International Finance

Chapter 07
Futures and Options on Foreign Exchange

Multiple Choice Questions

2. Yesterday, you entered into a futures contract to buy €62,500 at $1.50 per €. Suppose the futures price closes today at $1.46. How much have you made/lost?
A. Depends on your margin balance
B. You have made $2,500.00
C. You have lost $2,500.00
D. You have neither made nor lost money, yet.

3. In reference to the futures market, a “speculator”
A. attempts to profit from a change in the futures price
B. wants to avoid price variation by locking in a purchase price of the underlying asset through a long position in the futures contract or a sales price through a short position in the futures contract
C. stands ready to buy or sell contracts in unlimited quantity
D. b) and c)

4. Comparing “forward” and “futures” exchange contracts, we can say that:
A. They are both “marked-to-market” daily.
B. Their major difference is in the way the underlying asset is priced for future purchase or sale: futures settle daily and forwards settle at maturity.
C. A futures contract is negotiated by open outcry between floor brokers or traders and is traded on organized exchanges, while forward contract is tailor-made by an international bank for its clients and is traded OTC.
D. b) and c)

5. Comparing “forward” and “futures” exchange contracts, we can say that
A. Delivery of the underlying asset is seldom made in futures contracts
B. Delivery of the underlying asset is usually made in forward contracts
C. Delivery of the underlying asset is seldom made in either contract—they are typically cash settled at maturity.
D. a) and b)
E. a) and c).

6. In which market does a clearinghouse serve as a third party to all transactions?
A. Futures
B. Forwards
C. Swaps
D. None of the above

7. In the event of a default on one side of a futures trade,
A. The clearing member stands in for the defaulting party
B. The clearing member will seek restitution for the defaulting party
C. If the default is on the short side, a randomly selected long contract will not get paid. That party will then have standing to initiate a civil suit against the defaulting short.
D. a) and b)

10. Yesterday, you entered into a futures contract to buy €62,500 at $1.50/€. Your initial margin was $3,750 (= 0.04  €62,500  $1.50/€ = 4 percent of the contract value in dollars). Your maintenance margin is $2,000 (meaning that your broker leaves you alone until your account balance falls to $2,000). At what settle price (use 4 decimal places) do you get a margin call?
A. $1.4720/€
B. $1.5280/€
C. $1.500/€
D. None of the above

13. Today’s settlement price on a Chicago Mercantile Exchange (CME) Yen futures contract is $0.8011/¥100. Your margin account currently has a balance of $2,000. The next three days’ settlement prices are $0.8057/¥100, $0.7996/¥100, and $0.7985/¥100. (The contractual size of one CME Yen contract is ¥12,500,000). If you have a long position in one futures contract, the changes in the margin account from daily marking-to-market, will result in the balance of the margin account after the third day to be:
A. $1,425
B. $1,675
C. $2,000
D. $3,425

15. What paradigm is used to define the futures price?
A. IRP
B. Hedge Ratio
C. Black Scholes
D. Risk Neutral Valuation

16. Suppose you observe the following 1-year interest rates, spot exchange rates and futures prices. Futures contracts are available on €10,000. How much risk-free arbitrage profit could you make on 1 contract at maturity from this mispricing?

A. $159.22
B. $153.10
C. $439.42
D. None of the above

17. Which equation is used to define the futures price?
A.
B.
C.
D.

18. Which equation is used to define the futures price?
A.
B.
C.
D.
E.

19. If a futures contract is mispriced
A. Arbitrageurs will take advantage of the mispricing until the spot exchange rate changes.
B. Arbitrageurs will take advantage of the mispricing until the futures price adjusts.
C. Arbitrageurs will take advantage of the mispricing until domestic interest rates adjust.
D. Arbitrageurs will take advantage of the mispricing using the using the mechanism of covered interest arbitrage.

20. Open interest in currency futures contracts
A. Tends to be greatest for the near-term contracts
B. Tends to be greatest for the longer-term contracts
C. Typically decreases with the term to maturity of most futures contracts
D. a) and c)

21. The “open interest” shown in currency futures quotations is:
A. the total number of people indicating interest in buying the contracts in the near future
B. the total number of people indicating interest in selling the contracts in the near future
C. the total number of people indicating interest in buying or selling the contracts in the near future
D. the total number of long or short contracts outstanding for the particular delivery month

22. The most widely used futures contract for hedging short-term U.S. dollar interest rate risk is:
A. The Eurodollar contract
B. The Euroyen contract
C. The EURIBOR contract
D. None of the above

