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.
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.
