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Analytically Tractable Stochastic Stock Price Models

  • Archil¬†Gulisashvili

Part of the Springer Finance book series (FINANCE)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Archil Gulisashvili
    Pages 1-36
  3. Archil Gulisashvili
    Pages 37-65
  4. Archil Gulisashvili
    Pages 67-75
  5. Archil Gulisashvili
    Pages 77-108
  6. Archil Gulisashvili
    Pages 109-166
  7. Archil Gulisashvili
    Pages 167-199
  8. Archil Gulisashvili
    Pages 227-242
  9. Archil Gulisashvili
    Pages 243-272
  10. Archil Gulisashvili
    Pages 273-314
  11. Archil Gulisashvili
    Pages 315-345
  12. Back Matter
    Pages 347-359

About this book

Introduction

Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models.

The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory.

Keywords

91Gxx, 91G80, 91B25, 91G20 asymptotic formulas implied volatilities option pricing functions stochastic volatility models stock price densities

Authors and affiliations

  • Archil¬†Gulisashvili
    • 1
  1. 1.Department of MathematicsOhio UniversityAthensUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-31214-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-31213-7
  • Online ISBN 978-3-642-31214-4
  • Series Print ISSN 1616-0533
  • Series Online ISSN 2195-0687
  • Buy this book on publisher's site
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