Year of Award

2016

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics.

Principal Supervisor

Ling, Leevan

Keywords

Capital assets pricing model;Differential equations;Fractional calculus.

Language

English

Abstract

The standard Black-Scholes model is under the assumption of geometric Brownian motion, and the log-returns for Black-Scholes model are independent and Gaussian. However, most of the recent literature on the statistical properties of the log-returns makes this hypothesis not always consistent. One of the ongoing research topics is to nd a better nancial pricing model instead of the Black-Scholes model. In the present work, we concentrate on two typical 1-D option pricing models under the general exponential L evy processes, namely the nite moment log-stable (FMLS) model and the the Carr-Geman-Madan-Yor-eta (CGMYe) model, and we also propose a multivariate CGMYe model. Both the frameworks, and the numerical estimations and simulations are studied in this thesis. In the future work, we shall continue to study the fractional partial di erential equations (FPDEs) of the nancial models, and seek for the e cient numerical algorithms of the American pricing problems. Keywords: fractional partial di erential equation; option pricing models; exponential L evy process; approximate solution.

Comments

Principal supervisor: Doctor Ling Leevan. ; Thesis submitted to the Department of Mathematics. ; Thesis (Ph. D.)--Hong Kong Baptist University, 2015

Bibliography

Includes bibliographical references (pages 109-119)

Copyright

The author retains all rights to this work. The author has signed an agreement granting HKBU a non-exclusive license to archive and distribute their thesis.


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