a1 email@example.com, Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53113 Bonn, Germany
a2 firstname.lastname@example.org, DZ Bank AG, Platz der Republik, 60265 Frankfurt am Main, Germany
a3 email@example.com, Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
a4 firstname.lastname@example.org, Department of Economics, University of Bonn,Adenauerallee 24-42, 53113 Bonn, Germany
When managing risk, frequently only imperfect hedging instruments are at hand. We show how to optimally cross-hedge risk when the spread between the hedging instrument and the risk is stationary. For linear risk positions we derive explicit formulas for the hedge error, and for nonlinear positions we show how to obtain numerically efficient estimates. Finally, we demonstrate that even in cases with no clear-cut decision concerning the stationarity of the spread, it is better to allow for mean reversion of the spread rather than to neglect it.