23. Consider the position of a treasurer of a MNC, who has $20,000,000 that his firm will not need for the next 90 days:
A. He could borrow the $20,000,000 in the money market
B. He could take a long position in the Eurodollar futures contract.
C. He could take a short position in the Eurodollar futures contract
D. None of the above

24. A DECREASE in the implied three-month LIBOR yield causes Eurodollar futures price
A. To increase
B. To decrease
C. There is no direct or indirect relationship
D. None of the above

25. If you think that the dollar is going to appreciate against the euro
A. You should buy put options on the euro
B. You should sell call options on the euro
C. You should buy call options on the euro
D. None of the above

27. A European option is different from an American option in that
A. One is traded in Europe and one in traded in the United States
B. European options can only be exercised at maturity; American options can be exercised prior to maturity.
C. European options tend to be worth more than American options, ceteris paribus.
D. American options have a fixed exercise price; European options’ exercise price is set at the average price of the underlying asset during the life of the option.

28. An “option” is:
A. a contract giving the seller (writer) of the option the right, but not the obligation, to buy (call) or sell (put) a given quantity of an asset at a specified price at some time in the future
B. a contract giving the owner (buyer) of the option the right, but not the obligation, to buy (call) or sell (put) a given quantity of an asset at a specified price at some time in the future
C. a contract giving the owner (buyer) of the option the right, but not the obligation, to buy (put) or sell (call) a given quantity of an asset at a specified price at some time in the future
D. a contract giving the owner (buyer) of the option the right, but not the obligation, to buy (put) or sell (sell) a given quantity of an asset at a specified price at some time in the future

29. An investor believes that the price of a stock, say IBM’s shares, will increase in the next 60 days. If the investor is correct, which combination of the following investment strategies will show a profit in all the choices?

(i) – buy the stock and hold it for 60 days
(ii) – buy a put option
(iii) – sell (write) a call option
(iv) – buy a call option
(v) – sell (write) a put option
A. (i), (ii), and (iii)
B. (i), (ii), and (iv)
C. (i), (iv), and (v)
D. (ii) and (iii)

30. Most exchange traded currency options
A. Mature every month, with daily resettlement.
B. Have original maturities of 1, 2, and 3 years.
C. Have original maturities of 3, 6, 9, and 12 months.
D. Mature every month, without daily resettlement

31. The volume of OTC currency options trading is
A. Much smaller than that of organized-exchange currency option trading.
B. Much larger than that of organized-exchange currency option trading.
C. Larger, because the exchanges are only repackaging OTC options for their customers
D. None of the above

32. In the CURRENCY TRADING section of The Wall Street Journal, the following appeared under the heading OPTIONS:

Which combination of the following statements are true?
(i)- The time values of the 68 May and 69 May put options are respectively .30 cents and .50 cents.
(ii)- The 68 May put option has a lower time value (price) than the 69 May put option.
(iii) If everything else is kept constant, the spot price and the put premium are inversely related.
(iv)- The time values of the 68 May and 69 May put options are, respectively, 1.63 cents and 0.83 cents.
(v)- If everything else is kept constant, the strike price and the put premium are inversely related.
A. (i), (ii), and (iii)
B. (ii), (iii), and (iv)
C. (iii) and (iv)
D. ( iv) and (v)

33. With currency futures options the underlying asset is
A. Foreign currency.
B. A call or put option written on foreign currency.
C. A futures contract on the foreign currency.
D. None of the above.

34. Exercise of a currency futures option results in
A. A long futures position for the call buyer or put writer
B. A short futures position for the call buyer or put writer
C. A long futures position for the put buyer or call writer
D. A short futures position for the call buyer or put buyer

35. A currency futures option amounts to a derivative on a derivative. Why would something like that exist?
A. For some assets, the futures contract can have lower transactions costs and greater liquidity than the underlying asset
B. Tax consequences matter as well, and for some users an option contract on a future is more tax efficient
C. Transactions costs and liquidity.
D. All of the above

36. The current spot exchange rate is $1.55 = €1.00 and the three-month forward rate is $1.60 = €1.00. Consider a three-month American call option on €62,500. For this option to be considered at-the-money, the strike price must be:
A. $1.60 = €1.00
B. $1.55 = €1.00
C. $1.55  (1+i$)3/12 = €1.00  (1+i€)3/12
D. None of the above

37. The current spot exchange rate is $1.55 = €1.00 and the three-month forward rate is $1.60 = €1.00. Consider a three-month American call option on €62,500 with a strike price of $1.50 = €1.00. Immediate exercise of this option will generate a profit of
A. $6,125
B. $6,125/(1+i$)3/12
C. negative profit, so exercise would not occur
D. $3,125

39. Consider the graph of a call option shown at right. The option is a three-month American call option on €62,500 with a strike price of $1.50 = €1.00 and an option premium of $3,125. What are the values of A, B, and C, respectively?

