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Option Pricing in Fractional Brownian Markets

  • Stefan Rostek

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 622)

Table of contents

  1. Front Matter
    Pages 1-10
  2. Stefan Rostek
    Pages 1-4
  3. Stefan Rostek
    Pages 5-31
  4. Stefan Rostek
    Pages 33-55
  5. Stefan Rostek
    Pages 131-134
  6. Back Matter
    Pages 135-137

About this book

Introduction

The scientific debate of recent years about option pricing with respect to fractional Brownian motion was focused on the feasibility of the no arbitrage pricing approach. As the unrestricted fractional market setting allows for arbitrage, the conventional reasoning is that fractional Brownian motion does not qualify for modeling price process.

In this book, the author points out that arbitrage can only be excluded in case that market prices move at least slightly faster than any market participant can react. He clarifies that continuous tradability always eliminates the risk of the fractional price process, irrespective of the interpretation of the stochastic integral as an integral of Stratonovich or Itô type.

Being left with an incomplete market setting, the author shows that option valuation with respect to fractional Brownian motion may be solved by applying a risk preference based approach. The latter provides us with an intuitive closed-form solution for European options within the fractional context.

Keywords

Arbitrage Equilibrium Pricing Fractional Binomial Trees Fractional Brownian Motion Hurst Parameter Risk Preference Based Option Pricing modeling

Authors and affiliations

  • Stefan Rostek
    • 1
  1. 1.Fak. WirtschaftswissenschaftenUniversität TübingenTübingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-00331-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Business and Economics
  • Print ISBN 978-3-642-00330-1
  • Online ISBN 978-3-642-00331-8
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site