FFT-abstract

FFT-abstract - Merton’s Jump-diffusion(MJD models I will...

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Introduction to Fourier Transform Methods for Option Pricing Research Seminar in Financial Mathematics | Fall 2010 Pierre Garreau Florida State University 1017 Academic Way, 208 Love Building Tallahassee, FL 32306 www.math.fsu.edu/~pgarreau Department of Mathematics | Florida State University Abstract This paper introduces Fourier Transform methods for Option Pricing. I present the pricing problem and its dual in the context of a modelisation of asset returns thanks to random walks and their limits: infinitely divisible distributions. After a review of the Black-Scholes (BS) and
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Unformatted text preview: Merton’s Jump-diffusion (MJD) models, I will show how L´ evy processes arise naturally to model the dynamics of stocks and will focus on their characteristic function in connection with Fourier Transforms. Fast Fourier Transform methods are then discussed to price options as presented by P. Carr (1999). I then address convergence issues and will present the results obtained for BS, MJD and Variance Gamma. Key words: L´ evy processes, Fourier Transform, Option pricing, Black-Scholes, Jump-Diffusion....
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This note was uploaded on 01/15/2012 for the course MAT 5939 taught by Professor Garreau during the Fall '11 term at FSU.

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