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Description of Introduction to Option Pricing Theory

Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure.

This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations.

Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented.

A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.

Title Information

ISBN:

9780817641085

Pages:

269 pages

Format:

Hardback

Product Code:

14344

Publisher:

Springer Verlag GmbH

Published:

30/11/-0001

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Contents of Introduction to Option Pricing Theory

Preface

1. Stochastic Integration
2. Ito's Formula and its Applications
3. Representation of Square Integrable Martingales
4. Stochastic Differential Equations
5. Girsanov's Theorem and its Extensions
6. Option Pricing in Discrete Time
7. Introduction to Continuous Time Trading
8. Arbitrage and Equivalent Martingale Measures
9. Complete Markets
10. The Black and Scholes Theory
11. Discrete Approximations
12. American Options
13. Asset Pricing with Stochastic Volatility
14. The Russian Options

Bibliography
Index