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Introduction to Option Pricing Theory

  • Book
  • © 2000

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Authors:
  1. Gopinath Kallianpur

    1. Department of Statistics, University of North Carolina, Chapel Hill, USA

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  2. Rajeeva L. Karandikar

    1. Department of Mathematics & Statistics, Indian Statistical Institute, New Dehli, India

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-x
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  2. Stochastic Integration

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 1-45

  3. Itô’s Formula and its Applications

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 47-69

  4. Representation of Square Integrable Martingales

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 71-78

  5. Stochastic Differential Equations

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 79-93

  6. Girsanov’s Theorem

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 95-101

  7. Option Pricing in Discrete Time

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 103-122

  8. Introduction to Continuous Time Trading

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 123-135

  9. Arbitrage and Equivalent Martingale Measures

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 137-167

  10. Complete Markets

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 169-189

  11. Black and Scholes Theory

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 191-203

  12. Discrete Approximations

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 205-213

  13. The American Options

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 215-223

  14. Asset Pricing with Stochastic Volatility

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 225-239

  15. The Russian Options

    • Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 241-263

  16. Back Matter

    Pages 265-269
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Statistics, University of North Carolina, Chapel Hill, USA

    Gopinath Kallianpur

  • Department of Mathematics & Statistics, Indian Statistical Institute, New Dehli, India

    Rajeeva L. Karandikar

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