Stochastic Calculus Models for Finance

Book Description
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.        


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This is the first volume in a two volume sequence providing the foundational material on Stochastic calculus models in finance. This first volume is suitable for discrete-time finance. The only pre-requisite is standard calculus; may aspects such as martingales and change of measure are treated in detailed depth. Probability is covered in detail using the binomial model.The book will be suitable for advanced undergraduate courses and beginning masters-level students in mathematical finance and financial engineering. There are exercises and examples throughout and summaries at the end of each chapter.


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