The Black model should not be used for valuing American options on currency futures because it may be optimal to exercise the options early in the same way as it may be optimal to exercise options on the spot currency early. The binomial or the Barone-Adesi and Whaley models may be used for valuing those options.

The early exercise potential of American options on futures is different to that of options on the spot. Futures prices do not exhibit the discrete jumps that accompany spot market assets when the underlying spot asset makes discrete distributions. However, as the carry basis of the future converges to zero at delivery, the futures price converges to the spot price in an orderly manner. Thus, if carry basis is positive (i.e. F, > P,), the futures price will decline relative to the spot rate in a predictable manner. In effect, because of the daily marking to market, the future would be behaving like an asset that made a continuous distribution. Merton (1973) has shown that it may be optimal to exercise, at any time, an option on an asset that pays a continuous dividend. Thus when the carry basis is positive, it may be optimal to exercise American options on those futures at any time.

It will be recalled that carry basis is positive when the underlying asset pays no dividend or interest, or when the distribution that is paid is less than the borrowing and storage costs incurred in acquiring the underlying asset. Thus, in the case of currency futures, carry basis is positive if the domestic interest rate is above the foreign rate. Accordingly, in such circumstances the currency future can be treated as an asset that pays a continuous distribution, and it may be optimal to exercise American call options on such futures early. However, if the foreign interest rate is greater than the domestic rate, the futures price would be at a discount to the spot rate and the future would behave like an asset that continuously receives an injection of value. Accordingly, it would not be optimal to exercise call options on such futures prematurely, although it may be optimal to so exercise put options.

Thus, if r > r_f, it may be optimal to exercise call options on currency futures prematurely, but not puts, and the early exercise premium on calls should be valuable. If, on the other hand, r < r_f, it would not be optimal to exercise calls prematurely and therefore they can be valued as European options. However, puts may be optimally exercised prematurely and should exhibit an early exercise premium.

The relationship between American options on the future and American options on the spot currency also depends upon the relationship between the domestic and foreign interest rates. If domestic interest rates are above foreign rates, the forward currency will be at a premium and the futures price will be above the spot rate (remember direct quotes). American calls on the futures will be worth more than the otherwise identical American calls on the spot currency. On the other hand, American puts on the future will be worth less than American puts on the spot currency.

If the foreign interest rates were above the domestic rates, the forward currency would be at a discount to the spot and the futures price will be below the spot price. In such circumstances, American calls on the future must be worth less than otherwise identical American calls on the spot currency. By the same reasoning, American puts on the future must be worth more than puts on the spot currency.

Applications of currency options to currency risk management

Currency options, like their counterparts on other underlying assets, can be used for a variety of purposes and a great variety of strategies can be created. The basic strategies of buying or writing of calls and puts, the vertical, diagonal and calendar spreads, as well as the volatility spreads, are all applicable to the currency option market.

The relative cost of options

It is often stated that currency options are expensive instruments for use in risk management. This view is usually expressed relative to forward rates or futures prices, and is directed at the premium that is paid for options compared with the lack of premium for forwards or futures.

The view as to whether a currency option is expensive or not depends upon one’s view of expected volatility compared with that implied in the option’s price. It is not correct to consider an option to be expensive for risk management just because a premium is payable.

To understand this, we have only to compare the returns distribution that results from hedging a currency exposure with forwards, with that from using options.

Note that the exposure hedged with forwards has a much higher probability of achieving the expected return compared with the unhedged exposure. However, although there is no downside with the forward hedged position, there is no upside either. The risk of any downside has been removed without any payment for this service simply because the potential of any upside has been passed over to the counterparty in compensation.

If we look at the position of the exposure insured with an option, there is a very high probability of achieving the expected return and some probability of achieving an even higher return, but virtually no probability of suffering a lower return.

It is this asymmetry in the pay-offs from an option that results in the premium being payable. That premium clearly is a form of insurance premium.

The need to pay a premium for the asymmetrical pay-off does suggest that currency options, like other options, should be purchased in those situations where asymmetry is valuable. Examples would be where insurance against losses is preferable to hedging against all rate changes.

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