A. A = -$3,125 (or -$.05 depending on your scale); B = $1.50; C = $1.55
B. A = -€3,750 (or -€.06 depending on your scale); B = $1.50; C = $1.55
C. A = -$.05; B = $1.55; C = $1.60
D. None of the above

40. Which of the lines is a graph of the profit at maturity of writing a call option on €62,500 with a strike price of $1.20 = €1.00 and an option premium of $3,125?

A. A
B. B
C. C
D. D

True / False Questions

41. True or false: a put option on $15,000 with a strike price of €10,000 is the same thing as a call option on €10,000 with a strike price of $15,000.
True False

Multiple Choice Questions

42. The current spot exchange rate is $1.55 = €1.00; the three-month U.S. dollar interest rate is 2%. Consider a three-month American call option on €62,500 with a strike price of $1.50 = €1.00. What is the least that this option should sell for?
A. $0.0562,500 = $3,125
B. $3,125/1.02 = $3,063.73
C. $0.00
D. None of the above

43. Which of the follow options strategies are consistent in their belief about the future behavior of the underlying asset price?
A. selling calls and selling puts
B. buying calls and buying puts
C. buying calls and selling puts
D. None of the above

44. American call and put premiums
A. Should be at least as large as their intrinsic value
B. Should be at no larger than their moneyness
C. Should be exactly equal to their time value
D. Should be no larger than their speculative value

45. Which of the following is correct?
A. time value = intrinsic value + option premium
B. intrinsic value = option premium + time value
C. Option premium = intrinsic value – time value
D. Option premium = intrinsic value + time value

46. Which of the following is correct?
A. European options can be exercised early
B. American options can be exercised early
C. Asian options can be exercised early
D. All of the above

47. Assume that the dollar-euro spot rate is $1.28 and the six-month forward rate is . The six-month U.S. dollar rate is 5% and the Eurodollar rate is 4%. The minimum price that a six-month American call option with a striking price of $1.25 should sell for in a rational market is:
A. 0 cents
B. 3.47 cents
C. 3.55 cents
D. 3 cents

48. For European options, what of the effect of an increase in St?
A. Decrease the value of calls and puts ceteris paribus
B. Increase the value of calls and puts ceteris paribus
C. Decrease the value of calls, increase the value of puts ceteris paribus
D. Increase the value of calls, decrease the value of puts ceteris paribus

49. For an American call option, A and B in the graph are
A. Time value and intrinsic value
B. Intrinsic value and time value
C. In-the-money and out-of-the money
D. None of the above

50. For European options, what of the effect of an increase in the strike price E?
A. Decrease the value of calls and puts ceteris paribus
B. Increase the value of calls and puts ceteris paribus
C. Decrease the value of calls, increase the value of puts ceteris paribus
D. Increase the value of calls, decrease the value of puts ceteris paribus

51. For European currency options written on euro with a strike price in dollars, what of the effect of an increase in r$ relative to r€?
A. Decrease the value of calls and puts ceteris paribus
B. Increase the value of calls and puts ceteris paribus
C. Decrease the value of calls, increase the value of puts ceteris paribus
D. Increase the value of calls, decrease the value of puts ceteris paribus

52. For European currency options written on euro with a strike price in dollars, what of the effect of an increase in r$?
A. Decrease the value of calls and puts ceteris paribus
B. Increase the value of calls and puts ceteris paribus
C. Decrease the value of calls, increase the value of puts ceteris paribus
D. Increase the value of calls, decrease the value of puts ceteris paribus

53. For European currency options written on euro with a strike price in dollars, what of the effect of an increase r€?
A. Decrease the value of calls and puts ceteris paribus
B. Increase the value of calls and puts ceteris paribus
C. Decrease the value of calls, increase the value of puts ceteris paribus
D. Increase the value of calls, decrease the value of puts ceteris paribus

54. For European currency options written on euro with a strike price in dollars, what of the effect of an increase in the exchange rate S($/€)?
A. Decrease the value of calls and puts ceteris paribus
B. Increase the value of calls and puts ceteris paribus
C. Decrease the value of calls, increase the value of puts ceteris paribus
D. Increase the value of calls, decrease the value of puts ceteris paribus

