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Title:The Hilbert Transform and its Applications in Computational finance
Author(s):Lin, Xiong
Director of Research:Feng, Liming
Doctoral Committee Chair(s):Song, Renming
Doctoral Committee Member(s):Feng, Liming; Bauer, Robert; Sreenivas, Ramavarapu S.
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Hilbert transform
Fourier transform
Sinc series
Barrier option
Bermudan option
Lookback option
Abstract:This thesis is devoted to the study of the Hilbert transform and its applications in computational finance. We will show in this thesis that under some mild conditions, the Hilbert transform can be approximated by the discrete Hilbert transforms with exponentially decaying errors in both one dimensional and two dimensional cases. The resulting discrete Hilbert transform can be efficiently implemented using fast Fourier transform. Based on this theory, many effective numerical schemes are developed to price European and American type vanilla and exotic options under various financial assets models.
Issue Date:2011-01-21
Rights Information:Copyright 2010 Xiong Lin
Date Available in IDEALS:2011-01-21
Date Deposited:2010-12

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