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On hedging European options in geometric fractional Brownian motion market model

Author

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  • Azmoodeh Ehsan

    (Aalto University, Department of Mathematics and System Analysis, 00076 Aalto, Finnland)

  • Mishura Yuliya

    (Kyiv National Taras Shevchenko University, Department of Mechanics and Mathematics, Kyiv, Ukraine)

  • Valkeila Esko

Abstract

We work with fractional Brownian motion with Hurst index H > 1/2. We show that the pricing model based on geometric fractional Brownian motion behaves to certain extend as a process with bounded variation. This observation is based on a new change of variables formula for a convex function composed with fractional Brownian motion. The stochastic integral in the change of variables formula is a Riemann–Stieltjes integral. We apply the change of variables formula to hedging of convex payoffs in this pricing model. It turns out that the hedging strategy is as if the pricing model was driven by a continuous process with bounded variation. This in turn allows us to construct new arbitrage strategies in this model. On the other hand our findings may be useful in connection to the corresponding pricing model with transaction costs.

Suggested Citation

  • Azmoodeh Ehsan & Mishura Yuliya & Valkeila Esko, 2009. "On hedging European options in geometric fractional Brownian motion market model," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 129-144, December.
    • Handle: RePEc:bpj:strimo:v:27:y:2009:i:2:p:129-144:n:1
    DOI: 10.1524/stnd.2009.1021
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    References listed on IDEAS

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    Cited by:

    1. Mishura, Yuliya & Shevchenko, Georgiy & Valkeila, Esko, 2013. "Random variables as pathwise integrals with respect to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2353-2369.
    2. Azmoodeh, Ehsan & Tikanmäki, Heikki & Valkeila, Esko, 2010. "When does fractional Brownian motion not behave as a continuous function with bounded variation?," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1543-1550, October.

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