55. For European currency options written on euro with a strike price in dollars, what of the effect of an increase in the exchange rate S(€/$)?
A. Decrease the value of calls and puts ceteris paribus
B. Increase the value of calls and puts ceteris paribus
C. Decrease the value of calls, increase the value of puts ceteris paribus
D. Increase the value of calls, decrease the value of puts ceteris paribus

57. Find the value of a call option written on €100 with a strike price of $1.00 = €1.00. In one period there are two possibilities: the exchange rate will move up by 15% or down by 15% (i.e. $1.15 = €1.00 or $0.85 = €1.00). The U.S. risk-free rate is 5% over the period. The risk-neutral probability of a dollar depreciation is 2/3 and the risk-neutral probability of the dollar strengthening is 1/3.

A. $9.5238
B. $0.0952
C. $0
D. $3.1746

58. Use the binomial option pricing model to find the value of a call option on £10,000 with a strike price of €12,500.
The current exchange rate is €1.50/£1.00 and in the next period the exchange rate can increase to €2.40/£ or decrease to €0.9375/€1.00 (i.e. u = 1.6 and d = 1/u = 0.625).
The current interest rates are i€ = 3% and are i£ = 4%.Choose the answer closest to yours.
A. €3,275
B. €2,500
C. €3,373
D. €3,243

59. Find the hedge ratio for a call option on £10,000 with a strike price of €12,500.
The current exchange rate is €1.50/£1.00 and in the next period the exchange rate can increase to €2.40/£ or decrease to €0.9375/€1.00 (i.e. u = 1.6 and d = 1/u = 0.625).
The current interest rates are i€ = 3% and are i£ = 4%.
Choose the answer closest to yours.
A. 5/9
B. 8/13
C. 2/3
D. 3/8
E. None of the above

61. Draw the tree for a put option on $20,000 with a strike price of £10,000. The current exchange rate is £1.00 = $2.00 and in one period the dollar value of the pound will either double or be cut in half. The current interest rates are i$ = 3% and are i£ = 2%.
A.
B.
C. None of the above

62. Draw the tree for a call option on $20,000 with a strike price of £10,000. The current exchange rate is £1.00 = $2.00 and in one period the dollar value of the pound will either double or be cut in half. The current interest rates are i$ = 3% and are i£ = 2%.
A.
B.
C. None of the above

Short Answer Questions

Consider an option to buy £10,000 for €12,500. In the next period, if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent. On the other hand, the euro could depreciate against the pound by 20 percent.
Big hint: don’t round, keep exchange rates out to at least 4 decimal places.

63. alculate the current €/£ spot exchange rate.

64. Draw the binomial tree for this option

65. Find the risk neutral probability of an “up” move.

66. USING RISK NEUTRAL VALUATION (i.e. the binomial option pricing model) find the value of the call (in euro).

67. Calculate the hedge ratio

68. State the composition of the replicating portfolio; your answer should contain “trading orders” of what to buy and what to sell at time zero.

69. Find the value today of your portfolio in euro.

70. If the call finishes out-of-the-money what is your portfolio cash flow?

71. If the call finishes in-the-money what is your portfolio cash flow?

72. Use your results from the last three questions to verify your earlier result for the value of the call.

Consider an option to buy €12,500 for £10,000. In the next period, the euro can strengthen against the pound by 25% (i.e. each euro will buy 25% more pounds) or weaken by 20%.
Big hint: don’t round, keep exchange rates out to at least 4 decimal places.

73. Calculate the current €/£ spot exchange rate.

74. Draw the tree

75. Find the risk neutral probability of an “up” move.

76. USING RISK NEUTRAL VALUATION find the value of the call (in euro)

77. Calculate the hedge ratio

78. State the composition of the replicating portfolio; your answer should contain “trading orders” of what to buy and what to sell at time zero.

79. Find the cost today of your hedge portfolio in pounds.

80. If the call finishes out-of-the-money what is your portfolio cash flow?

81. If the call finishes in-the-money what is your portfolio cash flow?

82. Use your results from the last three questions to verify your earlier result for the value of the call.

83. Find the dollar value today of a 1-period at-the-money call option on ¥300,000. The spot exchange rate is ¥100 = $1.00. In the next period, the yen can increase in dollar value by 15 percent or decrease by 15 percent. The risk free rate in dollars is i$ = 5%; The risk free rate in yen is i¥ = 1%

Multiple Choice Questions

84. Find the hedge ratio for a put option on $15,000 with a strike price of €10,000. In one period the exchange rate (currently S($/€) = $1.50/€) can increase by 60% or decrease by 37.5% (i.e. u = 1.6 and d = 0.625).
A. -15/49
B. 5/13
C. 3/2
D. 15/49

