© 2005

Martingale Methods in Financial Modelling

  • Authors

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 36)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Spot and Futures Markets

    1. Front Matter
      Pages 1-1
    2. Marek Musiela, Marek Rutkowski
      Pages 3-34
    3. Marek Musiela, Marek Rutkowski
      Pages 35-111
    4. Marek Musiela, Marek Rutkowski
      Pages 113-179
    5. Marek Musiela, Marek Rutkowski
      Pages 181-204
    6. Marek Musiela, Marek Rutkowski
      Pages 205-228
    7. Marek Musiela, Marek Rutkowski
      Pages 229-252
    8. Marek Musiela, Marek Rutkowski
      Pages 253-314
    9. Marek Musiela, Marek Rutkowski
      Pages 315-347
  3. Fixed-income Markets

    1. Front Matter
      Pages 349-349
    2. Marek Musiela, Marek Rutkowski
      Pages 351-381
    3. Marek Musiela, Marek Rutkowski
      Pages 383-416
    4. Marek Musiela, Marek Rutkowski
      Pages 417-467
    5. Marek Musiela, Marek Rutkowski
      Pages 469-516
    6. Marek Musiela, Marek Rutkowski
      Pages 517-571
    7. Marek Musiela, Marek Rutkowski
      Pages 573-607
  4. Back Matter
    Pages 609-715

About this book


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.


Hedging Stochastic calculus arbitrage martingales mathematical finance modeling options stochastic volatility swaps term structure Quantitative Finance

About the authors


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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)