CHAPTER 9 FUTURES AND OPTIONS ON FOREIGN EXCHANGE
SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER
QUESTIONS AND PROBLEMS
1. Explain the basic differences between the operation of a currency forward market and a futures market.
Answer: The forward market is an OTC market where the forward contract for purchase or sale of foreign
currency is tailor-made between the client and its international bank. No money changes hands until the
maturity date of the contract when delivery and receipt are typically made. A futures contract is an
exchange-traded instrument with standardized features specifying contract size and delivery date. Futures
contracts are marked-to-market daily to reflect changes in the settlement price. Delivery is seldom made in
a futures market. Rather, a reversing trade is made to close out a long or short position.
2. In order for a derivatives market to function, two types of economic agents are needed: hedgers and
Answer: Two types of market participants are necessary for the operation of a derivatives market:
speculators and hedgers. A speculator attempts to profit from a change in the futures price. To do this,
the speculator will take a long or short position in a futures contract depending upon his expectations of
future price movement. A hedger, on the other hand, seeks to avoid price variation by locking in a
purchase price of the underlying asset through a long position in a futures contract or a sales price through
a short position. In effect, the hedger passes off the risk of price variation to the speculator who is better
able, or at least more willing, to bear this risk.
3. Why are most futures positions closed out through a reversing trade rather than held to delivery?
Answer: In forward markets, approximately 90 percent of all contracts that are initially established result in the
short making delivery to the long of the asset underlying the contract. This is natural because the terms of
forward contracts are tailor made between the long and short. By contrast, only about one percent of currency
futures contracts result in delivery. While futures contracts are useful for speculation and hedging, their
standardized delivery dates make them unlikely to correspond to the actual future dates when foreign exchange
IM-9 transactions will occur. Thus, they are generally closed out in a reversing trade. In fact, the commission that
buyers and sellers pay to transact in the futures market is a single amount that covers the round-trip transactions
of initiating and closing out the position.
4. How can the FX futures market be used for price discovery?
Answer: To the extent that FX forward prices are an unbiased predictor of future spot exchange rates, the
market anticipates whether one currency will appreciate or depreciate versus another. Because FX futures
contracts trade in an expiration cycle, different contracts expire at different periodic dates into the future.
The pattern of the prices of these contracts provides information as to the market’s current belief about the
relative future value of one currency versus another at the scheduled expiration dates of the contracts. One
will generally see a steadily appreciating or depreciating pattern; however, it may be mixed at times.
Thus, the futures market is useful for price discovery, i.e., obtaining the market’s forecast of the spot
exchange rate at different future dates.
5. What is the major difference in the obligation of one with a long position in a futures (or forward) contract
in comparison with an options contract?
Answer: A futures (or forward) contract is a vehicle for buying or selling a stated amount of foreign
exchange at a stated price per unit at a specified time in the future. If the long holds the contract to the
delivery date, he pays the effective contractual futures (or forward) price, regardless of whether it is an
advantageous price in comparison to the spot price at the delivery date. By contrast, an option is a contract
giving the long the right to buy or sell a given quantity of an asset at a specified price at some time in the
future, but not enforcing any obligation on him if the spot price is more favorable than the exercise price.
Because the option owner does not have to exercise the option if it is to his disadvantage, the option has a
price, or premium, whereas no price is paid at inception to enter into a futures (or forward) contract.
6. What is meant by the terminology that an option is in, at, or out of the money?
Answer: A call (put) option with S > E (Et> S) is referted to as trading in the money. If S ≅ E the optiont
is trading at the money. If S < Et(E < S) the tall (put) option is trading out of the money.
IM-9 7. List the arguments (variables) of which an FX call or put option model price is a function. How does the
call and put premium change with respect to a change in the arguments?
Answer: Both call and put options are functions of only six variables: S, E, r, r , T and σ.tWhen ail $lse
remains the same, the price of a European FX call (put) option will increase:
1. the larger (smaller) is S, the spot exchange rate
2. the smaller (larger) is E, the exercise exchange rate of the option
3. the smaller (larger) is r, , ihe interest rate in the foreign currency
4. the larger (smaller) is r , t$e interest rate in the domestic currency, say the Canadian dollar ($)
5. the larger (smaller) r is $elative to r, and i
6. the greater is σ , the volatility (standard deviation) of the exchange rate.