85. Find the hedge ratio for a put option on €10,000 with a strike price of $15,000. In one period the exchange rate (currently S($/€) = $1.50/€) can increase by 60% or decrease by 37.5% (i.e. u = 1.6 and d = 0.625).
A. -15/49
B. 8/13
C. -5/13
D. 15/49

86. Suppose that you have written a call option on €10,000 with a strike price in dollars. Suppose further that the hedge ratio is ½. Which of the following would be an appropriate hedge for this call option?
A. Buy €10,000 today at today’s spot exchange rate.
B. Buy €5,000 today at today’s spot exchange rate.
C. Agree to buy €5,000 at the maturity of the option at the forward exchange rate for the maturity of the option that prevails today. (i.e. go long in a forward contract on €5,000)
D. Buy the present value of €5,000 discounted at i€ for the maturity of the option.
E. Both c) and d) would work.
F. None of the above

87. Find the value of a one-year put option on $15,000 with a strike price of €10,000. In one year the exchange rate (currently S0($/€) = $1.50/€) can increase by 60% or decrease by 37.5% (i.e. u = 1.6 and d = 0.625). The current one-year interest rate in the U.S. is i$ = 4% and the current one-year interest rate in the euro zone is i€ = 4%
A. €1,525.52
B. $3,328.40
C. $4,992.60
D. €2,218.94
E. None of the above

88. Find the value of a one-year call option on €10,000 with a strike price of $15,000. In one year the exchange rate (currently S0($/€) = $1.50/€) can increase by 60% or decrease by 37.5% (i.e. u = 1.6 and d = 0.625). The current one-year interest rate in the U.S. is i$ = 4% and the current one-year interest rate in the euro zone is i€ = 4%
A. €1,525.52
B. $3,328.40
C. $4,992.60
D. €2,218.94
E. None of the above

89. Consider a 1-year call option written on £10,000 with an exercise price of $2.00 = £1.00. The current exchange rate is $2.00 = £1.00; The U.S. risk-free rate is 5% over the period and the U.K. risk-free rate is also 5%. In the next year, the pound will either double in dollar terms or fall by half (i.e. u = 2 and d = ½). If you write 1 call option, what is the value today (in dollars) of the hedge portfolio?
A. £6,666.67
B. £6,349.21
C. $12,698.41
D. $20,000
E. None of the above

93. Which of the following is correct?
A. The value (in dollars) of a call option on £5,000 with a strike price of $10,000 is equal to the value (in dollars) of a put option on $10,000 with a strike price of £5,000 only when the spot exchange rate is $2 = £1.
B. The value (in dollars) of a call option on £5,000 with a strike price of $10,000 is equal to the value (in dollars) of a put option on $10,000 with a strike price of £5,000.

94. Find the input d1 of the Black-Scholes price of a six-month call option written on €100,000 with a strike price of $1.00 = €1.00. The current exchange rate is $1.25 = €1.00; The U.S. risk-free rate is 5% over the period and the euro-zone risk-free rate is 4%. The volatility of the underlying asset is 10.7 percent.
A. d1 = 0.103915
B. d1 = 2.9871
C. d1 = -0.0283
D. None of the above

95. Find the input d1 of the Black-Scholes price of a six-month call option on Japanese yen. The strike price is $1 = ¥100. The volatility is 25 percent per annum; r$ = 5.5% and r¥ = 6%.
A. d1 = 0.074246
B. d1 = 0.005982
C. d1 = $0.006137/¥
D. None of the above

96. The Black-Scholes option pricing formulae
A. Are used widely in practice, especially by international banks in trading OTC options.
B. Are not widely used outside of the academic world.
C. Work well enough, but are not used in the real world because no one has the time to flog their calculator for five minutes on the trading floor.
D. None of the above.

