The Spaniards coming into the West Indies had many commodities of the country which they needed, brought unto them by the inhabitants, to who when they offered them money, goodly pieces of gold coin, the Indians, taking the money, would put it into their

currency options to their customers. Exchange-traded currency options were first offered in 1983 by the Philadelphia Stock Exchange (PHLX), where they are now traded on the United Currency Options Market (UCOM). Currency options are one of the fastest-growing segments of the global foreign exchange market, accounting for more than 9% of daily trading volume in 2004.

In principle, an option is a financial instrument that gives the holder the right—but not the obligation—to sell (put) or buy (call) another financial instrument at a set price and expiration date. The seller of the put option or call option must fulfill the contract if the buyer so desires it. Because the option not to buy or sell has value, the buyer must pay the seller of the option some premium for this privilege. As applied to foreign currencies, call options give the customer the right to purchase—and put options give the right to sell—the contracted currencies at the expiration date. Note that because a foreign exchange transaction has two sides, a call (put) option on a foreign currency can be considered a foreign currency put (call) option on the domestic currency. For example, the right to buy euros against dollar payment is equivalent to the right to sell dollars for euro payment. An American option can be exercised at any time up to the expiration date; a European option can be exercised only at maturity.

An option that would be profitable to exercise at the current exchange rate is said to be in-the-money. Conversely, an out-of-the-money option is one that would not be profitable to exercise at the current exchange rate. The price at which the option is exercised is called the exercise price or strike price. An option whose exercise price is the same as the spot exchange rate is termed at-the-money. That is,

Option Description

Strike Price Relative to Spot Rate

Effect of Immediate Exercise

In-the-money

Strike price < spot rate

Profit

At-the-money

Strike price = spot rate

Indifference

Out-of-the-money

Strike price > spot rate

Loss

Market Structure

Options are purchased and traded either on an organized exchange (such as the United Currency Options Market of the PHLX) or in the over-the-counter (OTC) market. Exchange-traded options or listed options are standardized contracts with predetermined exercise prices, and standard expiration months (March, June, September, and December plus two near-term months). UCOM options are available in six currencies—the Australian dollar, British pound, Canadian dollar, euro, Japanese yen, and Swiss franc—and are traded in standard contracts half the size of the CME futures contracts. The euro contracts have replaced contracts in the Deutsche mark and French franc. Contract specifications are shown in Exhibit 8.4. The PHLX trades only European-style standardized currency options. Its margin requirements change over time.

The PHLX also offers customized currency options, which allow users to customize various aspects of a currency option, including choice of exercise price, expiration date (up to two years out), and premium quotation as either units of currency or percentage of underlying value. Customized currency options can be traded on any combination of the six currencies for which standardized options are available, along with the Mexican peso and the U.S. dollar.² The contract size is the same as that for standardized contracts in the underlying currency. Other organized options exchanges are located in Amsterdam (European Options Exchange), Chicago (Chicago Mercantile Exchange), and Montreal (Montreal Stock Exchange).

Exhibit 8.4 Contract Specifications for PHLX Standardized Currency Options Contracts

*Even strike prices (i.e., 100, 102)

**Odd strike prices (i.e., 99, 101)

Source: Data collected from PHLX's Web site at www.phlx.com.

Over-the-counter (OTC) options are contracts whose specifications are generally negotiated as to the amount, exercise price and rights, underlying instrument, and expiration. OTC currency options are traded by commercial and investment banks in virtually all financial centers. OTC activity is concentrated in London and New York, and it centers on the major currencies, most often involving U.S. dollars against pounds sterling, euros, Swiss francs, Japanese yen, and Canadian dollars. Branches of foreign banks in the major financial centers are generally willing to write options against the currency of their home country. For example, Australian banks in London write options on the Australian dollar. Generally, OTC options are traded in round lots, commonly $5 million to $10 million in New York and $2 million to $3 million in London. The average maturity of OTC options ranges from two to six months, and very few options are written for more than one year. American options are most common, but European options are popular in Switzerland and Germany because of familiarity.

