This book evolved from the first ten years of the Carnegie Mellon professional Master's program in Computational Finance. The contents of the book have been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs. But more importantly, intuitive explanations, developed and refined through classroom experience with this material, are provided throughout the book. Volume I introduces the fundamental concepts in a discrete-time setting and Volume II builds on this foundation to develop stochastic calculus, martingales, risk-neutral pricing, exotic options, and term structure models, all in continuous time.

Written for: Graduate students and researchers

• General Probability Theory
• Information and Conditioning
• Brownian Motion
• Stochastic Calculus
• Risk-Neutral Pricing
• Connections with Partial Di.erential Equations
• Exotic Options
• American Derivative Securities
• Change of Numeraire
• Term Structure Models
• Introduction to Jump Processes

• A Advanced Topics in Probability Theory
• B Existence of Conditional Expectations
• C Completion of Proof of Second Fundamental Theorem of Asset Pricing