On the Application of Shannon Wavelet Inverse Fourier Techniques

An Extension to Asian Option Valuation and European Option Pricing under the SABR Model

Master thesis (2017)

Authors

E.I. Wagner Electrical Engineering, Mathematics and Computer Science

Contributors

C.W. Oosterlee (supervisor 1)
A.J. Ortiz Garcia (supervisor 1)
P. Cirillo (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Option Pricing SABR model Shannon wavelets Asian Options Levy process Fourier Transform
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Published Date

27-10-2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

This work is on the extension of the SWIFT method to option pricing problems where the sum of lognormals occurs. The SWIFT method (ShannonWavelet Inverse Fourier Technique) is extended to the valuation of geometric Asian options and arithmetic Asian options with a Lévy process as underlying price process and the valuation of European options under SABR dynamics. In both applications a sum of lognormals (or sum of increments) occurs. The main result in this thesis is the SWIFT-SIA method (SWIFT sinc integral approximation), which is applied to the valuation of arithmetic Asian options as well as to the valuation of European options under the SABRmodel. Within the SWIFT-SIA method the recovery of the probability density function is obtained by an approximation, instead of a numerical integration method, which results in a very fast method compared to an alternative method based on cosine expansions as well as high accuracy in the option values.

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