The OTC options market consists of two sectors: (1) a retail market composed of nonbank customers who purchase from banks what amounts to customized insurance against adverse exchange rate movements and (2) a wholesale market among commercial banks, investment banks, and specialized trading firms; this market may include interbank OTC trading or trading on the organized exchanges. The interbank market in currency options is analogous to the interbank markets in spot and forward exchange. Banks use the wholesale market to hedge, or “reinsure,” the risks undertaken in trading with customers and to take speculative positions in options.

Most retail customers for OTC options are either corporations active in international trade or financial institutions with multicurrency asset portfolios. These customers could purchase foreign exchange puts or calls on organized exchanges, but they generally turn to the banks for options in order to find precisely the terms that match their needs. Contracts are generally tailored with regard to amount, strike price, expiration date, and currency.

The existence of OTC currency options predates exchange-traded options by many years, but trading in OTC options grew rapidly at the same time that PHLX trading began. The acceleration in the growth of options trading in both markets appears to spring from the desire by companies to manage foreign currency risks more effectively and, in particular, from an increased willingness to pay a fee to transfer such risks to another party. Most commentators suggest that corporate demand has increased because the greater volatility of exchange rates has increasingly exposed firms to risks from developments that are difficult to predict and beyond their control.

The growth of listed options, especially for “wholesale” purposes, apparently is putting pressure on the OTC markets for greater standardization in interbank trading. In some instances, OTC foreign currency options are traded for expiration on the third Wednesday of March, June, September, and December, to coincide with expiration dates on the U.S. exchanges.

Although the buyer of an option can lose only the premium paid for the option, the seller's risk of loss is potentially unlimited. Because of this asymmetry between income and risk, few retail customers are willing to write options. For this reason, the market structure is distinctly asymmetrical when compared with the ordinary market for spot and forward foreign exchange, where there is a balance between customers who are purchasing or selling currency and the interbank market likewise has a reasonable balance.

1 Bradford Cornell and Marc Reinganum, “Forward and Futures Prices: Evidence from the Foreign Exchange Markets,” Journal of Finance, December 1981, pp. 1035-1045.

2 The Australian dollar may be matched only against the U.S. dollar.

Using Currency Options

To see how currency options might be used, consider a U.S. importer with a €62,500 payment to make to a German exporter in 60 days. The importer could purchase a European call option to have the euros delivered to him at a specified exchange rate (the strike price) on the due date. Suppose the option premium is $0.02 per euro and the exercise price is $1.44. The importer has paid $1,250 for a €144 call option, which gives it the right to buy €62,500 at a price of $1.44 per euro at the end of 60 days. If at the time the importer's payment falls due, the value of the euro has risen to, say, $1.50, the option would be in-the-money. In this case, the importer exercises its call option and purchases euros for $1.44. The importer would earn a profit of $3,750 (62,500 × 0.06), which would more than cover the $1,250 cost of the option. If the rate has declined below the contracted rate to, say, $1.41, the € 144 option would be out-of-the-money. Consequently, the importer would let the option expire and purchase the euros in the spot market. Despite losing the $1,250 option premium, the importer would still be $625 better off than if it had locked in a rate of $1.44 with a forward or futures contract.

Exhibit 8.5 illustrates the importer's gains or losses on the call option. At a spot rate on expiration of $1.44 or lower, the option will not be exercised, resulting in a loss of the $1,250 option premium. Between $1.44 and $1.46, the option will be exercised, but the gain is insufficient to cover the premium. The break-even price—at which the gain on the option just equals the option premium—is $1.46. Above $1.46 per euro, the option is sufficiently deep in-the-money to cover the option premium and yield a—potentially unlimited—net profit.

