Another way to bet on currency movements at a lower cost than buying a call or a put alone is to use knockout options. A knockout option is similar to a standard option except that it is canceled—that is, knocked out—if the exchange rate crosses, even briefly, a predefined level called the outstrike. If the exchange rate breaches this barrier, the holder cannot exercise this option, even if it ends up in-the-money. Knockout options, also known as barrier options, are less expensive than standard currency options precisely because of this risk of early cancelation.
There are different types of knockout options. For example, a down-and-out call will have a positive payoff to the option holder if the underlying currency strengthens but is canceled if it weakens sufficiently to hit the outstrike. Conversely, a down-and-out put has a positive payoff if the currency weakens but will be canceled if it weakens beyond the outstrike. In addition to lowering cost (albeit at the expense of less protection), down-and-out options are useful when a company believes that if the foreign currency declines below a certain level, it is unlikely to rebound to the point that it will cause the company losses. Up-and-out options are canceled if the underlying currency strengthens beyond the outstrike. In contrast to the previous knockout options, down-and-in and up-and-in options come into existence if and only if the currency crosses a preset barrier. The pricing of these options is extremely complex.
Option Pricing and Valuation
From a theoretical standpoint, the value of an option includes two components: intrinsic value and time value. The intrinsic value of the option is the amount by which the option is in-the-money, or S − X, where S is the current spot price and X the exercise price. In other words, the intrinsic value equals the immediate exercise value of the option. Thus, the further into the money an option is, the more valuable it is. An out-of-the-money option has no intrinsic value. For example, the intrinsic value of a call option on Swiss francs with an exercise price of $0.74 and a spot rate of $0.77 would be $0.03 per franc. The intrinsic value of the option for spot rates that are less than the exercise price is zero. Any excess of the option value over its intrinsic value is called the time value of the contract. An option will generally sell for at least its intrinsic value. The more out-of-the-money an option is, the lower the option price. These features are shown in Exhibit 8.10.
During the time remaining before an option expires, the exchange rate can move so as to make exercising the option profitable or more profitable. That is, an out-of-the-money option can move into the money, or one already in-the-money can become more so. The chance that an option will become profitable or more profitable is always greater than zero. Consequently, the time value of an option is always positive for an out-of-the-money option and is usually positive for an in-the-money option. Moreover, the more time that remains until an option expires, the higher the time value tends to be. For example, an option with six months remaining until expiration will tend to have a higher price than an option with the same strike price but with only three months until expiration. As the option approaches its maturity, the time value declines to zero.
The value of an American option always exceeds its intrinsic value because the time value is always positive up to the expiration date. For example, if S > X, then C(X) > S − X, where C(X) is the dollar price of an American call option on one unit of foreign currency. However, the case is more ambiguous for a European option because increasing the time to maturity may not increase its value, given that it can be exercised only on the maturity date.3 That is, a European currency option may be in-the-money before expiration; yet it may be out-of-the-money by the maturity date.