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Mathematics of Financial Markets

  • Textbook
  • © 2005

Overview

Authors:
  1. Robert J. Elliott

    1. Haskayne School of Business, University of Calgary, Calgary, Canada

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    You can also search for this author in PubMed   Google Scholar

  2. P. Ekkehard Kopp

    1. Department of Mathematics, University of Hull, Hull, Yorkshire, UK

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    You can also search for this author in PubMed   Google Scholar

  • Aimed at those who need to understand the mathematics behind the multitude of current financial instruments used in derivative markets, including risk managers and other practitioners
  • Begins with the mathematics used in discrete-time models, which can be more simply explained, then moves into the more difficult continuous-time models
  • Includes detailed analyses of the famous Black-Scholes theory, American put options, term structure models, and consumption-investment problems
  • Provides a clear understanding of pricing and hedging for call and put options
  • The mathematics used is accessible
  • The mathematics of martingales and stochastic calculus is developed where needed
  • The treatment is careful and detailed rather than comprehensive
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Finance (FINANCE)

Part of the book sub series: Springer Finance Textbooks (SFTEXT)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Pricing by Arbitrage

    Pages 1-26

  3. Martingale Measures

    Pages 27-55

  4. The First Fundamental Theorem

    Pages 57-85

  5. Complete Markets

    Pages 87-103

  6. Discrete-time American Options

    Pages 105-129

  7. Continuous-Time Stochastic Calculus

    Pages 131-165

  8. Continuous-Time European Options

    Pages 167-221

  9. The American Put Option

    Pages 223-245

  10. Bonds and Term Structure

    Pages 247-284

  11. Consumption-Investment Strategies

    Pages 285-302

  12. Measures of Risk

    Pages 303-328

  13. Back Matter

    Pages 329-352
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Keywords

About this book

This work is aimed at an audience with a sound mathematical background wishing to learn about the rapidly expanding ?eld of mathematical ?nance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and probability. The emphasis throughout is on developing the mathematical concepts required for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or ‘exotic’) ?nancial - struments that now appear on the derivatives markets; the focus throu- out remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to ?nancial markets. The ?rst ?ve chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by non-arbitrage) is presented in Chapter 1. The unique price for a European option in a single-period binomial model is given and then extended to multi-period binomial models. Chapter 2 introduces the idea of a martingale measure for price processes. Following a discussion of the use of self-?nancing tr- ing strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price p- cess is a martingale.

Reviews

From the reviews:

"...This book is a valuable addition to a graduate student's reference collection. The number of textbooks in mathematical finance is increasing much faster than the number of revolutionary contributions to the field, but this text stands above the crowd." SIAM Review, December 2005

From the reviews of the second edition:

"The book is very carefully formatted. … this book is a valuable addition to a graduate student’s reference collection. The number of textbooks in mathematical finance is increasing much faster than the number of revolutionary contributions to the field, but this text stands above the crowd." (Alexandre D’Aspremont, SIAM Reviews, December, 2005)

"The emphasis of the first edition of this book was on developing the mathematical concepts for the rapidly expanding field of mathematical finance. This second edition contains a significant number of changes and additions … . The target audience is readers with sound mathematical background on elementary concepts from measure-theoretic probability … . It should be an equally valuable resource to practitioners interested in the mathematical tools … . will be a very useful addition to any scholarly library." (Theofanis Sapatinas, Journal of Applied Sciences, Vol. 32 (6), 2005)

"The second edition adds new matieral from current active research areas. A new chapter on coherent risk measures for instance reflects the recent trend in research and applications in the area of risk management. In summary, this is an excellent textbook in mathematical finance, and I can definitely recommend it." (S. Peng, Short Book Reviews of the ISI, June 2006)

Authors and Affiliations

  • Haskayne School of Business, University of Calgary, Calgary, Canada

    Robert J. Elliott

  • Department of Mathematics, University of Hull, Hull, Yorkshire, UK

    P. Ekkehard Kopp

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