() and Henrik Hult
Tomas Björk: Dept. of Finance, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, SE-113 83 Stockholm, Sweden
Henrik Hult: Department of Applied Mathematics and Statistics, Postal: Copenhagen University, Universitetsparken 5 , 2100 Copenhagen, DENMARK
Abstract: In some recent papers, such as Elliott & van der Hoek, Hu & Öksendal, 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 Öksendal, a portfolio consisting of a positive number of shares of a stock with a positive price may, with positive probability, have a negative "value".
13 pages, April 25, 2005
Note: Published in: "Finance and Stochastics", Vol 9, No 2, pp 197-209, (2005).
Full text files
hastef0596.pdf Full text
Questions (including download problems) about the papers in this series should be directed to Helena Lundin ()
Report other problems with accessing this service to Sune Karlsson ().
This page generated on 2018-01-27 00:01:33.