Arbitrage with Fractional Brownian Motion

Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long–range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitr...

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Bibliographic Details
Published in:Mathematical finance 1997-01, Vol.7 (1), p.95-105
Main Author: Rogers, L. C. G.
Format: Article
Language:English
Subjects:
Arbitrage
Asset valuation
Brownian motion
equivalent martingale measure
Finance
fractional Brownian motion
Investment
long-range dependence
Mathematical models
Mathematics
Prices
Shares
Studies
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Summary:Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long–range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motion to model long–range dependence of returns while avoiding arbitrage.
ISSN:0960-1627
1467-9965
DOI:10.1111/1467-9965.00025