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Interest Rate Models — Theory and Practice: With Smile, Inflation and Credit

Damiano Brigo and Fabio Mercurio
Springer Verlag
Publication Date: 
Number of Pages: 
Springer Finance
BLL Rating: 

The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Ita Cirovic Donev
, on

This is the book on interest rate models and should proudly stand on the bookshelf of every quantitative finance practitioner and student involved with interest rate models. If you are looking for one reference on interest rate models then look no further as this text will provide you with excellent knowledge in theory and practice.

The book under review is the second edition and indeed waiting for it was worthwhile. The second edition grew to almost 1000 pages. If the size and table of contents does not already scare you away then we can try saying some more things about it.

There is a general "fault" in the publishing business when it comes to the area of mathematical finance: there are plenty of books that cover theoretical concepts, but, in most cases, it hard for an inexperienced reader to learn to apply these concepts in his daily activities. There is a lack of practical/applied books that provide the flavor of the theory but also give the reader the necessary connection to real world problems. Too many times we, the readers, are faced with artificial examples that really do not apply in practice. This book can be seen as an "outlier" from the general crowd as it marvelously blends theory and real practical examples.

The book is divided into eight parts:

  • Part I – Basic Definitions and No-Arbitrage
  • Part II – From Short Rate Models to HJM
  • Part III – Market Models
  • Part IV – The Volatility Smile
  • Part V – Examples of Market Payoffs
  • Part VI – Inflation
  • Part VII – Credit
  • Part VIII – Appendices

As the table of contents is rather detailed I will not go further and describe what is covered in the book, but focus rather on the style in which it was covered. The first thing I can appreciate is the mathematical formulation of even such “trivial” concepts as basic definitions of interest rates. Most books just explain these introductory concepts and move on, leaving a gap behind. In this book you will get acquainted with notation from the second page.

Given that this is a technical book, I should say that it is extremely easy to follow the mathematical expositions. There are no problems with “mysterious” notation. Overall the book is extremely detail oriented. Factor models, market models and discussion on calibration are covered carefully. Explanations are lucid, with numerous numerical examples. Part II, including one-factor and two-factor models, is also extremely detailed. The theory is so well presented and explained that you don’t have a feeling that you are dealing with theoretical exposition; this is not the usual very dry and narrow account. There are many graphical aids to help in understanding. Examples and useful suggestions are given throughout the text. This type of narrative style continues throughout the book.

Given so much intuitive explanation and useful advice, it is no wonder that the book has so many pages. In the end, if one covers this book cover to cover (in an efficient manner) one will definitely feel much, much more confident and knowledgeable about interest rate models.

It is hard to think who, assuming an interest in interest rate models, couldn’t benefit from this book. It is simply a must for all. Especially, I would recommend this to students who intend to have a career in mathematical finance, as this will provide them with theory but also, and maybe even more important, the actual real world problems and advice. Apart from students, most practitioners have been waiting for the book to come out. I believe that all groups of readers interested in the field will find this book extremely useful. Overall, this is by far the best interest rate models book on the market.

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.