When r and$r are nit too much different in size, a European FX call and put will increase in price when
the option term-to-maturity increases. However, when r is very much larg$r than r, a European FX call i
will increase in price, but the put premium will decrease, when the option term-to-maturity increases. The
opposite is true when r is veryimuch greater than r . For American FX $ptions the analysis is less
complicated. Since a longer term American option can be exercised on any date that a shorter term option
can be exercised, or a some later date, it follows that the all else remaining the same, the longer term
American option will sell at a price at least as large as the shorter term option.
1. Assume today’s settlement price on a CME CDN (Canadian dollar) futures contract is US$0.8400/C$.
You have a short position in one contract. Your margin account currently has a balance of US$1,700. The
next three days’ settlement prices are US$0.8386, US$0.8393, and US$0.8309. Calculate the changes in
the margin account from daily marking-to-market and the balance of the margin account after the third
Solution: US$1,700 + [(US$0.8400 - US$0.8386) + (US$0.8386 - US$0.8393)
+ (US$0.8393 - US$0.8309)] x 100,000
= US$ 2,610
where C$100,000 is the contract size of one Canadian dollar contract.
2. Repeat Problem 1 assuming you have a long position in the futures contract.
Solution: US$1,700 + [(US$0.8386 - US$0.8400) + (US$0.8393 - US$0.8386)
+ (US$0.8309 - US$0.8393)] x 100,000
= US$ 790
With only US$790 in your margin account, you can expect a “margin call” to restore your margin balance
back to the required level of US$1,700.
Note that in inasmuch as Problem 1 (the short position) and Problem 2 (the long position) are opposite
sides of the same contract, the gain on the short position in the margin account (2610-1700 = 910) equals
the loss on the long position (1700-790 = 910).
3. Using quotations in Exhibit 9.3, calculate the face value of the open interest in the June 2007 EURO
Solution: 1,840 contracts x € 125,000 = €230,000,000
where 125,000 is the contract size of one EURO contract.
4. From Exhibit 9.3, the June 2007 Mexican peso futures contract has a price of US$0.89975 per ten
Mexican Pesos. You believe the spot price in June 2007 will be US$0.94000. Using futures
contracts, what speculative position would you enter into to attempt to gain from your beliefs?
IM-9 Calculate your anticipated gains assuming you take a position in three contracts. What is the size
of your gain (loss) if the futures price is, indeed, an unbiased predictor of the future spot price and
this price materializes? All calculations should be reported in US dollars.
Solution: If you expect the price of 10 Mexican pesos to appreciate from $0.90100 to $0.94000, you
would take a long position in futures since the futures price of $0.89975 is less than your expectation of
the spot price at the time of futures settlement date (June 2007).
Your anticipated profit from a long position in three contracts is:
[3 x ($0.94000 - $0.89975) x 500,000] / 10 = $6,037.50
where 500,000 pesos is the contract size of one futures contract.
If the futures price is an unbiased predictor of the expected spot price, the expected spot price is the futures
price of $0.89975. If this expected spot price indeed materializes, you will not have any profit or loss
from your short position in three futures contracts: [3 x ($0.89975 - $0.89975) x 500,000] / 10 = 0.
5. Repeat Problem 4 assuming you believe the June 2007 spot price will be $0.85000 per ten Mexican pesos.
All calculations should be reported in US dollars.
Solution: If you expect the Mexican peso to depreciate from $0.90100 to $0.85000, you would take a
short position in futures since the futures price of $0.89975 is greater than your expectation of the spot
price at the time of futures settlement date (June 2007).
Your anticipated profit from a short position in three contracts is:
[3 x ($0.89975 - $0.85000) x 500,000] / 10 = $7,462.50
If the futures price is an unbiased predictor of the future spot price and this price indeed materializes, you
will not profit or lose from your long futures position.
6. For Problems 4 and 5, report the cost of the futures contracts and the possible gains or losses in Canadian
dollars assuming the US$/C$ exchange rate in June is US$0.8400/C$. What additional risk does a
Canadian speculator in Mexican pesos take on through futures contracts (on the CME) that are
denominated and settled in US dollars?
