The use of the Black-Scholes model and formula is pervasive in financial markets. There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of this book is to introduce advanced undergraduates and beginning graduate students studying the mathematics of finance to the Black-Scholes formula. The author uses a first-principles approach, developing only the minimum background necessary to justify mathematical concepts and placing mathematical developments in context.

The book skillfully draws the reader toward the art of thinking mathematically and then proceeds to lay the foundations in analysis and probability theory underlying modern financial mathematics. It rigorously reveals the mathematical secrets of topics such as abstract measure theory, conditional expectations, martingales, Wiener processes, the Itô calculus, and other ingredients of the Black-Scholes formula. In explaining these topics, the author uses examples drawn from the universe of finance. The book also contains many exercises, some included to clarify simple points of exposition, others to introduce new ideas and techniques, and a few containing relatively deep mathematical results.

The second edition contains numerous revisions and additional material designed to enhance the book's usability as a classroom text. These changes include insights gleaned by the author after teaching from the text, as well as comments and suggestions made by others who used the book. Whereas the revised edition maintains the original approach, format, and list of topics, most chapters are modified to some extent; in addition, the rearrangement of material resulted in a new chapter (Chapter 9).

With the modest prerequisite of a first course in calculus, the book is suitable for undergraduates and graduate students in mathematics, finance, and economics and can be read, using appropriate selections, at a number of levels.

Readership

Undergraduate and graduate students interested in probability and financial mathematics.

Reviews

From reviews for the First Edition:

"For budding financial engineers, this is an outstanding introduction to the mathematics that underlies derivatives pricing theory. ... It also offers plenty of exercises that will help you build mastery.

"Dineen won an award (Best Books of 2006) for providing a treatment of finanical engineering math that is simultaneously accessible and rigorous."

-- Glyn Holton, founder Contingency Analysis and Riskbook.com

"... an excellent choice ... This book provides a thorough presentation of the mathematics behind the derivatives pricing formula. It is written for mathematicians as well as finance students or professionals."

-- MAA Reviews

"... one of the author's aims is to entice the students by the beauty of mathematics, which he illustrates very well. If a course instructor teaching from the book succeeds in this, my guess is that the course will be a great success.

"It outshines most of its competitors ... variety of nice exercises and solutions ..."

-- Mathematical Reviews