ORCID Identifier(s)

0000-0001-5832-6714

Graduation Semester and Year

2021

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences

Department

Mathematics

First Advisor

Andrzej Korzeniowski

Abstract

Equity options are the most common types of financial derivatives that give an investor the right but not the obligation to buy or sell shares of stock at a given price in the future for a premium (option price) paid at present. The Classical Black- Scholes Formula solved a longstanding mathematical problem of finding no arbitrage option price by means of stochastic Ito calculus based on Geometric Brownian Motion dynamics of the stock price and a fixed interest rate over the option time horizon. We extend the Black-Scholes Model by adding a component of investor’s buying and selling strategies for Call and Put Option, in addition to relaxing the interest rate from fixed to evolving randomly, whereby reflecting the actual market environment. We first present a solution to an open problem regarding Call Option price under linear investment hedging for stochastic interest rate modeled by Cox-Ingersol-Ross process, via a Monte-Carlo simulation method. Next, we extend Put and Call Option pricing under linear investment strategy from the Black-Scholes setting to Hull-White interest rate model. Finally, based on our findings, we derive suitable modifications for practical implementation which inherently reflect the discrete nature of market transactions.

Keywords

European put options, Linear stock investment strategy, Cox-Ingersoll-Ross model, Hull-White model

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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