Applying economic restrictions to foreign exchange rate dynamics: spot rates, futures, and options

Extant models of exchange rate behavior have typically relied on statistical rather than economic considerations. The approach has been to employ a variant of the generalized central limit theorem to develop tests for the models proposed. ; We propose a minimal set of simple economic restrictions symmetry, invariance, and non-negativity that must be satisfied by an exchange rate process. By symmetry, we mean that both the direct and indirect exchange rate processes must belong to the same class of distributions. By invariance, we mean that the distribution for an exchange rate must be invariant to changes in the currency unit. By non-negativity, we mean that the exchange rate process must preclude negative values. We identify various alternative specifications for exchange rate processes and show that some of them do not possess some or all of the above properties. Finally, we propose a new exchange rate process -- the mean-reverting logarithmic process (MRL) -- and develop valuation equations for several exchange rate instruments, from forward and futures contracts to straight options on the spot rates to options on the futures contracts.