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Futures Cross-hedging with a Stationary Stefan Ankirchner Georgi Dimitroff Gregor Heyne

Summary: Futures Cross-hedging with a Stationary
Stefan Ankirchner Georgi Dimitroff Gregor Heyne
Christian Pigorsch
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. At the short end, the optimal hedge ratio
is close to the cross-correlation of the log returns, whereas at the long end, it is
optimal to fully hedge the position. For linear risk positions we derive explicit
formulas for the hedge error, and for non-linear 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.
This version : August 30, 2011
JEL Classification : C30, C51, G13
Keywords : risk management, cross-hedging, cointegration, futures
contracts, continuous-time model

Ankirchner, Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53113 Bonn,
Germany. Email: ankirchner@hcm.uni-bonn.de, http://www.iam.uni-bonn.de/people/ankirchner/,


Source: Ankirchner, Stefan - Institut für Angewandte Mathematik, Universität Bonn


Collections: Mathematics