Original Paper

Finance and Stochastics

, Volume 7, Issue 4, pp 533-553

First online:

Arbitrage in fractional Brownian motion models

  • Patrick CheriditoAffiliated withDepartement für Mathematik, Eidgenössische Technische Hochschule Zürich, 8092 Zürich, Switzerland (e-mail: dito@math.ethz.ch)

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Abstract.

We construct arbitrage strategies for a financial market that consists of a money market account and a stock whose discounted price follows a fractional Brownian motion with drift or an exponential fractional Brownian motion with drift. Then we show how arbitrage can be excluded from these models by restricting the class of trading strategies.

Key words: Fractional Brownian motion, arbitrage, strong arbitrage, exclusion of arbitrage