Chapter 20
Foreign Currency Futures and Options
QUESTIONS
1. How does a futures contract differ from a forward contract?
Answer: Foreign currency futures contracts, or futures contracts for short, allow individuals
and firms to buy and sell specific amounts of foreign currency at an agreed-upon price
determined on a given future day. Although this sounds very similar to forward contracts,
there are a number of important differences between forward contracts and futures contracts.
Chapter 20: Foreign Currency Futures and Options
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2. What effects does “marking to market” have on futures contracts?
Answer: The process of marking to market implies that futures contracts have daily cash
3. What are the differences between foreign currency option contracts and forward
contracts for foreign currency?
4. What are you buying if you purchase a U.S. dollar European put option against the
Mexican peso with a strike price of MXN10.0/$ and a maturity of July? (Assume that it
is May and the spot rate is MXN10.5/$.)
5. What are you buying if you purchase a Swiss franc American call option against the
U.S. dollar with a strike price of CHF1.30/$ and a maturity of January? (Assume that it
is November and the spot rate is CHF1.35/$.)
6. What is the intrinsic value of a foreign currency call option? What is the intrinsic value
of a foreign currency put option?
Answer: The immediate revenue from exercising an option is called the option’s intrinsic
7. What does it mean for an American option to be “in the money”?
8. Why do American option values typically exceed their intrinsic values?
Answer: The time value of an option is the current price or value of the option minus its
intrinsic value: Time value of an option = Option price – Intrinsic value
9. Suppose you go long in a foreign currency futures contract. Under what circumstances
is your cumulative payoff equal to that of buying the currency forward?
Answer: The payoffs of futures contracts and forward contracts are only “essentially the
same” because a slight difference in payoffs arises due to the fact that interest is earned on
10. What is basis risk?
Answer: The basis is the difference between the price of the futures contract at time t, for a
particular maturity in the future, and the spot rate at time t. At the maturity date, the basis is
11. Your CEO routinely approves changes in the fire insurance policies of your firm to
protect the value of its buildings and manufacturing equipment. Nevertheless, he argues
that the firm should not buy foreign currency options because, he says, “We don’t
speculate in FX markets!” How could you convince him that his positions are mutually
inconsistent?
Answer: Options provide payoffs that are analogous to insurance and can be used in hedging
situations. With fire insurance, you pay the insurance premium, and if there is a fire, the
12. Why do options provide insurance against foreign exchange risks in bidding situations?
Why can’t you hedge with a forward contract in a bidding situation?
Answer: Let’s assume the bidding situation involves the company determining a particular
amount of foreign currency for providing a service or selling some goods. By bidding a fixed
13. Suppose that you have a foreign currency receivable (payable). What option strategy
places a floor (ceiling) on your domestic currency revenue (cost)?
14. Describe qualitatively how changing the strike price of the option provides either more
or less expensive insurance.
15. Why does an increase in the strike price of an option decrease the value of a call option
and increase the value of a put option?
16. Why does an increase in the volatility of foreign exchange rates increase the value of
foreign currency options?
Answer: The easiest way to understand how an increase in variance affects option prices is to
17. How does increasing time to maturity affect foreign currency option value?
Answer: Here, it is important to distinguish clearly between American-style and European-
18. What is the payoff on an average-rate pound call option against the dollar?
Answer: The payoff per pound on an average-rate pound call option against the dollar with a
19. Suppose the current spot rate is $1.29/€. What is your payoff if you purchase a down–
and-in put option on the euro with a strike price of $1.31/€, a barrier of $1.25/€, and a
maturity of 2 months? When would someone want to do this?
Answer: For a down-and-in option, the exchange rate must first cross the barrier to activate
PROBLEMS
1. If you sold a Swiss franc futures contract at time t and the exchange rate has evolved as
shown here, what would your cash flows have been?
Day
Futures
Price
$/CHF
Change in
Futures
Price
Cumulative
Gain or
Loss
Margin
Account
t
0.7335
$2,000.00
0.0056
Chapter 20: Foreign Currency Futures and Options
8
t + 1
0.7391
-$700.00
$2,000.00
t + 2
0.7388
-0.0003
-$662.50
$2,037.50
t + 3
0.7352
-0.0036
-$212.50
$2,487.50
t + 4
0.7297
-0.0055
$475.00
$3,175.00
Answer: Because you sold the Swiss franc futures contract, you will gain when the Swiss
2. Given the following information, how much would you have paid on September 16 to
purchase a British pound call option contract with a strike price of 155 and a maturity
of October? Data for September 16
Calls Puts
50,000 Australian Dollar Options (cents per unit)
64 Oct
—
0.48
65 Oct
—
0.90
67 Oct
0.22
—
31,250 British Pounds (cents per unit)
152½ Dec
—
4.10
155 Oct
1.50
3.62
155 Nov
2.35
—
Answer: The correct price on September 16 for a British pound call option with a strike
Chapter 20: Foreign Currency Futures and Options
9
3. Using the data in problem 2, how much would you have paid to purchase a Australian
dollar put option contract with a strike price of 65 and an October maturity?
