@techreport{Bjork2005note,
abstract = {In some recent papers, such as Elliott & van der Hoek, Hu & \"{O}ksendal, a fractional Black-Scholes model have been proposed as an improvement of the classical Black-Scholes model. Common to these fractional Black-Scholes models, is that the driving Brownian motion is replaced by a fractional Brownian motion and that the Ito integral is replaced by the Wick integral, and proofs has been presented that these fractional Black-Scholes models are free of arbitrage. These results on absence of arbitrage complelety contradict a number of earlier results in the literature which prove that the fractional Black-Scholes model (and related models) will in fact admit arbitrage. The object of the present paper is to resolve this contradiction by pointing out that the definition of the self-financing trading strategies and/or the definition of the value of a portfolio used in the above cited papers does not have a reasonable economic interpretation, and thus that the results in these papers are not economically meaningful. In particular we show that in the framework of Elliott and van der Hoek, a naive buy-and-hold strategy does not in general qualify as self-financing. We also show that in Hu and \"{O}ksendal, a portfolio consisting of a positive number of shares of a stock with a positive price may, with positive probability, have a negative value.},
address = {Stockholm},
author = {Tomas Bj\"{o}rk and Henrik Hult},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {G10; 330; Mathematical Finance; Fractional Brownian motion; Arbitrage; option; financial derivatives; wick; Finanzmathematik; Black-Scholes-Modell; Arbitrage Pricing; Stochastischer Prozess; Theorie},
language = {eng},
number = {596},
publisher = {Ekonomiska Forskningsinst.},
title = {A note on Wick products and the fractional Black-Scholes model},
type = {SSE/EFI Working Paper Series in Economics and Finance},
url = {http://hdl.handle.net/10419/56125},
year = {2005}
}