Abstract
FX Open Forward is a derivative instrument where the contract holder has the obligation to purchase a specific amount of foreign currency under a fixed exchange rate by the contract expiry date. In contrast to a traditional forward contract, a distinctive feature of FX Open Forward is that the timing and notional size of the currency conversion can be freely chosen by the contract holder. Under a Black–Scholes model where interest rates can be negative, we provide a complete solution of the early exercise strategy of an FX Open Forward. When domestic rate and foreign rate are both positive (negative), the full contractual notional should be exercised when the spot FX level is sufficiently high (low). Unlike American options, the optimal waiting region of FX Open Forward is always connected even when interest rates are negative.
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