Cross Hedging and Liquidity: a note

Cross hedging is a way to improve statistical hedge results because of markets'incompletion. In this framework, several markets instead of just one market, are used to increase the hedger’s financial possibilities. In the Anderson-Danthine model (1981), the optimal hedge in the multivariate case is described and commented, but transaction costs are neglected. The aim of this note is to suggest a new version of the initial model, in which transaction costs are now taken into account. In a first step, benchmark case is formalized with deterministic costs. Secondly, we consider stochastic liquidity and statistical links between liquidity levels. In the first case, the intuitive non-optimality is shown as soon as transaction costs are integrated. In the second case, a more general model is suggested and a link is mentioned with the ”commonality in liquidity” concept.