Because this is a zero-sum game, the profit from selling a call, shown in Exhibit 8.6, is the mirror image of the profit from buying the call. For example, if the spot rate at expiration is above $1.46/€, the call option writer is exposed to potentially unlimited losses. Why would an option writer accept such risks? For one thing, the option writer may already be long euros, effectively hedging much of the risk. Alternatively, the writer might be willing to take a risk in the hope of profiting from the option premium because of a belief that the euro will depreciate over the life of the contract. If the spot rate at expiration is $1.44 or less, the option ends out-of-the-money and the call option writer gets to keep the full $1,250 premium. For spot rates between $1.44 and $1.46, the option writer still earns a profit, albeit a diminishing one.

In contrast to the call option, a put option at the same terms (exercise price of $1.44 and put premium of $0.02 per euro) would be in-the-money at a spot price of $1.41 and out-of-the-money at $1.50. Exhibit 8.7 illustrates the profits available on this euro put option. If the spot price falls to, say, $1.38, the holder of a put option will deliver €62,500 worth $86,250 (1.38 × 62,500) and receive $90,000 (1.44 × 62,500). The option holder's profit, net of the $1,250 option premium, is $2,500. As the spot price falls further, the value of the put option rises. At the extreme, if the spot rate falls to zero, the buyer's profit on the contract will reach $88,750 (1.44 × 62,500 − 1,250). Below a spot rate of $1.42, the gain on the put option will more than cover the $1,250 option premium. Between $1.42—the break-even price for the put option—and $1.44, the holder would exercise the option, but the gain would be less than the option premium. At spot prices above $1.44, the holder would not exercise the option and so would lose the $1,250 premium. Both the put and the call options will be at-the-money if the spot rate in 60 days is $1.44, and the call or put option buyer will lose the $1,250 option premium.

Exhibit 8.5 Profit from Buying a Call Option for Various Spot Prices at Expiration

As in the case of the call option, the writer of the put option will have a payoff profile that is the mirror image of that for the buyer. As shown in Exhibit 8.8, if the spot rate at expiration is $1.44 or higher, the option writer gets to keep the full $1,250 premium. As the spot rate falls below $1.44, the option writer earns a decreasing profit down to $1.42. For spot rates below $1.42/€, the option writer is exposed to increasing losses, up to a maximum potential loss of $88,750. The writer of the put option will accept these risks in the hope of profiting from the put premium. These risks may be minimal if the put option writer is already short euro.

Exhibit 8.6 Profit from Selling a Call Option for Various Spot Prices at Expiration

Typical users of currency options might be financial firms holding large investments overseas where sizable unrealized gains have occurred because of exchange rate changes and where these gains are thought likely to be partially or fully reversed. Limited use of currency options has also been made by firms that have a foreign currency inflow or outflow that is possibly but not definitely forthcoming. In such cases, when future foreign currency cash flows are contingent on an event such as acceptance of a bid, long call or put positions can be safer hedges than either futures or forwards.

Application Speculating with a Japanese Yen Call Option

In March, a speculator who is gambling that the yen will appreciate against the dollar pays $680 to buy a yen June 81 call option. This option gives the speculator the right to buy ¥6,250,000 in June at an exchange rate of ¥1 = $0.0081 (the 81 in the contract description is expressed in hundredths of a cent). By the expiration date in June, the yen spot price has risen to $0.0083. What is the investors net return on the contract?

Solution. Because the call option is in-the-money by 0.02 cents, the investor will realize a gain of $1,250 ($0.0002 × 6,250,000) on the option contract. This amount less the $680 paid for the option produces a gain on the contract of $570.

Exhibit 8.7 Profit from Buying a Put Option for Various Spot Prices at Expiration

For example, assume that a U.S. investor makes a firm bid in pounds sterling to buy a piece of real estate in London. If the firm wishes to hedge the dollar cost of the bid, it can buy pounds forward so that if the pound sterling appreciates, the gain on the forward contract will offset the increased dollar cost of the prospective investment. But if the bid is eventually rejected, and if the pound has fallen in the interim, losses from the forward position will have no offset. If no forward cover is taken and the pound appreciates, the real estate will cost more than expected.

