Early Exercise of Foreign Currency Options : Determinants of American Premium and the Critical Exchange Rate

Roll [JFE 1977] demonstrates that the probability of early exercise of equity call options is low for small dividend payouts. Geske and Shastri [JBF 1985] show that unless dividends are small, put equity options would not be exercised early. Subsequently, Shastri and Tandon [JFM 1986] argue that the probability of early exercise of foreign currency options is small since foreign interest rates are analogous to a continuous dividend payout. Based on this observation, they conclude that a European model is well-suited for pricing American foreign currency options, unless the foreign interest rate is unusually high/low for call/put options. This conclusion is supported by the observation that pricing errors of a European option model are insignificant. Our study compares the Barone-Adesi-Whaley [BA-W; JF 1987] American option-pricing model with the Garman-Kohihagen [JIMF 1983] and Grabbe [JIMF 1983] European model and tests the conditions under which foreign exchange options convey opportunities to profit from premature exercise. Our results demonstrate the following. (1) The BA-W model is only advantageous in pricing out-of-the-money, long-term options. (2) The probability of gainful early exercise of puts is more sensitive than that of calls to the interest rate differential, time to maturity, and volatility. (3) The critical spot rate in the BA-W model is based on the probability of gainful early exercise on a given date, not after that date. Based on this criterion, we find a large number of opportunities for early exercise among in-the-money options maturing in less than 45 days