The relationship between reciprocal currency futures prices

Consider a futures contract on Country 2's currency denominated in Country 1's currency, and its reciprocal, a futures contract on Country 1's currency denominated in Country 2's currency. Because both are marked to market in different currencies, the relationship between the associated futures prices is not simple. We investigate the functional relationship between these two futures prices.

► We investigate a continuous-time setting where a currency futures price is a function of time and its reciprocal futures price. ► Under certain conditions, this function satisfies a PDE developed in the paper. ► Under narrower conditions, the functional relationship between the reciprocal futures prices is analogous to the one between reciprocal forward prices.