Future exchange rates and Siegel's paradox

Siegel's paradox is a fundamental question in international trade about exchange rates for futures contracts and has puzzled many scholars for over forty years. The unorthodox approach presented in this article leads to an arbitrage-free solution which is invariant under currency re-denominations and symmetric, as explained. We will also give a complete classification of all such aggregators in the general case. The formula obtained in this setting therefore describes all the negotiated no-arbitrage forward exchange rates in terms of a reciprocity function.