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.
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13 of 18 people found the following review helpful:
5.0 out of 5 stars
A truly wonderful book,
This review is from: Introduction to Option Pricing Theory (Hardcover)
I am a relatively new student of stochastic processes. The first 4 chapters which are essentially devoted to explaining the theoretical concepts (Ito inetgration, semi-martingales, etc..) are so lucidly written that it is very easy for someone with a limited idea of stochastic process to comprehend them. After establishing these concepts, the book discusses how the earlier theory is applied to pricing by discussing the options pricing models under different scenarios. I felt that although i understood the earlier discussions regarding arbitrage, the part on how it relates with equivalent martingales was quite difficult to understand. But it is probably because i am new to this subject. In all this is an excellent effort by the authors to make a difficult topic readable and understandable. Finally i feel that people, who are genuinely interested in investing their hard earned money in options, should take the time and effort to learn from this book rather than the typical stereotype "How I Became a Millionaire Overnight Trading Options" books.
2 of 31 people found the following review helpful:
5.0 out of 5 stars
Introduction to option pricing theory,
By Tru - a mathematician (Australia) - See all my reviews
This review is from: Introduction to Option Pricing Theory (Hardcover)
Introduction to option pricing theory.Stochastic calculus.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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bounded variation paths, option coupons, discounted value process, local martingale, bounded predictable processes, augmented market, continuous semimartingale, continuous increasing process, finite stopping time, arbitrage property, martingale measure, quadratic variation process, tingent claim, stochastic integral with respect, stock price process, bounded martingale, admissible strategy, square integrable martingale, rational price, maximal inequality, canonical decomposition, specified company, arbitrage opportunity, stopping times, integrable martingales Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Fix, Remark Let, Proof Note, Proof Suppose, The Ito, Proof First, Definition An American New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
bounded variation paths, option coupons, discounted value process, local martingale, bounded predictable processes, augmented market, continuous semimartingale, continuous increasing process, finite stopping time, arbitrage property, martingale measure, quadratic variation process, tingent claim, stochastic integral with respect, stock price process, bounded martingale, admissible strategy, square integrable martingale, rational price, maximal inequality, canonical decomposition, specified company, arbitrage opportunity, stopping times, integrable martingales Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Fix, Remark Let, Proof Note, Proof Suppose, The Ito, Proof First, Definition An American New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
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6
books
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- Stochastic Differential Equations (Siam-Ams Proceedings Ser .: No 6) by N. Y.) Symposium in Applied Mathematics (1972 New York in Back Matter (1), and Back Matter (2)
- Stochastic Integration and Differential Equations by Philip E. Protter in Back Matter
- Lectures on the Mathmatics of Finance (CRM Monograph Series) by Ioannis Karatzas in Back Matter
- Historical Processes (Memoirs of the American Mathematical Society) by Donald A. Dawson in Back Matter
- Stochastic Integrals (Ams Chelsea Publishing) by Henry P. McKean in Back Matter
See all 19 books this book cites
- Stochastics in Finite and Infinite Dimensions (Trends in Mathematics) by Takeyuki Hida in Front Matter (1), and Front Matter (2)
- Introduction to the Mathematics of Finance: From Risk Management to Options Pricing (Undergraduate Texts in Mathematics) by Steven Roman in Back Matter
- Stochastic Differential Equations: An Introduction with Applications (Universitext) by Bernt Øksendal in Back Matter
- Zeitstetige Modellierung von Preisprozessen auf Finanzmärkten: Zur Interpretation und Notwendigkeit der Usual Conditions (German Edition) by Stefan Klößner in Back Matter
- Introduction to the Mathematics of Finance: From Risk Management to Options Pricing (Undergraduate Texts in Mathematics) by Steven Roman in Back Matter
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