Award Date

8-1-2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Hongtao Yang

Second Committee Member

Michael Marcozzi

Third Committee Member

Monika Neda

Fourth Committee Member

Pengtao Sun

Fifth Committee Member

Jianzhong Zhang

Number of Pages

136

Abstract

Pricing options under multi-factor models are challenging and important problems for financial applications. In particular, the closed form solutions are not available for the American options and some European options, and the correlations between factors increase the complexity and difficulty for the formulations and implements of the numerical methods.

In this dissertation, we first introduce a general transformation to decouple correlated stochastic processes governed by a system of stochastic differential equations. Then we apply the transformation to the popular two-factor models: the two-asset model, the stochastic volatility model, and the stochastic interest rate models. Based on our new formulations, we develop a mixed Monte Carlo method, a lattice method, and a finite volume-alternating direction implicit method for pricing the European and American options under these models. The proposed methods can be easily implemented and need less memory. Numerical results are also presented to validate our C++ programs and to examine our methods. It shows that our methods are very accurate and efficient.

Keywords

Decoupling; Finite volume - alternating direction implicit method; Lattice method; Mixed Monte Carlo method; Option pricing; Two-factor models

Disciplines

Applied Mathematics | Corporate Finance | Finance | Finance and Financial Management | Mathematics

Language

English


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