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Martingale Methods in Financial Modelling (Applications of Mathematics) [Hardcover]

M Musiela , Marek Rutkowski , Antonio Jose Engler
5.0 out of 5 stars  See all reviews (1 customer review)

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Martingale Methods in Financial Modelling (Stochastic Modelling and Applied Probability) Martingale Methods in Financial Modelling (Stochastic Modelling and Applied Probability) 5.0 out of 5 stars (1)
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Book Description

31 Oct 1998 Applications of Mathematics (Book 36)
This book provides a comprehensive and self-contained treat- ment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones but in a way that makes them consistent with the finance industry derivatives pricing practice. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful math. tools.


Product details

  • Hardcover: 530 pages
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K; 2nd printing edition (31 Oct 1998)
  • Language: English
  • ISBN-10: 354061477X
  • ISBN-13: 978-3540614777
  • Product Dimensions: 24.2 x 16.4 x 4 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 1,967,153 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

From the reviews:

" …This book is an impressive work of scholarship in mathematical finance in the area of option pricing. …contains the latest results and references. …The presence of many explicit formulae, for various types of derivatives, will make this book attractive to practitioners; and its breadth of content will make it useful for anyone who considers research in mathematical finance." (The Australian and New Zealand Journal of Statistics)

" …On the whole, this book presents a very wide range of topics and will appeal to both practitioners and mathematicians. …the second part gives an excellent overview of the state of the art in term structure research and will set a clear standard for some time to come." (MathSciNet)

" ...The book contains a wealth of material expressed in a clear mathematical way. A definite bonus is the very extensive list of references which gives the reader a most welcome basis from which to explore further the realm of mathematical finance. …The book can be used ideally both as an introductory and as an advanced text on mathematical finance." (Short Book Reviews)

" …This book is a comprehensive and up-to-date presentation of the martingale approach for pricing and hedging derivative securities. …provides a wide range of topics and will appeal to both practitioners and mathematicians. When only special cases or models are provided, the authors give useful references that will help researchers to obtain even more insight in the topics." (ZentralblattMATH)

From the reviews of the second edition:

"The book starts at an elementary level of mathematics as well as of market and product knowledge. … In summary, the book gives a very broad insight into advanced modern financial mathematics, in particular fixed income models. … It will serve as a basic source of knowledge of the described topics in financial mathematics." (Ludger Overbeck, Mathematical Reviews, Issue 2005 m)

--This text refers to the Paperback edition.

From the Back Cover

This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.

In the 2nd edition, some sections of the former Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk.

In the 3rd printing of the 2nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options are presented in some detail.

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.

Part II of the book has been revised fundamentally. The theme of volatility risk appears systematically. Much more detailed analysis of the various interest-rate models is 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. In particular, it should concentrate on defining liquid primary and derivative assets and identifying the relevant sources of trading risk.

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 the practical rather than the theoretical aspects of financial modelling.

--This text refers to the Paperback edition.

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Most Helpful Customer Reviews
25 of 28 people found the following review helpful
5.0 out of 5 stars Hardcore Financial Engineering for the Sultan 29 Aug 2001
By A Customer
Format:Hardcover
This is a classic book. However, it is not for the faint hearted and can at times feel like reading War & Peace in Russian when you only have a tourist phrasebook! Its tone is by nature academic and theoretical but if you want to have the most rigorous treatment of this exciting new area of derivative valuation then you must suffer this dryness. Anyone wanting Wilmott style antidotes and cartoons will be disappointed.
The use of martingale valuation in real world derivatives is still niche, however the authors show that the techniques are very important and can be applied to a wide variety of financial instruments - in many respects the martingale methods are simpler than the traditional partial differential techniques favoured by the mainstream. The book's audience is PhD level quants seeking to apply martingale techniques and anyone without a good grounding in calculus should not attempt this book. However, for the enlightened ones it is worth the effort and will provide many happy hours of reflection.
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Amazon.com: 4.8 out of 5 stars  8 reviews
57 of 62 people found the following review helpful
4.0 out of 5 stars yes, but ... 17 Mar 2000
By steve - Published on Amazon.com
Format:Hardcover
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.
19 of 19 people found the following review helpful
5.0 out of 5 stars At the Forefront of Modern Mathematical Finance 23 May 2005
By Paul Thurston - Published on Amazon.com
Format:Hardcover|Verified Purchase
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: Volume 1, Foundations and Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus. Suitable prerequisites are also covered by Karatzas and Shreve in Brownian Motion and Stochastic Calculus. A good foundation in arbitrage pricing theory is also needed. I recommend the nice treatment by Bjork in Arbitrage Theory in Continuous Time.

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.
9 of 11 people found the following review helpful
4.0 out of 5 stars Martingales & Finance 11 April 2003
By Surf/Bike - Published on Amazon.com
Format:Hardcover
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.
12 of 16 people found the following review helpful
5.0 out of 5 stars The best introduction to martingale method for asset pricing 3 Nov 1998
By danielng@unixg.ubc.ca - Published on Amazon.com
Format:Hardcover
This is an excellent introduction to martingale method for asset pricing. The authors spell out most of the technical details and make it accessible for most technical inclined readers. Furthermore, the book covers not only equity derivatives modelling, but also interest rates modeling.
5 of 6 people found the following review helpful
5.0 out of 5 stars Excellent introductory book to financial math 3 Nov 2006
By New York Guy - Published on Amazon.com
Format:Hardcover
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.
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