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Fractional Processes as Models in Stochastic Finance

In: Advanced Mathematical Methods for Finance

Author

Listed:
  • Christian Bender

    (Saarland University, Department of Mathematics)

  • Tommi Sottinen

    (University of Vaasa, Department of Mathematics and Statistics)

  • Esko Valkeila

    (Aalto University, Department of Mathematics and Systems Analysis)

Abstract

We survey some new progress on the pricing models driven by fractional Brownian motion or mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with transaction costs. We end the paper by giving some approximation results and indicating some open problems related to the paper.

Suggested Citation

  • Christian Bender & Tommi Sottinen & Esko Valkeila, 2011. "Fractional Processes as Models in Stochastic Finance," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 75-103, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18412-3_3
    DOI: 10.1007/978-3-642-18412-3_3
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