Answer: The correct price on September 16 for an Australian dollar put option with a strike
4. Suppose that you buy a €1,000,000 call option against dollars with a strike price of
$1.2750/€. Describe this option as the right to sell a specific amount of dollars for euros
at a particular exchange rate of euros per dollar. Explain why this latter option is a
dollar put option against the euro.
5. Assume that today is March 7, and, as the newest hire for Goldman Sachs, you must
advise a client on the costs and benefits of hedging a transaction with options. Your
client (a small U.S. exporting firm) is scheduled to receive a payment of €6,250,000 on
April 20, 44 days in the future. Assume that your client can borrow and lend at a 6%
p.a. U.S. interest rate.
a. Describe the nature of your client’s transaction exchange risk.
b. Use the appropriate American option with an April maturity and a strike price of
129¢/€ to determine the dollar cost today of hedging the transaction with an option
strategy. The cost of the call option is 3.93¢/€, and the cost of the put option is
1.58¢/€.
c. What is the minimum dollar revenue your client will receive in April? Remember to
take account of the opportunity cost of doing the option hedge.
Chapter 20: Foreign Currency Futures and Options
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d. Determine the value of the spot rate ($/€) in April that would make your client
indifferent ex post to having done the option transaction or a forward hedge. The
forward rate for delivery on April 20 is $1.30/€.
6. Assume that today is September 12. You have been asked to help a British client who is
scheduled to pay €1,500,000 on December 12, 91 days in the future. Assume that your
client can borrow and lend pounds at 5% p.a.
a. Describe the nature of your client’s transaction exchange risk.
b. What is the option cost for a December maturity and a strike price of £0.72/€ to
hedge the transaction? The option premiums per 100 euros are £1.70 for calls and
£2.40 for puts.
c. What is the maximum pound cost your client will experience in December?
d. Determine the value of the spot rate (£/€) in December that makes your client
indifferent ex post to having done the option transaction or a forward hedge if the
forward rate for delivery on December 11 is £0.70/€.
Answer: If the client does the forward hedge, their cost will be
7. Assume that today is June 11. Your firm is scheduled to pay £500,000 on August 15, 65
days in the future. The current spot is $1.75/£, and the 65-day forward rate is $1.73/£.
You can borrow and lend dollars at 7% p.a. Suppose you think options are overpriced
because you think the dollar will be in a tight trading range in the near future. You
have been thinking about selling an option as a way to reduce the dollar cost of your
pound payable.
a. If an August pound option with a strike price of 175¢/£ costs 4.5¢/£ per pound for
the call and 4¢/£ for the put, what is the minimum that you will have to pay in
August to eliminate your pound payable? Over what range of future exchange rates
will this price be achieved?
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b. How much must the pound appreciate before your speculative option strategy ends
up costing you more than the forward rate?
8. Upon arriving for work Monday, you observe a violation of put–call parity. In
particular, the synthetic forward price of dollars per yen is above the current forward
rate. How would you capitalize on this information?
Answer: Because the actual forward rate is below the synthetic forward rate, you would want
to contract to buy yen forward and then sell yen at the synthetic forward rate. Such an
9. Use interest rate parity to demonstrate that you can represent put-call parity as
Chapter 20: Foreign Currency Futures and Options
13
1 ($) 1 (€)
KS
PC ii
− = −
++
The derivation of put-call parity used the no-arbitrage idea that the forward rate should be equal
10. On April 28, 1995, the Paine Webber Group introduced a new type of security on the
NYSE: U.S. dollar increase warrants on the yen. At exercise, each warrant entitled the
holder to an amount of U.S. dollars calculated as
Greater of (i) 0 and (ii) $100 – [$100 × ¥83.65/$ / Spot rate)]
The “spot rate” in the formula refers to the yen/dollar rate on any day during the
exercise period, which extended until April 28, 1996. The 1-year forward rate on April
28 was ¥79.72/$, and the spot rate was ¥83.65/$.
a. What view on the future yen/dollar rate do investors in this security hold?
b. This security was issued at a price of $5.50. To see whether the security is fairly
priced, which option prices would you want to examine?
Answer: While the payoff on the security is non-linear in the yen-dollar exchange rate, it