Journal of Financial and Quantitative Analysis

Research Articles

Futures Cross-Hedging with a Stationary Basis

Stefan Ankirchnera1, Georgi Dimitroffa2, Gregor Heynea3 and Christian Pigorscha4

a1 ankirchner@hcm.uni-bonn.de, Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53113 Bonn, Germany

a2 dimitroff@gmail.com, DZ Bank AG, Platz der Republik, 60265 Frankfurt am Main, Germany

a3 heyne@math.hu-berlin.de, Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany

a4 christian.pigorsch@uni-bonn.de, Department of Economics, University of Bonn,Adenauerallee 24-42, 53113 Bonn, Germany

Abstract

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.

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