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. Theemphasis 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.

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) Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

Autorentext

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.

Inhalt
Derivative Pricing and Hedging.- A Simple Market Model.- Single-Period Models.- Multi-Period Models: No-Arbitrage Pricing.- Multi-Period Models: Risk-Neutral Pricing.- The Cox-Ross-Rubinstein model.- American Options.- Advanced Topics.