Currency call options can provide a better hedge in such a case. Purchased-pound call options would provide protection against a rising pound; and yet, if the bid were rejected and the pound had fallen, the uncovered hedge loss would be limited to the premium paid for the calls. Note that a U.S. company in the opposite position, such as one bidding to supply goods or services priced in pounds to a British project, whose receipt of future pound cash inflows is contingent on acceptance of its bid, would use a long pound put position to provide the safest hedge.

Exhibit 8.8 Profit from Selling a Put Option for Various Spot Prices at Expiration

Currency options also can be used by pure speculators, those without an underlying foreign currency transaction to protect against. The presence of speculators in the options markets adds to the breadth and depth of these markets, thereby making them more liquid and lowering transactions costs and risk.

Currency Spread.

A currency spread allows speculators to bet on the direction of a currency but at a lower cost than buying a put or a call option alone. It involves buying an option at one strike price and selling a similar option at a different strike price. The currency spread limits the holder's downside risk on the currency bet but at the cost of limiting the positions upside potential. As shown in Exhibit 8.9a, a spread designed to bet on a currency's appreciation—also called a bull spread—would involve buying a call at one strike price and selling another call at a higher strike price. The net premium paid for this position is positive because the former call will be higher priced than the latter (with a lower strike, the option is less out-of-the-money), but it will be less than the cost of buying the former option alone. At the same time, the upside is limited by the strike price of the latter option. Exhibit 8.9b shows the payoff profile of a currency spread designed to bet on a currency's decline. This spread—also called a bear spread—involves buying a put at one strike price and selling another put at a lower strike price.

Exhibit 8.9 Currency Spreads

Knockout Options.

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.

Exhibit 8.10 The Value of a Call Option before Maturity

Before expiration, an out-of-the-money option has only time value, but an in-the-money option has both time value and intrinsic value. At expiration, an option can have only intrinsic value. The time value of a currency option reflects the probability that its intrinsic value will increase before expiration; this probability depends, among other things, on the volatility of the exchange rate. An increase in currency volatility increases the chance of an extremely high or low exchange rate at the time the option expires. The chance of a very high exchange rate benefits the call owner. The chance of a very low exchange rate, however, is irrelevant; the option will be worthless for any exchange rate less than the striking price, whether the exchange rate is “low” or “very low.” Inasmuch as the effect of increased volatility is beneficial, the value of the call option is higher. Put options similarly benefit from increased volatility in the exchange rate.

Another aspect of time value involves interest rates. In general, options have a present intrinsic value, determined by the exercise price and the price of the underlying asset. Because the option is a claim on a specified amount of an asset over a period of time into the future, that claim must have a return in line with market interest rates on comparable instruments. Therefore, a rise in the interest rate will cause call values to rise and put values to fall.

Pricing foreign currency options is more complex because it requires consideration of both domestic and foreign interest rates. A foreign currency is normally at a forward premium or discount vis-å-vis the domestic currency. As we saw in Chapter 4, this forward premium or discount is determined by relative interest rates. Consequently, for foreign currency options, call values rise and put values fall when the domestic interest rate increases or the foreign interest rate decreases.

The flip side of a more valuable put or call option is a higher option premium. Hence, options become more expensive when exchange rate volatility rises. Similarly, when the domestic-foreign interest differential increases, call options become more expensive and put options less expensive. These elements of option valuation are summarized in Exhibit 8.11.

Exhibit 8.11 Currency Option Pricing and Valuation

3 For a technical discussion of foreign currency option pricing, see Mark B. Garman and Steven W. Kohlhagen, “Foreign Currency Option Values,” Journal of International Money and Finance, December 1983, pp. 231-237.

