Fractional Brownian motion, random walks and binary market models

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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Year of publication:	2001-07-12
Authors:	Sottinen, Tommi
Published in:	Finance and Stochastics. - Springer. - Vol. 5.2001, 3, p. 343-355
Publisher:	Springer
Subject:	Fractional Brownian motion \| random walk \| stock price model \| binary market model

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Extent:	application/pdf
Type of publication:	Article
Notes:	received: October 1999; final version received: August 2000
Classification:	C60 - Mathematical Methods and Programming. General ; G10 - General Financial Markets. General
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005184373