Introduction to the Mathematics of Finance

Arbitrage and Option Pricing

  • Steven Roman

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

Table of contents

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

    1. Front Matter
      Pages 11-11
    2. Steven Roman
      Pages 13-27
    3. Steven Roman
      Pages 29-37
  4. Discrete-Time Pricing Models

    1. Front Matter
      Pages 39-39
    2. Steven Roman
      Pages 41-83
    3. Steven Roman
      Pages 103-139
    4. Steven Roman
      Pages 141-155
    5. Steven Roman
      Pages 169-189
  5. The Black–Scholes Option Pricing Formula

    1. Front Matter
      Pages 191-191
    2. Steven Roman
      Pages 193-213
    3. Steven Roman
      Pages 215-244
  6. Back Matter
    Pages 245-287

About this book


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.


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

Authors and affiliations

  • Steven Roman
    • 1
  1. 1.IrvineUSA

Bibliographic information