Using Forward or Futures Contracts versus Options Contracts

Suppose that on July 1, an American company makes a sale for which it will receive €125,000 on September 1. The firm will want to convert those euros into dollars, so it is exposed to the risk that the euro will fall below its current spot rate of $1.4922 before September. The firm can protect itself against a declining euro by selling its expected euro receipts forward (using a futures contract at a futures rate of $1.4956) or by buying a euro put option.

Exhibit 8.12 shows possible results for each choice, using options with strike prices just above and just below the spot exchange of July 1 ($1.48 and $1.50). The example assumes a euro decline to $1.4542 and the consequent price adjustments of associated futures and options contracts. The put quotes are the option premiums per euro. Thus, the dollar premium associated with a particular quote equals the quote multiplied by the number of euros covered by the put options. For example, the quote of $0.0059 on July 1 for a September put option with a strike price of 148 (in cents) represents a premium for covering the exporter's €125,000 transaction equal to $0.0059 × 125,000 = $737.50. Note that the September futures price is unequal to the spot rate on September 1, and the put option premiums on September 1 do not equal their intrinsic values, because settlement of these contracts does not occur until later in the month.

Exhibit 8.12 Declining Exchange Rate Scenario

Exhibit 8.13 Hedging Alternatives: Offsetting A $4,750 Loss Due to a Declining Euro

In the example just described, a decision to remain unhedged would yield a loss of 125,000 X (1.4922 − 1.4542), or $4,750. The outcomes of the various hedge possibilities are shown in Exhibit 8.13.

Exhibit 8.13 demonstrates the following two differences between the futures and options hedging strategies:

1. The futures hedge offers the closest offset to the loss due to the decline of the euro.

2. The purchase of the in-the-money put option (the 150 strike price) offers greater protection (but at a higher premium) than the out-of-the-money put (the 148 strike price).

As the euro declines in value, the company will suffer a larger loss on its euro receivables, to be offset by a further increase in the value of the put and futures contracts.

Although the company wants to protect against the possibility of a euro depreciation, what would happen if the euro appreciated? To answer this question—so as to assess fully the options and futures hedge strategies—assume the hypothetical conditions in Exhibit 8.14.

In this scenario, the rise in the euro would increase the value of the unhedged position by 125,000 X (1.5338 − 1.4922), or $5,200. This gain would be offset by losses on the futures or options contracts, as shown in Exhibit 8.15.

We can see that the futures hedge again provides the closest offset. Because these hedges generate losses, however, the company would be better served under this scenario by the smallest offset. With rapidly rising exchange rates, the company would benefit most from hedging with a long put position as opposed to a futures contract; conversely, with rapidly falling exchange rates, the company would benefit most from hedging with a futures contract.

Exhibit 8.14 Rising Exchange Rate Scenario

Exhibit 8.15 hedging alternatives; offsetting a $5,200 gain Due to a Rising Euro

Application Biogen Assesses Its Hedging Options

Biogen, a U.S. company, expects to receive royalty payments totaling £1.25 million next month. It is interested in protecting these receipts against a drop in the value of the pound. It can sell 30-day pound futures at a price of $1.6513 per pound or it can buy pound put options with a strike price of $1.6612 at a premium of 2.0 cents per pound. The spot price of the pound is currently $1.6560, and the pound is expected to trade in the range of $1.6250 to $1.7010. Biogen's treasurer believes that the most likely price of the pound in 30 days will be $1.6400.

a. How many futures contracts will Biogen need to protect its receipts? How many options contracts?

Solution. With a futures contract size of £62,500, Biogen will need 20 futures contracts to protect its anticipated royalty receipts of £1.25 million. Since the option contract size is half that of the futures contract, or £31,250, Biogen will need 40 put options to hedge its receipts.

b. Diagram Biogen's profit and loss associated with the put option position and the futures position within its range of expected exchange rates (see Exhibit 8.7, p. 306). Ignore transaction costs and margins.

c. Calculate what Biogen would gain or lose on the option and futures positions within the range of expected future exchange rates and if the pound settled at its most likely value.

