|aStochastic calculus for finance II :|bContinuous-time models /|cby Steven E. Shreve.
|aNew York :|bSpringer,|cc2004.
|axix, 550 p. :|bill. ;|c24 cm.
|aSpringer finance. Textbook
|aIncludes bibliographical references and indexes.
|a"This book is being published in two volumes. The first volume presents the binomial asset pricing model primarily as a vehicle for introducing in a simple setting the concepts needed for the continuous-time theory in the second volume." The "second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options, and term structure models, all in continuous time"--Back covers.
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. 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.