Fractional Brownian Motion and the Inherent Exclusion of Arbitrage

21 Pages Posted: 4 Nov 2010

See all articles by Stefan Rostek

Stefan Rostek

University of Tuebingen - Faculty of Economics and Business Administration

Rainer Schoebel

University of Tuebingen - Faculty of Economics and Social Sciences

Date Written: March 29, 2010

Abstract

Over the last years, the usage of fractional Brownian motion for financial models was stuck. The favorable time-series properties of fractional Brownian motion exhibiting long-range dependence came along with an apparently insuperable shortcoming: the existence of arbitrage. In this article, we solve this dilemma: We provide a fractional analogue to the work of Sethi and Lehoczky (1981) thereby confirming that fractional Brownian motion and continuous tradability are incompatible. In the light of a market microstructure perspective to fractional Brownian motion, it becomes clear that the correct usage of fractional Brownian motion inherently implies dynamic market incompleteness.

Keywords: Fractional Brownian Motion, Wick-Itô Calculus, Fractional Stratonovich Calculus, Dynamic Incompleteness

JEL Classification: G12, G13

Suggested Citation

Rostek, Stefan and Schoebel, Rainer, Fractional Brownian Motion and the Inherent Exclusion of Arbitrage (March 29, 2010). Available at SSRN: https://ssrn.com/abstract=1701589 or http://dx.doi.org/10.2139/ssrn.1701589

Stefan Rostek (Contact Author)

University of Tuebingen - Faculty of Economics and Business Administration ( email )

Mohlstrasse 36
D-72074 Tuebingen, 72074
Germany

Rainer Schoebel

University of Tuebingen - Faculty of Economics and Social Sciences ( email )

Mohlstrasse 36
D-72074 Tuebingen
Germany
+49 7071 2977088 (Phone)

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