Solution. If Biogen buys the put options, it must pay a put premium of 0.02 × 1,250,000 = $25,000. If the pound settles at its maximum value, Biogen will not exercise and it loses the put premium. But if the pound settles at its minimum of $1.6250, Biogen will exercise at $1.6612 and earn $0.0362/£ for a total of 0.0362 × 1,250,000 = $45,250. Biogen's net garn will be $45,250 − $25,000 = $20,250.

With regard to the futures position, Biogen will lock in a price of $1.6513/£ for total revenue of $1.6513 × 1,250,000 = $2,064,125. If the pound settles at its minimum value, Biogen will have a gain per pound on the futures contracts of $1.6513 − $1.6250 = $0.0263/£ (remember it is selling pounds at a price of $1.6513 when the spot price is only $1.6250) for a total gain of 0.0263 × 1,250,000 = $32,875. On the other hand, if the pound appreciates to $1.70100, Biogen will lose $1.7010 − $1.6513 = $0.0497/£ for a total loss on the futures contract of 0.0497 × 1,250,000 = $62,125.

If the pound settles at its most likely price of $1.6400, Biogen will exercise its put option and earn $1.6612 − $1.6400 = $0.0212/£ or $26,500. Subtracting off the put premium of $25,000 yields a net gain of $1,500. If Biogen hedges with futures contracts, it will sell pounds at $1.6513 when the spot rate is $1.6400. This will yield Biogen a gain of $0.0113/£ for a total gain on the futures contract equal to 0.0113 × 1,250,000 = $14,125.

d. Show the total cash flow to Biogen (hedge plus the gain or loss on the hedge) using the options and futures contracts, as well as the unhedged position within the range of expected future exchange rates.

Solution. Biogen will receive £1.25 million. The first row shows the dollar values of this inflow for the range of expected future exchange rates. It represents what Biogen would receive if it were unhedged. The following rows show the hedged values of this inflow for the options and futures contracts.

As the table shows, the use of futures will lock in the royaltys net dollar value at $2,064,125. In contrast, using options will set a floor of $2,051,500 for Biogen's net dollar cash flow from the royalty. The upside is that the option-hedged royalty cash flow will exceed $2,064,125 if the future spot rate is greater than $1.6713. At this exchange rate, the royalty payment will be worth $2,089,125 and its net value after accounting for the $25,000 loss on the put option contracts will just equal $2,064,125. Over the same range of exchange rates, the unhedged royalty payment varies from $2,031,250 to $2,126,250.

e. What is Biogen's break-even future spot price on the option contract? On the futures contract?

Solution. On the option contract, the spot rate will have to sink to the exercise price less the put premium for Biogen to break even on the contract, or $1.6612 − $0.02 = $1.6412. In the case of the futures contract, break-even occurs when the spot rate equals the futures rate, or $1.6513.

f. Calculate the corresponding profit and loss and break-even positions on the futures and options contracts for those who took the other side of these contracts.

Solution. The sellers’ profit and loss and break-even positions on the futures and options contracts will be the mirror image of Biogen's position on these contracts. For example, the sellers of the futures and options contracts will break even at future spot prices of $1.6513/£ and $1.6412/£, respectively. Similarly, if the pound falls to its minimum value, the options sellers will lose $20,250 and the futures sellers will lose $32,875. But if the pound hits its maximum value of $1.7010, the options sellers will earn $25,000 and the futures sellers will earn $62,125.

