Cross hedging under multiplicative basis risk

Cross hedging price risk in an incomplete financial market creates basis risk. We propose a new way of modeling basis risk where price risk and basis risk are combined in a multiplicative way. Under this specification, positive prudence is a necessary and sufficient condition for underhedging in an unbiased market. Using the example of cross hedging jet fuel price risk with crude oil futures, we show that the new specification is superior in describing the price series and that optimal cross hedges differ significantly from those derived under the traditional additive cross hedging model.