97. Find the Black-Scholes price of a six-month call option written on €100,000 with a strike price of $1.00 = €1.00. The current exchange rate is $1.25 = €1.00; The U.S. risk-free rate is 5% over the period and the euro-zone risk-free rate is 4%. The volatility of the underlying asset is 10.7 percent.
A. Ce = $0.63577
B. Ce = $0.0998
C. Ce = $1.6331
D. None of the above

98. Use the European option pricing formula to find the value of a six-month call option on Japanese yen. The strike price is $1 = ¥100. The volatility is 25 percent per annum; r$ = 5.5% and r¥ = 6%.
A. 0.005395
B. 0.005982
C. $0.006137/¥
D. None of the above

99. Empirical tests of the Black-Scholes option pricing formula
A. Shows that binomial option pricing is used widely in practice, especially by international banks in trading OTC options.
B. Works well for pricing American currency options that are at-the-money or out-of-the-money.
C. Does not do well in pricing in-the-money calls and puts.
D. b) and c)

100. Empirical tests of the Black-Scholes option pricing formula
A. Have faced difficulties due to nonsynchronous data.
B. Suggest that when using simultaneous price data and incorporating transaction costs they conclude that the PHLX American currency options are efficiently priced.
C. Suggest that the European option-pricing model works well for pricing American currency options that are at- or out-of-the money, but does not do well in pricing in-the-money calls and puts.
D. All of the above

Chapter 07 Futures and Options on Foreign Exchange Answer Key

Multiple Choice Questions

1. A CME contract on €125,000 with September delivery
A. Is an example of a forward contract
B. Is an example of a futures contract
C. Is an example of a put option
D. Is an example of a call option
options trade on the CBOE, futures on the CME. Given the pace of mergers you might want to double check on-line before you use this question.

6. In which market does a clearinghouse serve as a third party to all transactions?
A. Futures
B. Forwards
C. Swaps
D. None of the above

8. Yesterday, you entered into a futures contract to buy €62,500 at $1.50 per €. Your initial performance bond is $1,500 and your maintenance level is $500. At what settle price will you get a demand for additional funds to be posted?
A. $1.5160 per €.
B. $1.208 per €.
C. $1.1920 per €.
D. $1.4840 per €.
To get a margin call, you have to lose $1,000. That will happen when the price FALLS (since you’re buying euro) to $1.4840 per €:
[$1.20/ € – $1.4840 per €]  €62,500 = $1,000.

9. Yesterday, you entered into a futures contract to sell €62,500 at $1.50 per €. Your initial performance bond is $1,500 and your maintenance level is $500. At what settle price will you get a demand for additional funds to be posted?
A. $1.5160 per €.
B. $1.208 per €.
C. $1.1920 per €.
D. $1.1840 per €.
To get a margin call, you have to lose $1,000. That will happen when the price RISES (since you’re selling euro at $1.50 per €.) to $1.5160 per €:
[$1.5160/ € – $1.50 per €]  €62,500 = $1,000.

11. Three days ago, you entered into a futures contract to sell €62,500 at $1.50 per €. Over the past three days the contract has settled at $1.50, $1.52, and $1.54. How much have you made or lost?
A. Lost $0.04 per € or $2,500
B. Made $0.04 per € or $2,500
C. Lost $0.06 per € or $3,750
D. None of the above
Losses will happen when the price RISES (since you’re selling euro at $1.50 per €.) Total loss
[$1.50/ € – $1.54 per €]  €62,500 = -$2,500

12. Today’s settlement price on a Chicago Mercantile Exchange (CME) Yen futures contract is $0.8011/¥100. Your margin account currently has a balance of $2,000. The next three days’ settlement prices are $0.8057/¥100, $0.7996/¥100, and $0.7985/¥100. (The contractual size of one CME Yen contract is ¥12,500,000). If you have a short position in one futures contract, the changes in the margin account from daily marking-to-market will result in the balance of the margin account after the third day to be
A. $1,425
B. $2,000
C. $2,325
D. $3,425
$2,325 = $2,000 +
¥12,500,000  [(0.008011 – 0.008057) + (0.008057 – 0.007996) + (0.007996 – 0.007985)] =
$2,000 + ¥12,500,000  [(0.008011 – 0.007985)]
Please note that $0.8011/¥100 = $0.008011/¥ and $0.8057/¥100 = $0.008057/¥, etc.

14. Suppose the futures price is below the price predicted by IRP. What steps would assure an arbitrage profit?
A. Go short in the spot market, go long in the futures contract.
B. Go long in the spot market, go short in the futures contract.
C. Go short in the spot market, go short in the futures contract.
D. Go long in the spot market, go long in the futures contract.
if the futures price is too low, you want to be buying. In order to lock in your arbitrage profit, you want to hedge this position with a short position in the spot market.

15. What paradigm is used to define the futures price?
A. IRP
B. Hedge Ratio
C. Black Scholes
D. Risk Neutral Valuation

A. $159.22
B. $153.10
C. $439.42
D. None of the above
The futures price of $1.48/€ is above the IRP futures price of $1.4641/€, so we want to sell (i.e. take a short position in 1 futures contract on €10,000, agreeing to sell €10,000 in 1 year for $14,800).

