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Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula

Séan Dineen
American Mathematical Society
Publication Date: 
Number of Pages: 
Graduate Studies in Mathematics 70
[Reviewed by
Ita Cirovic Donev
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The Black-Scholes formula is one of the most well-known, or at least most talked about, concepts in finance. It is used for derivative pricing. 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.

The presentation is very lucid. The book starts with a very gentle introduction to the time value of money, interest rates, hedging and arbitrage. Concepts from analysis and probability are included where needed. From the very start of the book the author combines finance with mathematics. The second part of the book deals with some more serious topics, such as measure theory, probability theory and some stochastic processes. The author explains as much as is needed for later derivation of the Black-Scholes formula. The presentation is quite refreshing (because more elementary) compared to what we are generally used to when in comes to measure theory or graduate level probability theory texts. Students should appreciate the effort put into this. Each chapter ends with plenty of exercises for which there are solutions at the end of the book. The author ends with the derivation of the Black-Scholes formula.

A nice thing about this book is that chapters are not "cut-off from each other" in the sense that the author explains one thing only; rather, there are large examples within the more theoretical parts of probability theory and stochastic processes that lead to either understanding of derivatives pricing or to the derivation of the Black-Scholes formula. This enables the reader to immediately see the application and later to relate more easily to the developed concepts.

A strong background in probability theory and analysis will be sufficient to master the book. This book is an excellent choice for graduate students in mathematical finance as well as practitioners with the required background.

Ita Cirovic Donev is a PhD candidate at the University of Zagreb. She hold a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical mehods of credit and market risk. Apart from the academic work she does consulting work for financial institutions.

  • Money and markets
  • Fair games
  • Set theory
  • Measurable functions
  • Probability spaces
  • Expected values
  • Continuity and integrability
  • Conditional expectation
  • Martingales
  • The Black-Scholes formula
  • Stochastic integration
  • Solutions
  • Bibliography
  • Index