The Hilbert Transform and its Applications in Computational finance

Lin, Xiong

Permalink

https://hdl.handle.net/2142/18601 Copy

Description

Title

The Hilbert Transform and its Applications in Computational finance

Author(s)

Lin, Xiong

Issue Date

2011-01-21T22:51:17Z

Director of Research (if dissertation) or Advisor (if thesis)

Feng, Liming

Doctoral Committee Chair(s)

Song, Renming

Committee Member(s)

• Feng, Liming
• Bauer, Robert
• Sreenivas, Ramavarapu S.

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2010-12

Permalink

http://hdl.handle.net/2142/18601

Copyright and License Information

Copyright 2010 Xiong Lin

Owning Collections