With respect to Problem 4 from the perspective of a Canadian speculator …
The spot US$/C$ exchange rate on 30 January 2007 is US$0.8458
The assumption is that the US$/C$ exchange rate (spot) in June will be US$0.8400/C$.
To proceed with the solution from the Canadian speculator’s perspective, we must introduce additional
detail. In particular, we must specify the US dollar amount of initial margin that the Canadian speculator
must deposit with his broker at the outset. Initial margin is typically 2 percent of the contract size.
Three June Mexican peso contracts cost [3 x 0.89975 x 500,000] / 10 = US$ 134,962.50
Two percent initial margin required for three contracts amounts to US$ $2,699.25
The Canadian dollar outlay for the initial margin is US$ 26,992.50 x (1/0.8458) = C$ $3191.36
As per Problem 4, the anticipated US dollar profit from a long position in three contracts is …
[3 x ($0.94000 - $0.89975) x 500,000] / 10 = US$ 6,037.50
The Canadian speculator’s C$ value of that payoff is US$ 6,037.50 /0.8400 = C$ 7,187.50.
The C$ value of the initial margin that will be returned to the speculator is …
US$ 2,699.25 x (1/0.8400) = C$ 3,213.39
The currency gain (in C$) on the margin held by the futures broker in US dollars is
(C$ 3,213.39- C$ 3,192.36) = C$ 22.04
The Canadian speculator who buys US dollar-denominated June Mexican peso futures based on the
explicit assumptions in Problem 4 plus the additional assumption that the US$/C$ exchange rate (spot) in
June will be US$0.8400/C$ has expected gains in two forms. She has an expected gain of C$7,187.50 on
the contract itself plus an additional expected (currency) gain of C$220.36 on funds deposited for initial
margin. Compared to a US speculator, the Canadian speculator’s expected gains are enhanced through the
assumption that the Canadian dollar will depreciate against the US dollar (US$ 0.8458 spot in January
versus US$ 0.8400 spot in June).
IM-9 We have ignored the issue of a broker’s call for intermediate variation margin, and we have also ignored
the cost of interest on the margin account. These factors create relatively small differences between the
all-in costs of peso speculation for a US speculator versus a Canadian speculator.
In buying futures contracts on the June Mexican peso where the contracts are denominated and settled in
US dollars, the Canadian speculator bears additional risk in the form of exchange rate uncertainty
involving the US$/C$ exchange rate.
With respect to Problem 5 from the perspective of a Canadian speculator …
Based on the assumptions in Problem 5, the anticipated profit (in US dollars from a short position in three
June Mexican peso futures contracts is:
[3 x (US$ 0.89975 - US$ 0.85000) x 500,000] / 10 = US$ 7,462.50
The Canadian speculator’s C$ value of that payoff is US$ 7,462.50 /0.8400 = C$ $8,883.93
For a Canadian speculator, initial margin required on a short position in three futures contracts is the same
as that calculated above for the long position, i.e., C$3,191.36.
Likewise, at a June US$/C$ spot of US$0.8400, the C$ value of the initial margin that will be returned to
the speculator is …
US$ 26,992.50 x (1/0.8400) = C$ 3,213.39
The currency gain (in C$) on the margin held by the futures broker in US dollars is
(C$ 3,213.39 - C$ 3,191.36) = C$ 22.04
The Canadian speculator who takes a short position on US dollar-denominated June Mexican peso futures
based on the explicit assumptions in Problem 5 plus the additional assumption that the US$/C$ exchange
rate (spot) in June will be US$0.8400/C$ has expected gains in two forms. She has an expected gain of
C$8,883.93 on the contract itself plus an additional expected (currency) gain of C$22.04 on funds
deposited for initial margin. Compared to a US speculator, the Canadian speculator’s expected gains are
enhanced through the assumption that the Canadian dollar will depreciate against the US dollar (US$
0.8458 spot in January versus US$ 0.8400 spot in June).
IM-9 Again, for a Canadian dealing in futures contracts on the June Mexican peso where the contracts are
denominated and settled in US dollars, the Canadian speculator bears additional risk in the form of
exchange rate uncertainty involving the US$/C$ exchange rate. Problem 6 simply makes a US$/C$
7. Recall the forward rate agreement (FRA) Example 6.2 in Chapter 6. Show how the bank can alternatively
use a position in Eurodollar futures contracts to hedge the interest rate risk created by the maturity
mismatch it has with the $3,000,000 six-month Eurodollar deposit and rollover Eurocredit position
indexed to three-month LIBOR. Assume the bank can take a position in Eurodollar futures contracts
maturing in three months’ time that have a futures price of 95.00.
