Keywords

Pade approximants, interest rate variations, density distribution

Abstract

This thesis is concerned with a brief summary of the theory of Pade 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 Pade 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 Pade 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 Pade[L/1] . We explore the criteria for convergence of a series approximated by Pade approximants and obtain its relationship to numerical analysis with the help of the Crank-Nicholson method. The second part shows how Pade approximants can be a smooth method to model the term structure of interest rates using stochastic processes and the no arbitrage argument. Pade approximants have been considered by physicists to be appropriate for approximating large classes of functions. This fact is used here to compare Pade approximants with very low indices and two parameters to interest rates variations provided by the Federal Reserve System in the United States.

Notes

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Graduation Date

2007

Semester

Spring

Advisor

Mohapatra, Ram

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0001682

URL

http://purl.fcla.edu/fcla/etd/CFE0001682

Language

English

Release Date

May 2007

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Included in

Mathematics Commons

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