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Futures Cross-Hedging with a Stationary Basis

Published online by Cambridge University Press:  26 October 2012

Stefan Ankirchner ,
Georgi Dimitroff ,
Gregor Heyne  and
Christian Pigorsch
Stefan Ankirchner
Affiliation:
ankirchner@hcm.uni-bonn.de, Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53113 Bonn, Germany
Georgi Dimitroff
Affiliation:
dimitroff@gmail.com, DZ Bank AG, Platz der Republik, 60265 Frankfurt am Main, Germany
Gregor Heyne
Affiliation:
heyne@math.hu-berlin.de, Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
Christian Pigorsch
Affiliation:
christian.pigorsch@uni-bonn.de, Department of Economics, University of Bonn,Adenauerallee 24-42, 53113 Bonn, Germany
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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.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 47 , Issue 6 , December 2012 , pp. 1361 - 1395
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2012

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