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Arbitrage with Fractional Brownian Motion

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  • L. C. G. Rogers

Abstract

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.

Suggested Citation

  • L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    • Handle: RePEc:bla:mathfi:v:7:y:1997:i:1:p:95-105
    DOI: 10.1111/1467-9965.00025
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