Springer Undergraduate Mathematics Series

Derivative Pricing in Discrete Time

Authors: Cutland, Nigel J., Roux, Alet

  • Provides a complete and rigorous treatment of no-arbitrage pricing for both European and American derivatives in complete and incomplete discrete markets
  • Requires only elementary linear algebra and probability theory, hence accessible to students of quantitative subjects (such as economics or physics) as well as students of mathematics
  • Provides a foundation for understanding the more advanced theory of continuous-time models
  • Contains copious fully worked out examples and numerous class-tested exercises (many with solutions)
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  • ISBN 978-1-4471-4408-3
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Softcover $49.95
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  • ISBN 978-1-4471-4407-6
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About this Textbook

This book provides an introduction to the mathematical modelling of real world financial markets and the rational pricing of derivatives, which is part of the theory that not only underpins modern financial practice but is a thriving area of mathematical research. The central theme is the question of how to find a fair price for a derivative; defined to be a price at which it is not possible for any trader to make a risk free profit by trading in the derivative. 
To keep the mathematics as simple as possible, while explaining the basic principles, only discrete time models with a finite number of possible future scenarios are considered. The theory examines the simplest possible financial model having only one time step, where many of the fundamental ideas occur, and are easily understood. Proceeding slowly, the theory progresses to more realistic models with several stocks and multiple time steps, and includes a comprehensive treatment of incomplete models. The emphasis throughout is on clarity combined with full rigour. 
The later chapters deal with more advanced topics, including how the discrete time theory is related to the famous continuous time Black-Scholes theory, and a uniquely thorough treatment of American options. The book assumes no prior knowledge of financial markets, and the mathematical prerequisites are limited to elementary linear algebra and probability. This makes it accessible to undergraduates in mathematics as well as students of other disciplines with a mathematical component. It includes numerous worked examples and exercises, making it suitable for self-study.

About the authors

​Nigel J. Cutland is Professor of Mathematics at the University of York, UK. 
Alet Roux also teaches at the University of York, UK, where she is Chair of the Board of Examiners and a member of the Mathematical Finance and Stochastic Analysis Research Group.

Reviews

From the reviews:

“Derivative Pricing in Discrete Time introduces the basic ideas of financial derivatives with a minimum of prerequisites. … Indeed, as an undergraduate-level mathematical treatment of the subject, this is the best textbook I have seen. … I would recommend the book to students preparing for financial careers, such as actuaries. Practical pricing models should make more sense with the theoretical grounding provided by this book.” (John Curran, MAA Reviews, May, 2014)


Table of contents (8 chapters)

  • Derivative Pricing and Hedging

    Cutland, Nigel J. (et al.)

    Pages 1-9

  • A Simple Market Model

    Cutland, Nigel J. (et al.)

    Pages 11-33

  • Single-Period Models

    Cutland, Nigel J. (et al.)

    Pages 35-87

  • Multi-Period Models: No-arbitrage Pricing

    Cutland, Nigel J. (et al.)

    Pages 89-131

  • Multi-Period Models: Risk-Neutral Pricing

    Cutland, Nigel J. (et al.)

    Pages 133-175

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4471-4408-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4471-4407-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Derivative Pricing in Discrete Time
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2013
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-4471-4408-3
DOI
10.1007/978-1-4471-4408-3
Softcover ISBN
978-1-4471-4407-6
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XV, 325
Number of Illustrations and Tables
63 b/w illustrations
Topics