Fractional Processes as Models in Stochastic Finance

Christian Bender (), Tommi Sottinen () and Esko Valkeila ()
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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

Chapter Chapter 3 in Advanced Mathematical Methods for Finance, 2011, pp 75-103 from Springer

Abstract: 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.

Keywords: Fractional Brownian motion; Arbitrage; Hedging in fractional models; Approximation of geometric fractional Brownian motion; 91Gxx; 91B70; 60G15; 60H05 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18412-3_3

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DOI: 10.1007/978-3-642-18412-3_3

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