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Best book on interest rate models 
This is the best book available on interest rate models. Very detailed. Much more focused and readable than Rebonato's book. More pragmatic and explicit than Musiela and Rutkowski. Not as theoretical as Hunt and Kennedy. James and Webber also looks very good, but I'm not that familiar with it. All other books have only bits and pieces on interest rates.
The best book I have read on the subject
With all the due respect to the other authors I would say that if one is interested in a good theoretical book whihc is also good on the implementation side then the book of Brigo and Mercurion is definetly the best book I have ever read on the subject. Anyone interested in implementing the LMM/BGM/MSS model in practice is well advised to read it. I would just say that this is certainly a must have in the field.
New stuff and nice overview: hard to beat!
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.
Nicely written overview of interest rate models 
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.
Well written and useful book
In my humble opinion, this is the best book on Interest Rate modeling out there. The writing style is clear and focused and the appendices are fantastic. The book is rigorous but someone with some background in Stochastic Calculus will find it easy to follow. If you need refresher, dont worry the authors have you covered, see the appendix on Stochastic Calculus. Not an introductory book. Very exciting book.
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