Profit =

To hedge, we borrow $14,077.67 today at 4%, convert to euro at the spot rate of $1.45/€, invest at 3%. At maturity, our investment matures and pays €10,000, which we sell for $14,800, and then we repay our dollar borrowing with $14,640.78. Our risk-free profit = $159.22 = $14,800 – $14,640.78

17. Which equation is used to define the futures price?
A.
B.
C.
D.
The interest rate parity condition is:

18. Which equation is used to define the futures price?
A.
B.
C.
D.
E.

22. The most widely used futures contract for hedging short-term U.S. dollar interest rate risk is:
A. The Eurodollar contract
B. The Euroyen contract
C. The EURIBOR contract
D. None of the above

24. A DECREASE in the implied three-month LIBOR yield causes Eurodollar futures price
A. To increase
B. To decrease
C. There is no direct or indirect relationship
D. None of the above

26. From the perspective of the writer of a put option written on €62,500. If the strike price is $1.55/€, and the option premium is $1,875, at what exchange rate do you start to lose money?
A. $1.52/€
B. $1.55/€
C. $1.58/€
D. None of the above
Per euro, the option premium is . Since it’s a put option, the writer loses money when the price goes down, thus he breaks even at $1.55/€ – $0.03/€ = $1.52/€

32. In the CURRENCY TRADING section of The Wall Street Journal, the following appeared under the heading OPTIONS:

38. The current spot exchange rate is $1.55 = €1.00 and the three-month forward rate is $1.60 = €1.00. Consider a three-month American call option on €62,500 with a strike price of $1.50 = €1.00. If you pay an option premium of $5,000 to buy this call, at what exchange rate will you break-even?
A. $1.58 = €1.00
B. $1.62 = €1.00
C. $1.50 = €1.00
D. $1.68 = €1.00
A $5,000 option premium on €62,500 amounts to $0.08 per euro. With a strike price of $1.50 = €1.00 the exchange rate has to go to $1.58 = €1.00 for you to break even.

40. Which of the lines is a graph of the profit at maturity of writing a call option on €62,500 with a strike price of $1.20 = €1.00 and an option premium of $3,125?

A. A
B. B
C. C
D. D

True / False Questions

41. True or false: a put option on $15,000 with a strike price of €10,000 is the same thing as a call option on €10,000 with a strike price of $15,000.
TRUE
a put option on $15,000 with a strike price of €10,000 gives the holder the right but not the obligation to exchange $15,000 for €10,000.

Multiple Choice Questions

46. Which of the following is correct?
A. European options can be exercised early
B. American options can be exercised early
C. Asian options can be exercised early
D. All of the above
By the way, Asian options exist; their payoff depends on the average price of the underlying asset during the life of the option. For example a call gives you the right to buy at the strike price, but the payoff is the difference between the strike price and the average price, not the price on the day of exercise. They are quite popular OTC options with corporate treasurers who are exposed to the average value of an exchange rate over a quarter.

49. For an American call option, A and B in the graph are
A. Time value and intrinsic value
B. Intrinsic value and time value
C. In-the-money and out-of-the money
D. None of the above
Exhibit 7.10

56. The hedge ratio
A. Is the size of the long (short) position the investor must have in the underlying asset per option the investor must write (buy) to have a risk-free offsetting investment that will result in the investor perfectly hedging the option.
B.
C. Is related to the number of options that an investor can write without unlimited loss while holding a certain number of shares.
D. All of the above.
a) and b) are straight out of the book; c) is true (it’s also a pretty mild statement) but not explicitly stated in the book, but a good student would know that if a) and b) are true, then the right answer must be d).

A. $9.5238
B. $0.0952
C. $0
D. $3.1746
Equation 9.10:

And thereby the value call is

60. You have written a call option on £10,000 with a strike price of $20,000. The current exchange rate is $2.00/£1.00 and in the next period the exchange rate can increase to $4.00/£1.00 or decrease to $1.00/€1.00 (i.e. u = 2 and d = 1/u = 0.5). The current interest rates are i$ = 3% and are i£ = 2%. Find the hedge ratio and use it to create a position in the underlying asset that will hedge your option position.
A. Buy £10,000 today at $2.00/£1.00
B. Enter into a short position in a futures contract on £6,666.67
C. Lend the present value of £6,666.67 today at i£ = 2%.
D. Enter into a long position in a futures contract on £6,666.67
E. Both c) and d) would work
F. None of the above
the hedge ratio is ⅔, so to hedge a call, we need a position in £6,666.67 = ⅔  £10,000. We don’t need to own them today, but we do need to have £6,666.67 at the maturity of the option. We can accomplish this two ways: Lend the present value of £6,666.67 today at i£ = 2% or agree today to buy £6,666.67 in one period at a price agreed upon today.

