On the Application of Shannon Wavelet Inverse Fourier Techniques

On the Application of Shannon Wavelet Inverse Fourier Techniques: An Extension to Asian Option Valuation and European Option Pricing under the SABR Model

Wagner, Emma (TU Delft Electrical Engineering, Mathematics and Computer Science)

Oosterlee, Kees (mentor)
Ortiz Garcia, Antonio (mentor)
Cirillo, Pasquale (graduation committee)

Delft University of Technology

Applied Mathematics

2017-10-27

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.

Shannon wavelets
Option Pricing
Asian Options
SABR model
Fourier Transform
Levy process

http://resolver.tudelft.nl/uuid:246714bf-fd09-4b04-90b9-b1a070b3c9a3

Student theses

master thesis