Springer Finance

Analytically Tractable Stochastic Stock Price Models

Authors: Gulisashvili, Archil

  • Comprehensive in scope
  • Results discussed appear for the first time in a mathematical monograph
  • Unique source of information about analytically tractable stochastic volatility models​
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About this book

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.

About the authors

Archil Gulisashvili received his Ph.D. degree and Doctor of Science degree from the Tbilisi State University in Tbilisi, Georgia. Currently he is a Professor of Mathematics at Ohio University. Prior to joining Ohio University, he has held visiting positions at Boston University, Cornell University, and Howard University. His research interests include financial mathematics, Schrödinger semigroups, Feynman-Kac propagators, and Fourier analysis.

Table of contents (11 chapters)

  • Volatility Processes

    Gulisashvili, Archil

    Pages 1-36

  • Stock Price Models with Stochastic Volatility

    Gulisashvili, Archil

    Pages 37-65

  • Realized Volatility and Mixing Distributions

    Gulisashvili, Archil

    Pages 67-75

  • Integral Transforms of Distribution Densities

    Gulisashvili, Archil

    Pages 77-108

  • Asymptotic Analysis of Mixing Distributions

    Gulisashvili, Archil

    Pages 109-166

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-31214-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-3-642-31213-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover n/a
  • ISBN 978-3-642-43386-3
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Analytically Tractable Stochastic Stock Price Models
Authors
Series Title
Springer Finance
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-31214-4
DOI
10.1007/978-3-642-31214-4
Hardcover ISBN
978-3-642-31213-7
Softcover ISBN
978-3-642-43386-3
Series ISSN
1616-0533
Edition Number
1
Number of Pages
XVIII, 362
Topics