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  • Book
  • © 1999

Mathematics of Financial Markets

Authors:

  1. Robert J. Elliott

    1. Department of Mathematical Sciences, University of Alberta, Edmonton, Canada

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    You can also search for this author in PubMed   Google Scholar

  2. P. Ekkehard Kopp

    1. Pro-Vice-Chancellors’ Office, The University of Hull, Hull, UK

    View author publications

    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

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 (10 chapters)

  1. Front Matter

    Pages i-xi
    PDF

  2. Pricing by Arbitrage

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 1-22

  3. Martingale Measures

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 23-43

  4. The Fundamental Theorem of Asset Pricing

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 45-61

  5. Complete Markets and Martingale Representation

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 63-74

  6. Stopping Times and American Options

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 75-98

  7. A Review of Continuous-Time Stochastic Calculus

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 99-133

  8. European Options in Continuous Time

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 135-185

  9. The American Option

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 187-210

  10. Bonds and Term Structure

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 211-249

  11. Consumption-Investment Strategies

    • Robert J. Elliott, P. Ekkehard Kopp
    Pages 251-270

  12. Back Matter

    Pages 271-292
    PDF
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About this book

This work is aimed at an audience with asound mathematical background wishing to leam about the rapidly expanding field of mathematical finance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and prob ability. The emphasis throughout is on developing the mathematical concepts re­ quired for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or 'exotic') financial instru­ ments that now appear on the derivatives markets; the focus throughout 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 financial markets. The first five 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 nonarbitrage) 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 intro duces the idea of a martingale measure for price pro­ cesses. Following a discussion of the use of self-financing trading strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price process is a mar­ tingale.
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Keywords

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Authors and Affiliations

  • Department of Mathematical Sciences, University of Alberta, Edmonton, Canada

    Robert J. Elliott

  • Pro-Vice-Chancellors’ Office, The University of Hull, Hull, UK

    P. Ekkehard Kopp

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Bibliographic Information

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Buy it now

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

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