Martingale Methods in Financial Modelling (Stochastic Modelling and Applied Probability) by Marek Musiela and Marek Rutkowski

Martingale Methods in Financial Modelling (Stochastic Modelling and Applied Probability)

Features

Cover Type: Hard Cover with 636 pages

Published by: Springer; 2nd ed. 2005. Corr. 2nd printing edition June 11, 2007

Written in: English

ISBN 10 Number: 3540209662

ISBN 13 Number: 978-3540209669

Book Dimensions: 9.5 x 6.4 x 1.6 inches

Weighs: 2.3 pounds

Product 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 great 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)

Product 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.

Reader Reviews
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. Comment | | (Report this)

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Updated on 6-4-2008.