No-Arbitrage Bounds for Scenarios and Financial Optimization

European Journal of Operational Research, Vol. 236, No. 2, 2014, 657-663

18 Pages Posted: 15 Sep 2011 Last revised: 30 Jan 2018

See all articles by Alois Geyer

Alois Geyer

VGSF / WU

Michael Hanke

University of Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen

Date Written: September 8, 2012

Abstract

We derive no-arbitrage bounds for expected excess returns to generate scenarios used in financial optimization. The bounds allow to distinguish three regions: one where arbitrage opportunities will never exist, a second where arbitrage may be present, and a third, where arbitrage opportunities will always exist. No-arbitrage bounds are derived in closed form for a given covariance matrix using the least possible number of scenarios. The same setting is also used in an algorithm to generate discrete scenarios and trees. Numerical results from solving two-stage asset allocation problems indicate that even for minimal tree size very accurate results can be obtained.

Keywords: no-arbitrage bounds, scenario generation, financial optimization

JEL Classification: C61, G11

Suggested Citation

Geyer, Alois and Hanke, Michael and Weissensteiner, Alex, No-Arbitrage Bounds for Scenarios and Financial Optimization (September 8, 2012). European Journal of Operational Research, Vol. 236, No. 2, 2014, 657-663. Available at SSRN: https://ssrn.com/abstract=1927222 or http://dx.doi.org/10.2139/ssrn.1927222

Alois Geyer (Contact Author)

VGSF / WU ( email )

Welthandelsplatz 1
Institute for Financial Research
Vienna, 1020
Austria

HOME PAGE: http://www.wu.ac.at/~geyer

Michael Hanke

University of Liechtenstein ( email )

Fuerst Franz Josef-Strasse
Vaduz, FL-9490
Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen ( email )

Universitätsplatz 1
Bolzano, 39100
+39 0471 013496 (Phone)

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