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
Date Written: September 8, 2012
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: Suggested Citation