Steven Shreve

Stochastic Calculus for Finance I (eBook, PDF)

The Binomial Asset Pricing Model

• Format: PDF

Produktbeschreibung

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has 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 refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stchastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.

This book is being published in two volumes. The first volume presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the concepts needed for the continuous-time theory in the secondvolume.

Chapter summaries and detailed illustrations are included. Classroom tested exercises conclude every chapter. Some of these extend the theory and others are drawn from practical problems in quantitative finance.

Advanced undergraduates and Masters level students in mathematical finance and financial engineering will find this book useful.

Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 187
• Erscheinungstermin: 1. November 2019
• Englisch
• ISBN-13: 9780387225272
• Artikelnr.: 60046992

Autorenporträt

 

Inhaltsangabe

1 The Binomial No-Arbitrage Pricing Model.- 1.1 One-Period Binomial Model.- 1.2 Multiperiod Binomial Model.- 1.3 Computational Considerations.- 1.4 Summary.- 1.5 Notes.- 1.6 Exercises.- 2 Probability Theory on Coin Toss Space.- 2.1 Finite Probability Spaces.- 2.2 Random Variables, Distributions, and Expectations.- 2.3 Conditional Expectations.- 2.4 Martingales.- 2.5 Markov Processes.- 2.6 Summary.- 2.7 Notes.- 2.8 Exercises.- 3 State Prices.- 3.1 Change of Measure.- 3.2 Radon-Nikodým Derivative Process.- 3.3 Capital Asset Pricing Model.- 3.4 Summary.- 3.5 Notes.- 3.6 Exercises.- 4 American Derivative Securities.- 4.1 Introduction.- 4.2 Non-Path-Dependent American Derivatives.- 4.3 Stopping Times.- 4.4 General American Derivatives.- 4.5 American Call Options.- 4.6 Summary.- 4.7 Notes.- 4.8 Exercises.- 5 Random Walk.- 5.1 Introduction.- 5.2 First Passage Times.- 5.3 Reflection Principle.- 5.4 Perpetual American Put: An Example.- 5.5 Summary.- 5.6 Notes.- 5.7 Exercises.- 6 Interest-Rate-Dependent Assets.- 6.1 Introduction.- 6.2 Binomial Model for Interest Rates.- 6.3 Fixed-Income Derivatives.- 6.4 Forward Measures.- 6.5 Futures.- 6.6 Summary.- 6.7 Notes.- 6.8 Exercises.- Proof of Fundamental Properties of Conditional Expectations.- References.

Rezensionen

From the reviews of the first edition:

"Steven Shreve's comprehensive two-volume Stochastic Calculus for Finance may well be the last word, at least for a while, in the flood of Master's level books.... a detailed and authoritative reference for 'quants' (formerly known as 'rocket scientists'). The books are derived from lecture notes that have been available on the Web for years and that have developed a huge cult following among students, instructors, and practitioners. The key ideaspresented in these works involve the mathematical theory of securities pricing based upon the ideas of classical finance. ...the beauty of mathematics is partly in the fact that it is self-contained and allows us to explore the logical implications of our hypotheses. The material of this volume of Shreves's text is a wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach. It is accessible to a broad audience and has been developed after years of teaching the subject. It should serve as an excellent introduction for anyone studyin the mathematics of the classical theory of finance."
-- SIAM, 2005

'This is the first of the two-volume series evolving from the author's mathematics courses in M.Sc. Computational Finance program at Carnegie Mellon University (USA). The content of this book is organized such as to give the reader precise statements of results, plausibility arguments, mathematical proofs and, more importantly, the intuitive explanations of the financial and economic phenomena. Each chapter concludes with summary of the discussed matter, bibliographic notes, and a set of really useful exercises.' (Neculai Curteanu, Zentralblatt MATH, Vol. 1068, 2005)