CHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGE
ANSWERS & SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS
QUESTIONS
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
2. In order for a derivatives market to function most efficiently, two types of economic agents
are needed: hedgers and speculators. Explain.
Answer: Two types of market participants are necessary for the efficient operation of a
derivatives market: speculators and hedgers. A speculator attempts to profit from a change in
3. Why are most futures positions closed out through a reversing trade rather than held to
delivery?
only about one percent of currency futures contracts result in delivery. While futures contracts are
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.
5. What is the major difference in the obligation of one with a long position in a futures (or
forward) contract in comparison to 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,
6. What is meant by the terminology that an option is in-, at-, or out–of–the-money?
Answer: A call (put) option with St > E (E > St) is referred to as trading in–the-money. If St E
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: St, E, ri, r$, T and
.
When r$ and ri are not 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 larger than ri,
a European FX call will increase in price, but the put premium will decrease, when the option
PROBLEMS
1. Assume today’s settlement price on a CME EUR futures contract is $1.3140/EUR. You have
a short position in one contract. Your performance bond account currently has a balance of
$1,700. The next three days’ settlement prices are $1.3126, $1.3133, and $1.3049. Calculate
the changes in the performance bond account from daily marking-to-market and the balance of
the performance bond account after the third day.
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+ ($1.3133 – $1.3049)] x EUR125,000 = $2,837.50, where EUR125,000 is the contract size of
one EUR contract.
2. Do problem 1 again assuming you have a long position in the futures contract.
3. Using the quotations in Exhibit 7.3, calculate the face value of the open interest in the
September 2016 Swiss franc futures contract.
4. Using the quotations in Exhibit 7.3, note that the September 2016 Mexican peso futures
contract has a price of $0.05481 per MXN. You believe the spot price in September will be
$0.06133 per MXN. What speculative position would you enter into to attempt to profit from
your beliefs? Calculate your anticipated profits, assuming you take a position in three contracts.
What is the size of your profit (loss) if the futures price is indeed an unbiased predictor of the
future spot price and this price materializes?
5. Do problem 4 again assuming you believe the September 2016 spot price will be $0.04829
per MXN.
6. Using the market data in Exhibit 7.6, show the net terminal value of a long position in one 90
Sep Japanese yen European call contract at the following terminal spot prices (stated in U.S.
cents per 100 yen): 81, 85, 90, 95, and 99. Ignore any time value of money effect.
Solution: The net terminal value of one call contract is:
7. Using the market data in Exhibit 7.6, show the net terminal value of a long position in one 90
Sep Japanese yen European put contract at the following terminal spot prices (stated in U.S.
cents per 100 yen): 81, 85, 90, 95, and 99. Ignore any time value of money effect.
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of McGraw-Hill Education.
At 90: [Max[90 – 90, 0] – 1.80] x JPY1,000,000/100 ÷ 100¢ = -$180
At 95: [Max[90 – 95, 0] – 1.80] x JPY1,000,000/100 ÷ 100¢ = -$180
At 99: [Max[90 – 99, 0] – 1.80] x JPY1,000,000/100 ÷ 100¢ = -$180
8. Assume that the Japanese yen is trading at a spot price of 92.04 cents per 100 yen. Further
assume that the premium of an American call (put) option with a striking price of 93 is 2.10
(2.20) cents. Calculate the intrinsic value and the time value of the call and put options.
9. Assume spot Swiss franc is $0.7000 and the six-month forward rate is $0.6950. What is the
minimum price that a six-month American call option with a striking price of $0.6800 should sell
for in a rational market? Assume the annualized six-month Eurodollar rate is 3 ½ percent.
Solution:
Note to Instructor: A complete solution to this problem relies on the boundary expressions
presented in footnote 3 of the text of Chapter 7.
10. Do problem 9 again assuming an American put option instead of a call option.
11. Use the European option-pricing models developed in the chapter to value the call of
problem 9 and the put of problem 10. Assume the annualized volatility of the Swiss franc is
14.2 percent. This problem can be solved using the FXOPM.xls spreadsheet.
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of McGraw-Hill Education.
d2 = d1 – .142
.50 = .2765 – .1004 = .1671
N(d1) = .6055
N(d2) = .5664
N(-d1) = .3945
N(-d2) = .4336
Ce = [69.50(.6055) – 68(.5664)]e-(.035)(.50) = 3.51 cents
Pe = [68(.4336) – 69.50(.3945)]e-(.035)(.50) = 2.03 cents
12. Use the binomial option-pricing model developed in the chapter to value the call of problem 9.
The volatility of the Swiss franc is 14.2 percent.
Thus, the call premium is:
A speculator is considering the purchase of five three-month Japanese yen call options with
a striking price of 96 cents per 100 yen. The premium is 1.35 cents per 100 yen. The spot price
is 95.28 cents per 100 yen and the 90-day forward rate is 95.71 cents. The speculator believes
the yen will appreciate to $1.00 per 100 yen over the next three months. As the speculator’s
assistant, you have been asked to prepare the following:
1. Graph the call option cash flow schedule.
2. Determine the speculator’s profit if the yen appreciates to $1.00/100 yen.
3. Determine the speculator’s profit if the yen only appreciates to the forward rate.
4. Determine the future spot price at which the speculator will only break even.
Suggested Solution to the Options Speculator: