Book Description
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 several new chapters. 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 new chapters. 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.
Customer Reviews:
Best book on interest rate models.......2002-12-14
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.......2002-05-06
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!.......2002-01-17
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.......2001-12-15
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.......2001-11-04
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.
Book Description
This introductory text provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. M. Joshi covers the strengths and weaknesses of such models as stochastic volatility, jump diffusion, and variance gamma, as well as the Black-Scholes. Examples and exercises, with answers, as well as computer projects, challenge the mind and encourage learning how to become a good quantitative analyst.
Customer Reviews:
An excellent starting point. ... .......2007-01-24
This book is excellent for a deeper introductory look at mathematical
finance. It is well-written, and strikes a nice balance
between sophistication and accessiblity. Its companion volume on
C++ development in the context of quantitative finance is also well
worth examining. I look forward to seeing the follow up volume, which
will cover additional, more advanced topics.
Very Good.......2006-11-03
I'm totally satisfied. About the timing of the shipment, to me very quick and about the quality of the product, that was in good condition.
Very useful book.......2006-02-01
This is a great book for those who want to learn quantitative finance, but don't have the benefit of being enrolled in a financial engineering program. It has the advantage of being self-contained and begins instruction from the ground up: you can "cold start" on the subject with this book. Just a basic knowledge of differential equations (non-stochastic) is required.
It is natural to compare Joshi's book with Hull, but I would recommend reading them together as they have complementary strengths. Hull is over-simplified but provides financial intuition and descriptions of real-world practices. However it does not have modern notation. It also does not teach you how to solve actual pricing problems from the mathematical or computational point of view. Joshi's book does all of that and even helps you develop some mathematical intuition for the models. It also has some computing projects in c++ that a student could do.
The real comparison should be with Neftci's mathematical finance book and Baxter and Rennie. I think Joshi's book is much better than either of the two. I could barely read Neftci after a while because of the errors and bad organization. B&R is way too formal in my opinion for such an applied subject. Joshi's book has good notation and organization which builds confidence in the author, plus it is very applied so you feel you are learning something useful. It has none of that lemma-proof style which can be so unappealing to non-pure mathematicians.
If you already know the field.......2005-10-11
If you already know almost everything it is a very good book. No error and the guy knows what he is doing. However, if you know everything, why do you want to buy this book?
Unfortunately, if you do not know everything, the book is very difficult to understand. At a first lecture I never get the point. After reading some others books and implement the problem, I can indeed understand the chapter... but what is the use? Maybe we (the author and me) do not have the same way of thinking...
Another bad point is that there is no implementation. So if you are blocked somewhere you are dead.
Moreover the authors spend 16 chapter of 18 on equities and 2 on interest rate. But this last field correspond to 90% of the market! ...
Well,..., However,... not so bad ... so, 3 stars
This is a highly recommended work for any quant........2005-06-18
As I write this in June of 2005, quantitative finance has grown up. What was once a cross-over subfield of finance with a veneer of mathematics is now a field unto itself, and hence, in the past decade there have been an explosion of books which often replicate or restate what has been said before with little new to add. Also, there remains an unforgiving gap between introductory texts that are too superficial and specialists' mathematics books that are rigorous and difficult works beyond the commitment for mastery of the busy, intelligent, practical front-line quant. In addition, works that were once adequate are now simplistic and under serve their readers by lulling them into false confidence. Into this fray Dr. Mark S. Joshi's "The Concepts and Practice of Mathematical Finance" enters with a modern voice and delivers what previous texts have only promised and failed to. The work lives up to its title by presenting both concepts and practicalities, and makes other works that do neither well obsolete. Those familiar with my other reviews on quantitative finance texts know that I place a premium on clarity, and on this front Joshi deserves six stars, for he is a master of what William Strunk called "the plain style." I am always sensitive to the fact that many of the world's best quants come from nations where English is not the first language. Readers from China, France, Germany, Greece, Italy, Norway, Sweden, Russia and eastern Europe will enjoy Joshi's clarity and find his English easy to follow. It would be impossible to cover everything in quanfin in a single volume, however there is nothing horribly glossed over here and neither is there a single wasted word or equation.
I recommend Amazon review readers refer to the table of contents in the "Look Inside" feature to see what Joshi covers, but my own highlight is how welcome it is that Joshi focuses on risk from the very first word. Since Louis Bachelier risk measurement is what separates quantitative finance from "finance." Other books, including some quantitative finance works, start with cash flows, valuation, and discounting, and only add risk as an antecedent. Joshi correctly emphasizes risk first, last, and always, and for that elevation alone his work deserves five stars. From this foundation Joshi then covers very well pricing methods and arbitrage, simple and high dimensional trees, and the useful shortcuts of Ito calculus that makes tractable Zeno's paradox. Joshi also covers risk neutral and martingale methods, continuous barrier options, multi-look exotic options and incomplete markets and jump processes with an aim of showing these as typical problems for the working quant. Joshi's own references, index, and footnotes testify that by no means is he offering the first, nor the last, word on these knotty subjects, but his treatment is welcome just the same.
The target audience who would benefit from this text over others is four-fold. The primary audience is for first semester students in a graduate financial engineering program, for Joshi's "Concepts and Practice" will be handy throughout his or her studies and career. For those students unsure of their skills and with a limited budget considering between this and an introductory quantitative finance text I recommend Joshi over, say, Wilmott, for this work is more rigorous and in the long run will provide the better value as a practical companion. Within this audience I include professors looking for a high level foundational text for teaching practical risk management and derivatives pricing: this is the book to adopt, yes, even over Hull.
The second audience is for those trained in other science fields: pure mathematics, statistics, physics, etc. who are moving to finance jobs. This volume is an easy "one-stop shop" for you to re-tool your own background towards those topics and techniques used on a quant desk. While by no means covering everything, Joshi speaks your language and after digesting this work all else will fall into place and be understood and used with greater efficiency.
The third and broadest audience is one I am a member of: the already trained and practical "quant." Why should we need this book? My observation is that between reading (for example) Hull and Wilmott, Joshi's "Concepts" unavoidably covers many of the same topics, but also some things they do not and in ways they never could. Joshi is an expert practitioner at the top of his art, and that practical spirit is in every single page. For example, while Hull and Wilmott cover the concept and mathematics of stochastic volatility, Joshi writes from the point of view of the coding quant and discusses the issues of implementation. Joshi's "Concepts and Practice" serves a two fold purpose for a qaunt: it provides an additional voice and explanation of inescapably fundamental material, while bridging the gap of technical deployment for front line practitioners. This is not to say that Joshi offers us up a cookbook, for by no means is this such. Anyone who thinks they can simply buy this book and in a sleepy afternoon plug away code and technique and be done is missing the point: for this is a teaching text. Moreover, each house and set of problems and instruments and structured products to offer are different, to say nothing of the platforms one will be working on. That is why they call it "work." Therefore the practical quant should look to this text as a reference guidebook in a tool box.
As a fourth audience I cautiously recommend this book for those who are going into exotic product sales, but only those who have a good grounding in upper level calculus, linear and matrix algebra, time series analysis, and trees. Why? Simply put, you will be offering products built by quants who simply assume the knowledge in this book is a given. In addition, your better clients will (or should) have quants speaking this language, and the greater your own understanding of the concerns of your team and your clients the better your sales. If this work is too rigorous, then Wilmott's "Introduction to Quantitative Finance" quickly followed by Joshi's "Concepts and Techniques" is the course to follow.
Who is this work not for? Here are some tests. If you are a quant who can type at five lines of code a minute and can read Shreve and Karatzas drinking beer, then this work is too redundant for you. On my desk is a paper on a stochastic process with drift and viscosity under regime switching. If you are reading the same journal, then this work is too simple for you. If you have no idea what I've written about in the past three sentences, then this work is too hard for you.
In summary, Dr. Mark Joshi advances his excellent reputation as an intelligent, practical, and generous quant in offering "The Concepts and Practice of Mathematical Finance" and I recommend this book's wide adoption in graduate programs and its addition to reference libraries.
Book Description
In Volatility and Correlation 2
nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over
80ew or fully reworked material and is a must have both for practitioners and for students.
The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options.
The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface.
Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes.
Praise for the First Edition:
“In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.… The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.”
—Professor Ian Cooper, London Business School
“Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion…A rare combination of intellectual insight and practical common sense.”
—Anthony Neuberger, London Business School
Download Description
In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the perfect-replication approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author's philosophical approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes.
Customer Reviews:
Very good but missing little things here and there.......2007-02-08
Although the author warns the reader in the Preface, that because he ran out of pages (come on it is more than 800!) he omited dealing with Copulas, it is still a pitty that a book about correlation does not present at least a small chapter on this new (state-of-the-art) area.
Everything else is very good, solid material with a good balance between maths surrounding the topic, explanations and worked out examples.
very informative and reader friendly.......2007-01-09
for the first time I really understood risk neutral probability, explanations are excellent. unfortunately I am only read about 10 chapters int he book, should spend more time with it.
Average customer rating:
- It might be a good finance book,
- superb coverage of subject matter
- good but not excellent
- Good book to understand quantitative finance
- Investment Science must have
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Investment Science
David G. Luenberger
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ASIN: 0195108094 |
Book Description
Fueled in part by some extraordinary theoretical developments in finance, an explosive growth of information and computing technology, and the global expansion of investment activity, investment theory currently commands a high level of intellectual attention. Recent developments in the field are being infused into university classrooms, financial service organizations, business ventures, and into the awareness of many individual investors. Modern investment theory using the language of mathematics is now an essential aspect of academic and practitioner training. Representing a breakthrough in the organization of finance topics, Investment Science will be an indispensable tool in teaching modern investment theory. It presents sound fundamentals and shows how real problems can be solved with modern, yet simple, methods. David Luenberger gives thorough yet highly accessible mathematical coverage of standard and recent topics of introductory investments: fixed-income securities, modern portfolio theory and capital asset pricing theory, derivatives (futures, options, and swaps), and innovations in optimal portfolio growth and valuation of multiperiod risky investments. Throughout the book, he uses mathematics to present essential ideas of investments and their applications in business practice. The creative use of binomial lattices to formulate and solve a wide variety of important finance problems is a special feature of the book. In moving from fixed-income securities to derivatives, Luenberger increases naturally the level of mathematical sophistication, but never goes beyond algebra, elementary statistics/probability, and calculus. He includes appendices on probability and calculus at the end of the book for student reference. Creative examples and end-of-chapter exercises are also included to provide additional applications of principles given in the text. Ideal for investment or investment management courses in finance, engineering economics, operations research, and management science departments, Investment Science has been successfully class-tested at Boston University, Stanford University, and the University of Strathclyde, Scotland, and used in several firms where knowledge of investment principles is essential. Executives, managers, financial analysts, and project engineers responsible for evaluation and structuring of investments will also find the book beneficial. The methods described are useful in almost every field, including high-technology, utilities, financial service organizations, and manufacturing companies.
Customer Reviews:
It might be a good finance book,.......2007-08-14
but it's a terrible math book.
Too often, explanations, examples, and problems do not clearly explain the meanings of variables and applicable assumptions. This poor presentation of material makes the book barely usable to someone trying to learn the material for the first time.
superb coverage of subject matter.......2007-07-30
Prof. Luenberger currently teaches at Stanford and this book is used as the textbook for a 2-quarter series in investment science there. The coverage is concise and the math is manageable and yet extremely practical. I agree that this an excellent self-study book in the subject of investment science.
good but not excellent.......2007-03-15
This book serves very good introduction to mathematical finance. Particularly,
I enjoyed the discussion of bonds immunization, mean-variance theory, CAPM, APT.
It's most suitable for senior undergraduates or any junior graduate students.
But it doesn't deserve 5 star for the following reasons:
1) Most of the theories discussed so far in the book are TOO idealized and
over simplified. Financial data is dynamic and massive. In model quantitative/computational finance, the most important thing is to understand what the data says rather than what one thinks the data structure might be. With the book, one probably can only do some macroeconomic/very coarse analysis. Author should incorporate more data analysis evidence together with proposed theories.
2) The proof of ito's lemma is wrong(i.e. "Deltaz^2 --> deterministic as Deltat --> 0"). It's surprising since most books make the same mistake. It is the law of the large number contributes to the equality!(i.e. integration sense). The misunderstanding of the proof might lead to the misunderstanding of the hedging process.
3) In the commodity option pricing session, author demonstrated the use of futher market to price the option. This should be discussed further (i.e. black's model).
4) The volatility pumping session should be further researched. The explanation is
not satisfactory.
Good book to understand quantitative finance.......2005-06-10
Luenberger was a professor of optimization and his books on that subject are also very good. Clear and Precise. But sometimes he is extremely concise, so that you need to work a bit to completely understand a point.
In this book, we have again the same style (after all, it is the author style): Clear and precise book, GOOD choice of notation (I cant say the same thing about HULL's books) but sometimes extremely concise.
Overall, a good book to start learning and on a solid foundation.
Investment Science must have.......2005-03-24
Great book, covers lots of material and goes beyond by using the log utility to portfolio growth. Great buy!!!!
Book Description
In the 2nd edition some sections of Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.
The theme of stochastic volatility also reappears systematically in the second part of the book, which has been revised fundamentally, presenting much more detailed analyses of the various interest-rate models available: the authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions, never neglecting to examine liquid primary and derivative assets and identifying the sources of trading risk associated. This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on practical rather than theoretical aspects of financial modelling.
Customer Reviews:
Excellent introductory book to financial math.......2006-11-03
This book takes you through the math of finance step-by-step, passing through very simple examples first and then slowly adding complexity to the models studied. It is written very clearly and the prerequisites to reading this book are only some basic notions of probabilities (sigma-fields, probability measures).
Sometimes, the problem with math books is that they are "dry" and contain only a succession of theorems and proofs. In this one, the authors make a point of explaining in detail how different theorems and models relate to each other, and make extensive comparisons between them so that you get a better feel for how they work in practice.
The book is primarily a math book and can be light on market specifics. Do not buy this book as a practical "howto" in derivatives trading.
At the Forefront of Modern Mathematical Finance.......2005-05-23
This advanced text provides an excellent account of the current state-of-the art of options pricing/hedging models and interest rate term structure models. The book is accessible to both advanced practitioners of mathematical finance as well as to pure researchers in the field.
The book is in written in a mathematical style and contains rigorous proofs of many results. However, the main focus of the text is to describe the frontier of knowledge in the subject. Each section contains copious references to the literature and is so current that several references are to working papers. Many sections detail open problems and other areas suitable for scholarly research.
In their second edition, the authors provide an extremely useful critique of each modeling paradigm that they investigate. They also provide evidence for their position in the form of literature references which instruct the reader as to the shortcomings/limitations of a particular model. This information should prove quite valuable to model practitioners and implementers.
The authors assume an advanced background from the field of stochastic analysis, although they do provide an appendix which summarizes key results needed from the field. For the stochastic calculus prerequisites, I recommend Rogers & Williams "Diffusions, Markov Processes and Martingales" volumes I and II. Suitable prerequisites are also covered by Karatzas and Shreve in "Brownian Motion and Stochastic Calculus" 2nd edition. A good foundation in arbitrage pricing theory is also needed. I recommend the nice treatment by Bjork in "Arbitrage Theory in Continuous Time" 2nd edition.
The book is divided into two parts. The first part deals with options pricing in equity markets. Chapter 1 sets premlinaries required for the arbitrage theoretic framework, while Chapter 2 has a very nice treatment of discrete time models and finite financial markets.
In Chapter 3, the authors develop the Black-Scholes model along with the Bachelier model using arbitrage techniques. The models are compared and used as benchmark continuous time models and form the basis for all subsequent analysis.
Chapter 4 provides a nice survey of techniques used to price/hedge options in foreign equity and currency markets. The authors assume familarity of the basic workings of foriegn markets.
Chapter 5 is a terrific chapter on valuing American-style options. The American call option is thoroughly studied and approximation techniques for the American put option are introduced. The explicit derivations of the formulas are referenced to the literature.
Chapter 6 provides an introduction to exotic options, although the authors vary their use of the term 'exotic' to meaning 'not a standard European-style or American-style' in this chapter to meaning 'no readily available liquid market' in Chapter 7. The descriptions are quite accessible and the basic properties of the options are described along with pricing formulas (assuming the Black-Scholes framework).
Chapter 7 provides as complete an accounting as I have ever seen of the generalizations of the Black-Scholes model and motivates this from the point of view of volatility surfaces. Many of the well-known models are studied in detail, such as CEV, local volatility, and mixture models. The strengths and weaknesses of each model are analyzed. The stochastic volatility models of Wiggins (via Orenstien-Uhlenbeck processes), Hull-White, and Heston are studied, as is the SABR model. The chapter wraps up with a study of the SIV models, describes how the stochastic volatility models can be obtained via limits of GARCH models and surveys Jump-diffusion processes and Levy processes.
The second part of the book is concerned with term structure models and interest rate derivatives. The authors are quite well-know for their many contributions to this study and their treatment is authoritative.
Martingales & Finance.......2003-04-12
I have used this book for two courses in my MSc degree in Financial Maths...well this book is hard to understand at first glance, but, once you are introduced with a good course on stochastic analysis and applied probability, this is an illuminating book...I particularly enjoyed the part on foreing equity derivatives and exotic derivatives.....Harmed with patience this is definitely the book by which you can effectively gain a sound a knowledge on modern mathematical finance theory....reading in conjunction with Bingham-Kiesel book, could help understanding the foundation of the subject.
yes, but ..........2000-03-17
I've been using this book on and off over the last year. At first I was very impressed with the level of detail in the mathematics, especially as it was the only book at the time focussing on risk-neutral methods and covering BGM. But I've become increasing disillusioned with it of late. It's difficult to explain, but although the whole book is written in traditional theorem-proof style, there are no real proofs! (I have a PhD in math and have done research for 10 years so I should know a little about proofs.) The only "proofs" provided are basically symbol shifting, but the heart of the math is strangely absent. This is especially strange given the Springer series in which it appears.
In short, if you want a catalogue of methods this book does the job, but if you want a deeper understanding try Lars Nielsens book.
excellent book for post-John-Hull readers.......1999-08-17
This book covers essentially everything needed for a serious financial math study. It captures the spirit of modern financial math. For people with math, physics or engineering background, when you feel comfortable woth John Hull's books, then this book is right one, and a must one.
Average customer rating:
- Good explained yield curve fitting
- Could have been very good. A new edition could earn 5 stars.
- A real must !
- A must-have encyclopedia on term structure modeling
- Extraordinary
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Interest Rate Modelling: Financial Engineering
Jessica James , and
Nick Webber
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover
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ASIN: 0471975230 |
Book Description
This book provides a comprehensive resource on all the main aspects of valuing and hedging interest rate products. A series of introductory chapters reviews the theoretical background, pointing out the problems in using naïve valuation and implementation techniques. There follows a full analysis of interest rate models including major categories, such as affine, HJM and market models, and in addition, lesser well known types that include Consol, random field and jump-augmented models. Implementation methods are discussed in depth including the latest developments in the use of finite difference, lattice and Monte Carlo methods and their particular application to the valuation of interest rate derivatives. Containing previously unpublished material.
Interest Rate Modelling is a key reference work both for practitioners developing and implementing models for real and for academics teaching and researching in the field.
Interest Rate Modelling is an encyclopedic treatment of interest rates and their related financial derivatives. It combines advanced theory with extensive and down-to-earth data analysis in a way which is truly unique. For practitioners, students and scholars in the field, this impressive wok will be the standard reference for years to come.", Professor Tomas Bjork, , Stockholm School of Economics#
"...an excellent book. I am particularly pleased by its breadth and range of topics...the reader is provided with an informative and readable exposition.", Dr Farshid Jamshidian, , NetAnalytic#
"I particularly like the strong emphasis on the practicalities and calibration of interest rate models. This book will be invaluable as a comprehensive reference to students, researchers, and practitioners.", Professor Francis Longstaff, , The Anderson School at UCLA#"
This is a carefully written, scholarly but fascinating presentation of the field of Interest Rate Modelling. It combines the best of two worlds: the rigour expected from finance in acamedia with the relevance expected from finance in practice. James and Webber are truly masters of their market since this book is surely a must-buy for both researchers and practitioners. If only all finance books were written with this care and attention to detail.", Dr Neil Johnson, , Clarendon Laboratory, Oxford#
"Today, interest rates are key economic instruments. This is a mammoth treatise and must surely rank as one of the most comprehensive available on the topic. Anyone interested in modelling or simulating the behaviour of interest rates, be they practitioner, economist, mathematician or new entrant to the subject, will find within a wealth of pertinent material.", Professor Peter Richmond, , Trinity College Dublin#
Customer Reviews:
Good explained yield curve fitting.......2005-08-15
List different way of yield curve fitting method, and good explain why B-spline
is good. Also term structure on general manifold is interesting, although a review don't
think it's useful.
Could have been very good. A new edition could earn 5 stars........2005-03-01
While very ambitious and containing some very good material, I think there are too many errors, typos, and gaps in this book. For example, the derivation of equation (3.20) on page 43, a not insignificant result on swap rates, is embarrasingly wrong. They make 2 fundamental errors in equations (3.15) and (3.16) and appear fortunate to arrive at (3.20) which is correct. These errors are not mere typos. Their examples related to the concept of a filtration on top of page 58 appear to be wrong. Elsewhere in the book notation is often used inconsistently and without adequate definition. There are also gaps. For example, when discussing volatility structures in Section 16.1, they use equation (16.6) (which is correct) in a number of examples, but I could not find where they actually derived that equation. (It should have been in the HJM chapter) but was not there.
I like the fact that they wanted to include a chapter on term structures from the macro-economic perspective. Unfortunately this chapter is difficult to read, provides no macroeconomic intuition and again appears to omit too many details. For example, the description of the IS-LM-Phillips model is inadequate and either should be expanded or dropped from future editions. Likewise, the description of the Sommer model is inadequate. Equation (11.3) in the statement of Sommer's Theorem would appears to be wrong at first sight. The left-hand-side of that equation is known by time t, but the right-hand-side would appear to be UNknown by time t. This apparnet contradiction can be explained but the authors never comment on such matters, often making the material more difficult to follow.
Chapter 17 on GMM and MLE methods is quite nice but again, not everything is adequately explained. The examples of Section 17.2.5, for example, seem to assume that certain variables are observable in the market place (e.g. volatility, v_t in equation 17.38) but this seems inapproriate as v_t would generally be unobservable. Indeed this is stated in Chapter 18. Again, however, James and Webber provide no clarification whatsoever of this issue, leaving the reader to wonder what exactly was done.
Some sections are also poorly motivated. For example, Section 16.4, "Processes on Manifolds", in the chapter on Principal Components Analysis is not motivated properly. While the material is quite straightforward to read (though they should define terms like diffeomorphism if they want to use them in a financial engineering text), it is not clear why you need to bring in the language of manifolds and tangency spaces etc. After all, where is this material used in the example of Section 16.4.5? It seems to me that the examples of Section 16.4 are interesting and do lead to new types of term structure models, but that this material could be presented without the jargon of manifolds. Again, I may be wrong but then I would blame the authors for not writing clearly.
A final criticism is that it seems on occasion that the authors are writing about material that they are not particularly familiar with, all for the sake of being encyclopedic. This thought crossed my mind when reading the chapter on Monte Carlo simulation. For example, with reference to equations (13.11)-(13.13) it would have taken very little to point out that Jensen's Inequality implies that some estimated security prices will be biased. Indeed the authors hint at this in the final paragraph on page 350 but do not make the point.
There are many other examples of these errors / typos / gaps in the book. And as far as I know there is no list of errata available.
I will not mention the many good things in this book as other reviewers have already done so. However, I think their praise has been excessive and feel that 3 stars is appropriate.
A real must !.......2001-12-30
As a math grad student who is interested in the term structure modelling, I found that this book is really useful! It just tells you everything about interest rate modelling,not just for the no-arbitrage modelling issue, they even have a chapter about the macroeconomic foundation for interest rate fluctuation! The math used in this book is very concise without too much measure theory twaddle,Everyone who works in this field should have a copy. It's a real must!
A must-have encyclopedia on term structure modeling.......2001-05-26
I have spent a number of years in building & implementing models for interest-rate-dependent claims, but should admit: I learned more from this book. I view it as an encyclopedia on the subject, in which the authors (never heard their names before - what a shame!) have done an excellent job on reviewing hundreds of publications. The theory of term structure modeling has been grown to a separate subject - thanks to Hull and White, Jamshidian, HJM, BGM, Hughston - among main contributors. You can find all methods in one place and in a very accesible form. For example, HJM is described better and simpler than in the author's original paper. Most models are reviewed with practical implementation in mind.
It is not a "first book" on "introduction" on the subject; it is rather a good desk reference for prepared professionals.
Extraordinary.......2001-03-17
There are plenty of books on fixed income mathematics. This one is extraordinary. It is simultaneously practical, theoretically sophisticated and a pleasure to read. The treatment of term-structure models, including HJM, is the most accessible I have seen anywhere. There is a lot of information on yield curve building. This includes both bootstrapping and more recent research in parameterised curves. There are plenty of topics that other books might label "beyond the scope of ...", but James and Webber jump right in, with meaty discussions of the Kalman filter, lattice methods of valuation and GARCH models. Despite all the theory, the authors are always in touch with practical details. They take into account stub dates, and are precise about day counts. These are obviously practitioners!
Book Description
The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives.
This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.
Customer Reviews:
Helpful addition to comprehension and discussion, but with frustrating errors....not for amatures.......2007-04-02
Pricing interest rate derivatives with short term interest rate models has been like a game of FANTAN for nearly a decade, until the LIBOR Market Model (LMM, aka the BGM model) came along. Before, everyone was using Vasicek and periodically someone would sweep the table of everyone's winnings. In the discrete world of increasingly complex structured trades and advancing "mark to market" mandates driven by bank regulators and BASEL II, the seat of the pants confessions of exotic interest rate traders using cobbled together non-published short term interest rate models for valuation fell under justified suspicions.
Along comes BGM (Bachert, Gatarek and Maksymiuk)....while not exactly "to the rescue" giant sighs of relief were expelled worldwide as it has been widely adopted, as the ghostly hand of Fischer Black almost endorses it from beyond.
BGM is especially beloved by those who have to price complex derivatives and exotics because fundamental inputs are a snap to observe: a set of LIBOR forward rates. (Actually, anyone should love this feature). Then the fun starts, each forward rate is modelled by a (pesky, defensible, arguable) lognormal process first made famous and advocated by Fischer Black. The LMM (BGM) model therefore is simplistically looked at as a collection of little Black models. The trouble is, how do we collect them and calibrate them?
So it isn't just that simple, and this book explains in more detail just what the BGM model is, explores uses and limitations, etc.
Use the "LOOK INSIDE" feature to see the contents, but briefly there are three parts - theory, calibration and simulation. Drift is the topic of the day, and BGM don't disappoint. The parametric and nonparametric calibrations section is impenetrable to me, but this isn't my space.
Smile modelling has gotten into a chant at a football match: "uncertain volatility approach" shouts one side, "ARCH, GARCH, FART" shouts the other. Whatever. If you really want to dig into the volatility argument I suggest Knight & Stachell's third edition of "Forecasting Volatility" but you'll need your head examined before you can keep the players straight and need a scorecard handy. A discussion and comparison of HJM (Heath-Jarrow-Morton) in comparison and contrast with BGM is covered here.
Okay, the problems: this book is written in Engrishlovakian, not English. The copy editor should be shot.
There are lots, and I mean LOTS of typos, of which about 50% are easy to figure out what was intended. The other 50% enjoy too high an uncertainty coefficient to be comprehensible. An ERRATA sheet should be inserted into copies of future shipments ASAP.
Which leads me to my gigantic Grand Canyon-size hole in my knowledge: I just skip about 60% of the equations I read in any book, expecting the narrative to support what is explicit in the equations. I have no idea if these equations are edited correctly, and I suspect they are better than the English...but on the other hand, the English is so poor it makes you suspect the whole darn thing.
Who is this book for: general quantfin readers like me will find this tough sledding, this is a printed whiteboard and marker walk through of BGM from start to finish with current state-of-the-art discussions (with unfortunately a lot of whiteboard sloppiness mapped into the "book" state space). I suspect that as a conversation among experts, this book is a nice round-up straight from the source. Experts can probably see past the errors easier than others and both find it sloppy, but still comprehensible. I would dis-recommend this book for a clueless beginner, as the text assumes a readership pretty familiar with the complex and not-inconsiderably large discussion of forward rate and term structure models. For example, maximum smoothness of cubic splines are pretty much assumed and quite possibly laughed at by this crowd.
James "Not-Vasichek"
Book Description
The field of financial mathematics has developed tremendously over the past thirty years, and the underlying models that have taken shape in interest rate markets and bond markets, being much richer in structure than equity-derivative models, are particularly fascinating and complex. This book introduces the tools required for the arbitrage-free modelling of the dynamics of these markets. Andrew Cairns addresses not only seminal works but also modern developments. Refreshingly broad in scope, covering numerical methods, credit risk, and descriptive models, and with an approachable sequence of opening chapters, Interest Rate Models will make readers--be they graduate students, academics, or practitioners--confident enough to develop their own interest rate models or to price nonstandard derivatives using existing models.
The mathematical chapters begin with the simple binomial model that introduces many core ideas. But the main chapters work their way systematically through all of the main developments in continuous-time interest rate modelling. The book describes fully the broad range of approaches to interest rate modelling: short-rate models, no-arbitrage models, the Heath-Jarrow-Morton framework, multifactor models, forward measures, positive-interest models, and market models. Later chapters cover some related topics, including numerical methods, credit risk, and model calibration. Significantly, the book develops the martingale approach to bond pricing in detail, concentrating on risk-neutral pricing, before later exploring recent advances in interest rate modelling where different pricing measures are important.
Customer Reviews:
An excellent book!!!.......2004-03-29
This book provides an excellent reference and point of view of old and new topics in the interest rate modelling field.
From short rate models, HJM model, multifactor models, positive interest models and market models, it gives you a very well explanation all without forget the calibration of them.
You can not find many books about this topic. This one gives a clear and easy to follow chapters in order to increase your knowledge of this not easy field. The formality is a key point in all the book.
Book Description
In recent years, interest-rate modeling has developed rapidly in terms of both practice and theory. The academic and practitioners' communities, however, have not always communicated as productively as would have been desirable. As a result, their research programs have often developed with little constructive interference. In this book, Riccardo Rebonato draws on his academic and professional experience, straddling both sides of the divide to bring together and build on what theory and trading have to offer.
Rebonato begins by presenting the conceptual foundations for the application of the LIBOR market model to the pricing of interest-rate derivatives. Next he treats in great detail the calibration of this model to market prices, asking how possible and advisable it is to enforce a simultaneous fitting to several market observables. He does so with an eye not only to mathematical feasibility but also to financial justification, while devoting special scrutiny to the implications of market incompleteness.
Much of the book concerns an original extension of the LIBOR market model, devised to account for implied volatility smiles. This is done by introducing a stochastic-volatility, displaced-diffusion version of the model. The emphasis again is on the financial justification and on the computational feasibility of the proposed solution to the smile problem. This book is must reading for quantitative researchers in financial houses, sophisticated practitioners in the derivatives area, and students of finance.
Customer Reviews:
why bother.......2003-02-14
It's hard to believe a reviewer with such a myopic view of Derivatives pricing could go through the whole book, understood it and found time to rate it. Mindblowing waste of time !
Few hundreds years ago, he would have recommended burning the Madmen claiming the earth was round.
Anyway, while Derivatives Pricing achieves little for the welfare of mankind, the recent need for assets based on ever complex market scenarios calls for a more refined pricing methodology. There no supply and demand here, only customers who want hedge/trade/tradge assets /liabilities and traders who need to make sure their firms don't go burst when market move.
The author answers that demand by formatting and publishing his papers.
rebonato does it again.......2003-01-18
My avid reading kept jostling out superb hot ideas from this book. Rebonato carries out a comprehensive survey of the LIBOR market model. He tackles historical background, calibration, and effective implementation. The later chapters also cover extensions to the LIBOR market model to take account of smile and skew. In particular, there is extensive discussion of the cutting-edge Joshi-Rebonato stochastic-vol, displaced-diffusion LIBOR market model.
If you are working on the pricing of exotic interest rate derivatives, this book is a must buy.
Such pearls of wisdom.......2003-01-09
I am not qualified to write a review of this book, but neither is the above author as his "review" is nothing more than an uninformed assault on modern finance.
In fact, I submit, that said reviewer knows nothing of finance whatsoever.
(Since this book happens to be well regarded, I'll give it a five)
A theoretical substitute for supply and demand.......2002-12-20
A complicated body of mathematical theory, developed over a period of about 30 years, addresses the question: how should derivative X be valued if we know certain parameters, especially the volatility of the price of its underlying asset?
But why exactly does the question need answering? After all, the price of X, like that of its underlying, is determined by the point at which the demand for X is equal to the supply of X. One doesn't need a computer for that, one just needs a liquid marketplace. I can look up the price of a share of Microsoft's equity in my daily newspaper. I'm not tempted to develop a body of theory to figure it out, when I can flip through a few pages and find it.
Nowadays, I can also look up the price of a standardized option to buy Microsoft in the newspaper. In 1973, when people like Fischer Black began developing this body of theory, that was not yet the case.
This brings us to the point of my little sermon. The purpose of this body of theory is to produce a price figure in cases where there is not a liquid market for X. The theories answer the question a portfolio manager must often ask himself: if I were able to find a buyer for X, how much could I charge for it?
This book has its moments, but in general I believe this body of theory accomplishes less than its adepts believe. The imagery of a God-like Newton on the dust jacket indicates, I submit, some of the pretentiousness that gets into their ivory towers.
Book Description
Written in a reader-friendly manner, this reference is designed to meet the needs of readers who want to master the interest theory and finance topics addressed in the Financial Mathematics exam.
Requires an algebra background; calculus not a prerequisite. Encourages readers to practice writing throughout, and more than 30 end-of-chapter writing exercises are included. Provides more than 240 worked examples in a wide range of difficulty. Features abundant examples, discussion, and problems throughout.
A useful guide for readers planning to take the Financial Mathematics exam.
Mathematical Interest Theory, 1/E
James W. Daniel
Leslie Jane Federer Vaaler
Customer Reviews:
One of the worst books .......2007-05-23
I'm a computer engineering and math double major. I took a math class about interest and this is the book associated with the class. This is one of the worst books, the sections do not prepare you for the end of chapter problems. The questions are unclear it's either that they need to improve the questions or the sections. This book sucks, I rated it 1 star because there are no negative stars. This is the worst book ever. I was so angry at this book I actually burnt it after I was done with that class. Waste of money, waste of time. Infact my I.Q. probably decreased after reading this book and attempting the excersises at the end of the chapter.
Purchase at your own risk.......2007-05-05
To begin with, I think that this book is written for those who already have a familiarity with the material. Just so you know my experience with this book, I took a college math course where this was the required text. I soon found out, that the examples through the chapter were decent, but the questions at the end had little or no correlation to those previously read in the chapter. I should add that what made these questions decent is that you could decipher the meaning of the chapter examples because the examples solutions were directly after.
I think that if the author spent a little more time making the review problems a little more understandable and similar to those seen previously, than thinking up different names for the people in every single problem, He may have written a decent book. And that is a BIG MAYBE!
If you are thinking of purchasing this book to prepare for the Actuary FM Exam, DON'T. Stick to the ones on the SOA recommended list, or one of the Temple or Actex study manuals.
Stick to SOA/CAS Syllabi.......2007-03-20
I used this text in a class designed to prepare me for my FM exam. It didn't. The text has some usefull calculator exercises but the homework problems are not comensurate with the level of difficulty in the section examples. If you are preparing for the actuarial FM exam, don't use this book. Stick to the texts reccomended by the SOA and CAS.
Perfect for FM exam.......2006-07-26
I highly recommend this book for students studying for the FM exam. I read the book cover to cover and passed the exam. It is easy to read and is full of examples to illustrate the concepts. The difficulty levels presented make a nice range; there are a good mix of problems designed to reinforce the concept as well as problems using a combination of concepts (much like the FM exam).
Where to get more information.......2006-03-24
Of course I like the book---I'ma co-author. For sample sections and more information, see http://www.actuarialseminars.com/book.html .
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