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Shannon wavelets in computational finance
Abstract
Derivative securities, when used correctly, allow investors to increase their expected profits and minimize their exposure to risk. Options offer leverage and insurance for risk-averse investors while they can be used as ways of speculation for the more risky investors. When an option is issued, we face the problem of determining the price of a product at the same time we must make sure to eliminate arbitrage opportunities. In this thesis, we introduce a robust, accurate, and highly efficient financial option valuation technique, the so-called SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error bounds. This method is adapted to the pricing of European options and Discrete Lookback options. Numerical experiments show exponential convergence and confirm the robustness, efficiency and versatility of the method- Master thesis
- Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
- Fourier analysis
- Option pricing
- European options
- Lookback options
- Shannon wavelets
- Sinus cardinal function
- Fourier transform inversion
- Fourier, Anàlisi de
- Classificació AMS::65 Numerical analysis::65T Numerical methods in Fourier analysis