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PADE APPROXIMANTS AND ONE OF ITS APPLICATIONS

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Date Issued:
2007
Abstract/Description:
This thesis is concerned with a brief summary of the theory of Padé approximants and one of its applications to Finance. Proofs of most of the theorems are omitted and many developments could not be mentioned due to the vastness of the field of Padé approximations. We provide reference to research papers and books that contain exhaustive treatment of the subject. This thesis is mainly divided into two parts. In the first part we derive a general expression of the Padé approximants and some of the results that will be related to the work on the second part of the thesis. The Aitken's method for quick convergence of series is highlighted as Padé . We explore the criteria for convergence of a series approximated by Padé approximants and obtain its relationship to numerical analysis with the help of the Crank-Nicholson method. The second part shows how Padé approximants can be a smooth method to model the term structure of interest rates using stochastic processes and the no arbitrage argument. Padé approximants have been considered by physicists to be appropriate for approximating large classes of functions. This fact is used here to compare Padé approximants with very low indices and two parameters to interest rates variations provided by the Federal Reserve System in the United States.
Title: PADE APPROXIMANTS AND ONE OF ITS APPLICATIONS.
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Name(s): fowe, Tame-kouontcho, Author
Mohapatra, Ram, Committee Chair
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2007
Publisher: University of Central Florida
Language(s): English
Abstract/Description: This thesis is concerned with a brief summary of the theory of Padé approximants and one of its applications to Finance. Proofs of most of the theorems are omitted and many developments could not be mentioned due to the vastness of the field of Padé approximations. We provide reference to research papers and books that contain exhaustive treatment of the subject. This thesis is mainly divided into two parts. In the first part we derive a general expression of the Padé approximants and some of the results that will be related to the work on the second part of the thesis. The Aitken's method for quick convergence of series is highlighted as Padé . We explore the criteria for convergence of a series approximated by Padé approximants and obtain its relationship to numerical analysis with the help of the Crank-Nicholson method. The second part shows how Padé approximants can be a smooth method to model the term structure of interest rates using stochastic processes and the no arbitrage argument. Padé approximants have been considered by physicists to be appropriate for approximating large classes of functions. This fact is used here to compare Padé approximants with very low indices and two parameters to interest rates variations provided by the Federal Reserve System in the United States.
Identifier: CFE0001682 (IID), ucf:47217 (fedora)
Note(s): 2007-05-01
M.S.
Sciences, Department of Mathematics
Masters
This record was generated from author submitted information.
Subject(s): Pade approximants
interest rate variations
density distribution
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0001682
Restrictions on Access: public
Host Institution: UCF

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