Solution: To hedge the interest rate risk created by the maturity mismatch, the bank would need to buy
(take a long position on) three Eurodollar futures contracts. If on the last day of trading, three-month
LIBOR is 5 1/8%, the bank will earn a loss of $937.50 from its futures position. This is calculated as:
[94.875 - 95.00] x 100 bp x $25 x 3 contracts = $-937.50.
Note that this sum differs from the $6,550.59 profit that the bank will earn from the FRA for two reasons.
First, the Eurodollar futures contract assumes an arbitrary 90 days in a three-month period, whereas the
FRA recognizes that the actual number of days in the specific three-month period is 91 days. Second, the
Eurodollar futures contract pays off in future value terms, or as of the end of the three-month period,
whereas the FRA pays off in present value terms, or as of the beginning of the three-month period.
8. Barrick Gold of Toronto is considering a possible six-month US$100 million LIBOR-based, floating-rate
bank loan to fund a mining project at terms shown in the table below. The Chief Financial Officer (CFO)
at Barrick fears a possible rise in the LIBOR rate by December and wants to use the December Eurodollar
futures contract to hedge this risk. The contract expires December 20, 2007, has a contract size of US$ 1
million and an implied LIBOR yield of 7.3 percent.
The CFO will ignore the cash flow implications of marking to market, initial margin requirements, and
any timing mismatch between exchange-traded futures contract cash flows and the interest payments due
IM-9 Loan Terms
September 20, 2007 December 20, 2007 March 20, 2008
• Borrow $100 million at • Pay interest for first three • Pay back principal
September 20 LIBOR + 200 months plus interest
basis points (bps) • Roll loan over at
• September 20 LIBOR = 7% December 20 LIBOR +
Loan First loan payment (9%) Second payment
initiated and futures contract expires and principal
↓ ↓ ↓
• • •
9/20/07 12/20/07 3/20/08
a. Formulate Barrick’s September 20 floating-to-fixed-rate strategy using the Eurodollar future contracts
discussed in the text above. Show that this strategy would result in a fixed-rate loan, assuming an
increase in the LIBOR rate to 7.8 percent by December 20, which remains at 7.8 percent through March
20. Show all calculations.
The basis point value (BPV) of a Eurodollar futures contract is found by substituting the contract
specifications into the following money market relationship:
BPV FUT= Change in Value = (face value) x (days to maturity / 360) x (change in yield)
= ($1 million) x (90 / 360) x (.0001)
The number of contracts, N, can be found by:
N = (value of spot position) / (face value of each futures contract)
= ($100 million) / ($1 million)
N = (value of spot position) / (value of futures position)
IM-9 = ($100,000,000) / ($981,750)
where value of futures position = $1,000,000 x [1 – (0.073 / 4)]
≈ 102 contracts
Barrick is also considering a 12-month loan as an alternative. This approach will result in two additional
uncertain cash flows, as follows:
Loan Dec ’07 March ’08 June’08 Sept ‘08 payment
initiated Payment (9%) Payment Payment and principal
↓ ↓ ↓ ↓ ↓
• • • • •
9/20/07 12/20/07 3/20/08 6/20/08 9/20/08
b. Describe how Barrick could use a “string of futures” contracts tohedge the 12-month loan, turning the
floating rate debt into fixed rate.. No calculations are needed.
a. As per the calculations in the HINT, the required number of contracts is (approximately) 100. On
September 20, Barrick would sell 100 (or 102) December Eurodollar futures contracts at the 7.3 percent
yield. The implied LIBOR rate in December is 7.3 percent as indicated by the December Eurofutures
discount yield of 7.3 percent. Thus a borrowing rate of 9.3 percent (7.3 percent + 200 basis points) can be
locked in if the hedge is correctly implemented.
A rise in the rate to 7.8 percent represents a 50 basis point (bp) increase over the implied LIBOR rate.
For a 50 basis point increase in LIBOR, the cash flow on the short futures position is: