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Fractional Brownian motion, random walks and binary market models

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Author Info
Tommi Sottinen () (Department of Mathematics, University of Helsinki, P.O. Box 4, 00014 Helsinki, Finland Manuscript)

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Abstract

We prove a Donsker type approximation theorem for the fractional Brownian motion in the case $H>1/2.$ Using this approximation we construct an elementary market model that converges weakly to the fractional analogue of the Black-Scholes model. We show that there exist arbitrage opportunities in this model. One such opportunity is constructed explicitly.

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Publisher Info
Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 5 (2001)
Issue (Month): 3 ()
Pages: 343-355
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Handle: RePEc:spr:finsto:v:5:y:2001:i:3:p:343-355

Note: received: October 1999; final version received: August 2000
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Related research
Keywords: Fractional Brownian motion; random walk; stock price model; binary market model;

Find related papers by JEL classification:
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

Cited by:
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  1. Andrea Cavanzo & Liliana Blanco, 2005. "El movimiento browniano fraccional como límite de ciertos tipos de procesos estocásticos," Revista Colombiana de Estadística, REVISTA COLOMBIANA DE ESTADISTICA. [Downloadable!]
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