This book explores the mathematics that underpins pricing models for derivative securities such as options, futures and swaps in modern markets. Models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory.

Pricing by Arbitrage * Martingale Measures * The Fundamental Theorem of Asset Pricing * Complete Markets and Martingale Representation * Stopping Times and American Options * A Review of Continuous Time Stochastic Calculus * European Options in Continuous Time * The American Option * Bonds and Term Structure * Consumption-Investment Strategies *