Mini-Case Carrier Lumber Evaluates Its Futures

Suppose that Carrier Lumber Ltd, a Canadian forest products company, sells lumber to Home Depot. In return, Home Depot will pay Carrier U.S.$1,000,000 in 90 days. At a current exchange rate of U.S.$0.83/Can$, the receivable is worth Can$1,204,819. However, if the Canadian dollar appreciates by U.S.$0.01 within the next three months, the receivable will lose Can$14,343 in value. Carrier is concerned about the potential for losses as it has been advised that the spot rate in 90 days can vary between U.S.$0.81 and U.S.$0.85.

In order to offset any potential losses in the value of the U.S. dollar receivable, Carrier is considering the use of Canadian dollar futures to hedge its exposure. Since each Canadian dollar futures contract is worth Can$100,000, Carrier would buy 12 futures contracts if it decided to hedge with futures. This figure is found by dividing the face value of the exposure (U.S.$1million = Can$1,204,819) by the contract value (Can$100,000) and rounding to the nearest contract. If the Canadian dollar appreciates within the next three months, the futures position will gain U.S.$12,000 for every one cent increase in the USD/CAD exchange rate (U.S.$1,000 × 12 contracts). This figure translates into a gain of Can$14,458 at today's exchange rate (12,000/0.83). The current three-month futures rate is $0.8325.

Carrier, at the suggestion of its banker, is also considering the use of currency options to hedge its receivable. By using options rather than futures, management would be able to minimize its down-side risk in the event that the Canadian dollar appreciates, yet at the same time benefit from any depreciation that may occur within the next three months. To hedge its downside risk, Carrier would buy 24 three-month Canadian dollar call options (since each Can$ options contract is worth Can$50,000). If it used currency options to hedge its receivable, Carrier decided that it would buy these call options with an at-the-money strike price. The premium paid for these options would be around U.S.$0.87 per Can$100, or Can$12,578.31 at the current exchange rate (0.87 × 1,000 × 12/0.83).

Questions

1. Develop a table showing Carrier's Can$ profit and loss associated with the futures position and the options position within its range of expected exchange rates at U.S.$0.01 increments. Ignore transaction costs and margins.

2. Show the total Can$ cash flow to Carrier (hedge plus the gain or loss on the hedge) using the options and futures contracts, as well as the unhedged position within the range of expected future exchange rates.

3. What is Carrier's break-even 90-day spot price on the option contracts? On the futures contracts?

4. Would you recommend Carrier hedge with the futures contracts or the options contracts? Why?

Futures Options

In January 1984, the CME introduced a market in options on DM (now replaced by euro) futures contracts. Since then, the futures option market has grown to include options on most of its currency futures contracts. Trading involves purchases and sales of puts and calls on a contract calling for delivery of a standard CME futures contract in the currency rather than the currency itself. When such a contract is exercised, the holder receives a short or long position in the underlying currency futures contract that is marked to market, providing the holder with a cash gain. (If there were a loss on the futures contract, the option would not be exercised.) Specifically,

• If a call futures option contract is exercised, the holder receives a long position in the underlying futures contract plus an amount of cash equal to the current futures price minus the strike price.

• If a put futures option is exercised, the holder receives a short position in the futures contract plus an amount of cash equal to the strike price minus the current futures price.

The seller of these options has the opposite position to the holder after exercise: a cash outflow plus a short futures position on a call and a long futures position on a put option.

Application Exercising a Pound Call Futures Option Contract

An investor is holding a pound call futures option contract for June delivery (representing £62,500) at a strike price of $1.5050. The current price of a pound futures contract due in June is $1.5148. What will the investor receive if she exercises her futures option?

Solution. The investor will receive a long position in the June futures contract established at a price of $1.5050 and the option writer has a short position in the same futures contract. These positions are immediately marked to market, triggering a cash payment to the investor from the option writer of 62,500($1.5148 − $1.5050) = $612.50. If the investor desires, she can immediately close out her long futures position at no cost, leaving her with the $612.50 payoff.

Application Exercising a Swiss Franc Put Futures Option Contract

An investor is holding one Swiss franc March put futures option contract (representing SFr 125,000) at a strike price of $0.8132. The current price of a Swiss franc futures contract for March delivery is $0.7950. What will the investor receive if she exercises her futures option?

