Ortiz Gracia, LuisVives i Santa Eulàlia, Josep, 1963-Garcı́a Villa, Felipe2019-03-052019-03-052018-09-11https://hdl.handle.net/2445/129546Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Luis Ortiz Gracia i Josep Vives i Santa Eulàlia[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).63 p.application/pdfengcc-by-sa (c) Felipe Garcı́a Villa, 2018http://creativecommons.org/licenses/by-nc-sa/3.0/es/Espais de HilbertOndetes (Matemàtica)Treballs de fi de màsterDistribució (Teoria de la probabilitat)Matemàtica financeraMètode de MontecarloOpcions (Finances)Hilbert spaceWavelets (Mathematics)Master's thesesDistribution (Probability theory)Business mathematicsMonte Carlo methodOptions (Finance)info:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess