Binomial models in finance.

*(English)*Zbl 1107.91056
Springer Finance. New York, NY: Springer (ISBN 0-387-25898-1/hbk). xiii, 303 p. (2006).

The book is written by leading specialists in modern stochastic financial modelling. This is a comprehensive contemporary analysis of the most popular discrete time stochastic financial model, the binomial model.

The authors cover both classical topics involving binomial models and some very recent developments. A variety of questions are discussed for different type of options. New methods for approximate option pricing are presented and compared with other methods.

The chapter headings give a right impression about the content of the book:

1. Introduction. 2. The binomial model for stock options. 3. The binomial model for other contracts. 4. Multiperiod binomial models. 5. Hedging. 6. Forward and futures contracts. 7. American and exotic option pricing. 8. Path-dependent options. 9. The Greeks. 10. Dividents. 11. Implied voliatility trees. 12. Implied binomial trees. 13. Interest rate models. 14. Real options. There are Appendices (on binomial distribution, application of linear programming, voliatility estimation, etc.) Finally, there is a list of 79 well chosen references and a subject index.

The book is well written, with a good balance between mathematical tools and arguments and financial topics. It is nice to see proofs of several important properties of financial characteristics and rules for option pricing. Specific numerical examples are given to illustrate ideas and rules. Exercices are given at the end of each chapter.

The content and the way of writing will make this book popular for a wide category of readers. Among them are specialists in stochastic financial modelling, university students following a program in Financial mathematics and financial engineers. The book, in a combination with a couple of other sources, can be used for self-education, especially if the authors decide to include in the next edition at least hints to the exercices.

This reviewer is going to add the book to his golden collection of sources used for the course “Stochastic financial modelling” here at Newcastle University (UK).

Without any reservations the book can be strongly recommended not only to instituional libraries but also to anybody working or with interests in stochastic financial modelling.

The authors cover both classical topics involving binomial models and some very recent developments. A variety of questions are discussed for different type of options. New methods for approximate option pricing are presented and compared with other methods.

The chapter headings give a right impression about the content of the book:

1. Introduction. 2. The binomial model for stock options. 3. The binomial model for other contracts. 4. Multiperiod binomial models. 5. Hedging. 6. Forward and futures contracts. 7. American and exotic option pricing. 8. Path-dependent options. 9. The Greeks. 10. Dividents. 11. Implied voliatility trees. 12. Implied binomial trees. 13. Interest rate models. 14. Real options. There are Appendices (on binomial distribution, application of linear programming, voliatility estimation, etc.) Finally, there is a list of 79 well chosen references and a subject index.

The book is well written, with a good balance between mathematical tools and arguments and financial topics. It is nice to see proofs of several important properties of financial characteristics and rules for option pricing. Specific numerical examples are given to illustrate ideas and rules. Exercices are given at the end of each chapter.

The content and the way of writing will make this book popular for a wide category of readers. Among them are specialists in stochastic financial modelling, university students following a program in Financial mathematics and financial engineers. The book, in a combination with a couple of other sources, can be used for self-education, especially if the authors decide to include in the next edition at least hints to the exercices.

This reviewer is going to add the book to his golden collection of sources used for the course “Stochastic financial modelling” here at Newcastle University (UK).

Without any reservations the book can be strongly recommended not only to instituional libraries but also to anybody working or with interests in stochastic financial modelling.

Reviewer: Jordan M. Stoyanov (Newcastle upon Tyne)

##### MSC:

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

91G20 | Derivative securities (option pricing, hedging, etc.) |

91G30 | Interest rates, asset pricing, etc. (stochastic models) |

91G50 | Corporate finance (dividends, real options, etc.) |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |