] European options are financial derivatives, governed by the solution of an integral, the so-called discounted expectation of the pay-off function. For the computation of the expectation we require knowledge about the probability density function of the stochastic asset price process, which is typically available by its Fourier transform. In this project, we will explore wavelets theory to be able to construct the Shannon wavelets and use them to describe the density function. Also, a numerical method proposed by Luis Ortiz-Gracia and Cornelis W. Oosterlee to price these derivatives will be presented. This is called SWIFT (Shannon wavelet inverse Fourier technique).