# Introduction to the Mathematics of Finance

## Arbitrage and Option Pricing

• Steven Roman
Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xvi
2. Steven Roman
Pages 1-10
3. ### Options and Arbitrage

1. Front Matter
Pages 11-11
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Pages 13-27
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Pages 29-37
4. ### Discrete-Time Pricing Models

1. Front Matter
Pages 39-39
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Pages 41-83
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Pages 85-102
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Pages 103-139
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Pages 141-155
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Pages 157-168
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Pages 169-189
5. ### The Black–Scholes Option Pricing Formula

1. Front Matter
Pages 191-191
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Pages 193-213
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Pages 215-244
6. Back Matter
Pages 245-287

### Introduction

The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model.

This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed.

The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options.

### Keywords

Black-Scholes option pricing formula Discrete-time model Martingale measures arbitrage binomial model discrete probability mathematical finance optimal stopping option pricing pricing nonattainable alternatives stochastic processes

• Steven Roman
• 1
1. 1.IrvineUSA