This book evolved from the first ten years of the Carnegie Mellon
professional Masters 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.
The book includes a self-contained treatment of the probability
theory needed for stochastic calculus, including Brownian motion
and its properties. Advanced topics include foreign exchange
models, forward measures, and jump-diffusion processes.
Classroom-tested exercises conclude every chapter; some of these
extend the theory while others are drawn from practical problems in
quantitative finance. Instructor's manual available.
General
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