14:15
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 effcient 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.
The talk is based on joint work with Georgi Dimitroff, Gregor Heyne and Christian Pigorsch.