Interest Rate Models [Hardcover]

Damiano Brigo (Author), Fabio Mercurio (Author)

Book Description

ISBN-10: 3540417729 | ISBN-13: 978-3540417729 | Publication Date: August 9, 2001 | Edition: 1

The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced.   The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered.   The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives.   The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.

Editorial Reviews

Review

From the reviews: SHORT BOOK REVIEWS "The text is no doubt my favorite on the subject of interest rate modeling. It perfectly combines mathematical depth, historical perspective and practical relevance. The fact that the authors combine a strong mathematical (finance) background with expert practice knowledge (they both work in a bank) contributes hugely to its format. I also admire the style of writing: at the same time concise and pedagogically fresh. The authors’ applied background allows for numerous comments on why certain models have (or have not) made it in practice. The theory is interwoven with detailed numerical examples…For those who have a sufficiently strong mathematical background, this book is a must." From the reviews of the second edition: "The book ‘Interest Rate Models – Theory and Practice’ provides a wide overview of interest rate modeling in mathematical depth. … The authors found a good approach to present a mathematically demanding area in a very clear, understandable way. The book will most likely become … one of the standard references in the area. … if one were to buy only one book about interest rate models, this would be it." (David Skovmand and Michael Verhofen, Financial Markets and Portfolio Management, Vol. 21 (1), 2007) "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. … is simply a must for all. Especially, I would recommend this to students … . Overall, this is by far the best interest rate models book in the market." (Ita Cirovic Donev, MathDL, May, 2007) "This is a very detailed course on interest rate models. Its main goal is to construct some kind of bridge between theory and practice in this field. From one side, the authors would like to help quantitative analysts and advanced traders handle interest-rate derivatives with a sound theoretical apparatus. … Advanced undergraduate students, graduate students and researchers should benefit from reading this book and seeing how some sophisticated mathematics can be used in concrete financial problems." (Yuliya S. Mishura, Zentralblatt MATH, Vol. 1109 (11), 2007)

From the Publisher

Please note that the first edition is out of print and the second will be available in March 2006 (ISBN 3540221492)

Product Details

• Hardcover: 518 pages
• Publisher: Springer; 1 edition (August 9, 2001)
• Language: English
• ISBN-10: 3540417729
• ISBN-13: 978-3540417729
• Product Dimensions: 9.2 x 6.1 x 1.3 inches
• Shipping Weight: 2 pounds
• Average Customer Review: 4.7 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #1,035,092 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

46 of 47 people found the following review helpful:

4.0 out of 5 stars Nicely written overview of interest rate models, December 15, 2001

By 

Rama CONT (New York) - See all my reviews
(REAL NAME)   

This review is from: Interest Rate Models (Hardcover)

This recent book, written by two Italian "quants" Mercurio & Brigo, gives a nice and accessible overview of interest rate models which is a compromise between the practitioner viewpoint, expressed for ex. in Rebonato's book "Interet Rate option models"
and the theoretical viewpoint such as the one in Musiela & Rutkowski.
The authors, themselves PhDs in quantitative finance/ applied maths, wrote this book while working as quants in an Italian bank and this first hand contact with the market gave them a
practical view on the subject which markes this book very interesting.

The book contains a "rational" catalogue of models used in practice ( as opposed to models which are impossible to implement!).

In contrast with academic books on interest rate modeling which deal with HJM formulation, there is a lot of emphasis here on LIBOR and Swap market models
(BGM -Jamshidian models) which reflects the current market practice. This is a positive point since there are not many books with details on implementing and using these "market models".

Part II: Interest rate models in practice is particularly useful because it deals with implementation and calibration which, as any practitioner knows, are important and usually delicate issues.
However calibration issues are dealt with somewhat lightly, especially recent developments on modeling cap/swaption smiles
are not included here.

This book can also be used for a graduate level/PhD course on interest rate models.

There are a lot of numerical examples in the book and mathematics is kept to the necessary level while keeping the
approach both rigorous and understandable.

Overall, it is one of the best books written on the subject.
I highly recommend it to PhD students, quants and researchers interested in this field.

38 of 40 people found the following review helpful:

5.0 out of 5 stars New stuff and nice overview: hard to beat!, January 16, 2002

By A Customer

This review is from: Interest Rate Models (Hardcover)

In the late nineties I went through Brigo's innovative work on stochastic nonlinear filtering with differential geometry techniques. I was favorably impressed by results and style, particularly in his dissertation and in his 'geometry in present day science' very readable overview. Interesting results are found and nicely told with accurate - but not pointlessly complicated - advanced mathematics for the problems at hand, I reasoned.

I've followed a similar path from control to finance, and having worked with interest rate models, I couldn't help but order this Brigo-Mercurio book. I had high expectations 'cause these two guys are working in a bank on the real thing.

Sure enough I'm not disappointed.

1-factor models are handled with great care, a ton of formulas and recipes are given. I've never seen this kind of analysis of pricing with Gaussian 1-f models. The new upgrade of the CIR model is interesting and accurate. "CIR++" is now my favorite 1-f model. I like the treatment of lognormal 1-f models and the explanation of Monte Carlo and trees -- the flow-chart for Bermudan swaptions is crystal clear! Plots of market implied structures and volatility calibration are useful additions.

The chapter on 2-f extensions has one of the best discussions on volatility, and two tons of useful formulas/recipes. Two dimensional trees!

The HJM chapter size is OK. I agree - the useful models embedded in HJM are short rate models and market models.

Market models - these three chapters alone are worth the book. You'll find yourself nodding as you read the guided tour. They make it look easy all the time. The exposition is focused, clear, intuitive, detailed. There's also new stuff, just check the calibration discussion! Smile modeling begins with a brilliant tour and ends with Brigo-Mercurio's new approach - the mixing dynamics - deserving a whole chapter if expanded.

The detailed explanation on products is a much welcome original addition. Cross currency derivatives!

Quotes - as in Brigo's old work - are a pleasant diversion while reading. The 500 and more pages are a treat given the competitive price.

Still there's room for improvements - more "CIR2++"! Something on 3-f models. Historical estimation of the correlation matrix and low-rank optimized approximations. Expand smile modeling! More hedging. Something on structured products. Cross currency libor model. chapter 9 - other interest rate models - sounds out of place and can be suppressed for other things.

This book rings true and has useful teachings for students, academics and practitioners. Although it requires some background in stochastic calculus, it's hard to beat on the pricing front. Kudos to Brigo and Mercurio! It only harms there aren't enough books like this.

22 of 23 people found the following review helpful:

5.0 out of 5 stars Definitely a must for quants and financial engineer !!!, September 11, 2001

By 

razafindrakoto jean-claude (Paris, FRANCE) - See all my reviews

This review is from: Interest Rate Models (Hardcover)

Though not precisely at beginner level, it is one of the best financial mathematics book combining rigourous theory with actual practice. I use this book as a reference book in combination with Kennedy and Hunt (Financial Derivatives), with Wilmott's Derivatives. Brigo and Mercurio's book gives an accurate account of the latest research on interest rate derivatives. They provide very good information (theory and practice) on calibration to cap/floor, swaptions data. A "must buy it immediately" book for quants and financial engineers, and also for graduates in quantitative finance. Could be recommended to newcomers in the area of mathematical finance, interested in knowing how mathematics is applied to concrete financial problems.