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Introduction to Option Pricing Theory

  • Gopinath Kallianpur
  • Rajeeva L. Karandikar

Table of contents

  1. Front Matter
    Pages i-x
  2. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 1-45
  3. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 47-69
  4. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 71-78
  5. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 79-93
  6. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 95-101
  7. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 103-122
  8. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 123-135
  9. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 137-167
  10. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 169-189
  11. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 191-203
  12. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 205-213
  13. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 215-223
  14. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 225-239
  15. Gopinath Kallianpur, Rajeeva L. Karandikar
    Pages 241-263
  16. Back Matter
    Pages 265-269

About this book

Introduction

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.

Keywords

Black-Scholes Finance Ornstein-Uhlenbeck process Probability theory Semimartingale Statistik Stochastic Differential Equations Stochastic processes Wahrscheinlichkeitsrechnung filtration geometric Brownian motion ksa quadratic variation statistics stochastic finance

Authors and affiliations

  • Gopinath Kallianpur
    • 1
  • Rajeeva L. Karandikar
    • 2
  1. 1.Department of StatisticsUniversity of North CarolinaChapel HillUSA
  2. 2.Department of Mathematics & StatisticsIndian Statistical InstituteNew DehliIndia

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