Solution. The investor will receive a short position in the March futures contract established at a price of $0.8132, and the option writer has a long position in the same futures contract. These positions are immediately marked to market and the investor will receive a cash payment from the option writer of 125,000($0.8132 − 0.7950) = $2,275. If the investor desires, she can immediately close out her short futures position at no cost, leaving her with the $2,275 payoff.

A futures option contract has this advantage over a futures contract: With a futures contract, the holder must deliver one currency against the other or reverse the contract, regardless of whether this move is profitable. In contrast, with the futures option contract, the holder is protected against an adverse move in the exchange rate but may allow the option to expire unexercised if using the spot market would be more profitable.

8.3 Reading Currency Futures and Options Prices

Futures and exchange-listed options prices appear daily in the financial press. Exhibit 8.16 shows prices for May 19, 2008. Futures prices on the CME are listed for seven currencies, with two to four contracts quoted for each currency: June, July, and September 2008. Included are the opening and last settlement (settle) prices, the change from the previous trading day, the range for the day, and the number of contracts outstanding (open interest). For example, the June euro futures contract opened at $1.5562 per euro and closed at $1.5489, down $0.0069 per euro relative to its previous closing price of $1.5558. Futures prices are shown in Exhibit 8.16a.

Exhibit 8.16b shows the Chicago Mercantile Exchange (CME) options on CME futures contracts. To interpret the numbers in this column, consider the June euro call options. These are rights to buy the June euro futures contract at specified prices—the strike prices. For example, the call option with a strike price of 15350 means that you can purchase an option to buy a June euro futures contract up to the June settlement date for $1.5350 per euro. This option will cost $0.0213 per euro, or $2,662.50, plus brokerage commission, for a €125,000 contract. The price is high because the option is in-the-money (you can buy a futures contract worth $1.5489 per euro at a price of just $1.5350 per euro). In contrast, the June futures option with a strike price of 15600, which is out-of-the-money, costs only $0.0083 per euro, or $1,037.50 for one contract. These option prices indicate that the market expects the dollar price of the euro to exceed $1.5350 but is relatively confident it will not rise much beyond $1.5600 by June.

Exhibit 8.16 Currency Futures and Options Contracts

As we have just seen, a futures call option allows you to buy the relevant futures contract, which is settled at maturity. On the other hand, the Philadelphia call options contract is an option to buy foreign exchange spot, which is settled when the call option is exercised; the buyer receives foreign currency immediately.

Price quotes usually reflect this difference. For example, PHLX call options for the June euro, with a strike price of $1.5350, were $0.0249 per euro (versus $0.0213 for the June futures call option), or $1,556.25, plus brokerage fees for one contract of €62,500. Brokerage fees here would be about the same as on the CME: about $16 per transaction round trip per contract. Exhibit 8.17 summarizes how to read price quotations for futures and options on futures using a euro illustration.

Exhibit 8.17 How to Read Futures and Futures Options Quotations

8.4 Summary and Conclusions

In this chapter, we examined the currency futures and options markets and looked at some of the institutional characteristics and mechanics of these markets. We saw that currency futures and options offer alternative hedging (and speculative) mechanisms for companies and individuals. Like forward contracts, futures contracts must be settled at maturity. By contrast, currency options give the owner the right but not the obligation to buy (call option) or sell (put option) the contracted currency. An American option can be exercised at any time up to the expiration date; a European option can be exercised only at maturity.

Futures contracts are standardized contracts that trade on organized exchanges. Forward contracts, on the other hand, are custom-tailored contracts, typically entered into between a bank and its customers. Options contracts are sold both on organized exchanges and in the over-the-counter (OTC) market. Like forward contracts, OTC options are contracts whose specifications are generally negotiated as to the terms and conditions between a bank and its customers.

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