By the way, you can value this option at $6,599.40 as the present value of the risk-free payoff of the hedge portfolio discounted at i$ = 3%:
In the up state the payoff is $6,797.38 = $20,000 option income from exercise less the cost of buying £6,666.67 at the forward rate and the cost of buying £3,333.33 at $4/£.
The down state payoff is $6,797.38 = sell £6,666.66 at $1/£ less buy £6,666.67 at the forward rate.

American students will tend to miss this as they prefer to price everything in dollars; students who have traveled abroad tend to get this one right as they tend to lack that encumbrance.

Short Answer Questions

63. alculate the current €/£ spot exchange rate.

64. Draw the binomial tree for this option

65. Find the risk neutral probability of an “up” move.

66. USING RISK NEUTRAL VALUATION (i.e. the binomial option pricing model) find the value of the call (in euro).

67. Calculate the hedge ratio

68. State the composition of the replicating portfolio; your answer should contain “trading orders” of what to buy and what to sell at time zero.

69. Find the value today of your portfolio in euro.

70. If the call finishes out-of-the-money what is your portfolio cash flow?

71. If the call finishes in-the-money what is your portfolio cash flow?

72. Use your results from the last three questions to verify your earlier result for the value of the call.

73. Calculate the current €/£ spot exchange rate.

74. Draw the tree

75. Find the risk neutral probability of an “up” move.

76. USING RISK NEUTRAL VALUATION find the value of the call (in euro)

77. Calculate the hedge ratio

78. State the composition of the replicating portfolio; your answer should contain “trading orders” of what to buy and what to sell at time zero.

79. Find the cost today of your hedge portfolio in pounds.

80. If the call finishes out-of-the-money what is your portfolio cash flow?

81. If the call finishes in-the-money what is your portfolio cash flow?

82. Use your results from the last three questions to verify your earlier result for the value of the call.

Multiple Choice Questions

Note:

90. Value a 1-year call option written on £10,000 with an exercise price of $2.00 = £1.00. The spot exchange rate is $2.00 = £1.00; The U.S. risk-free rate is 5% and the U.K. risk-free rate is also 5%. In the next year, the pound will either double in dollar terms or fall by half (i.e. u = 2 and d = ½). Hint: H = ⅔.
A. $6,349.21
B.
C.
D. None of the above
The hedge ratio is ⅔, so to hedge 1 written call you should buy the present value of £6,666.67. If at maturity the exchange rate is $4/£ then the option will be exercised and you will receive $20,000. You have to deliver £10,000, as you already own £6,666.67 you will have to buy an additional £3,333.33 at $4/£.
Net cash flow = $20,000 – $13,333.33 = $6,666.67
If at maturity the exchange rate is $1/£ then the option will not be exercised and you will be able to sell your now-surplus £6,666.67 at $1/£.
Net cash flow = $6,666.67
Since you have a riskless payoff of $6,666.67 the value today of this is

The cost of the hedge today is

The value of the call option is therefore $6,349.21 = $12,698.41 – $6,349.21
You could also value the call as

91. Consider a 1-year call option written on £10,000 with an exercise price of $2.00 = £1.00. The current exchange rate is $2.00 = £1.00; The U.S. risk-free rate is 5% over the period and the U.K. risk-free rate is also 5%. In the next year, the pound will either double in dollar terms or fall by half (i.e. u = 2 and d = ½). If you write 1 call option and hedge it using an appropriate position in pounds what is your net cash flow (in dollars) at maturity if the exchange rate increases? Hint: H = ⅔.
A. £6,666.67
B.
C.
D. None of the above
The hedge ratio is ⅔, so to hedge 1 written call you should buy the present value of £6,666.67. If at maturity the exchange rate is $1/£ then the option will not be exercised and you will be able to sell your now-surplus £6,666.67 at $1/£. Net cash flow = $6,666.67

92. Consider a 1-year call option written on £10,000 with an exercise price of $2.00 = £1.00. The spot exchange rate is $2.00 = £1.00; The U.S. risk-free rate is 5% and the U.K. risk-free rate is also 5%. In the next year, the pound will either double in dollar terms or fall by half (i.e. u = 2 and d = ½). If you write 1 call option and hedge it using an appropriate position in pounds, what is your net cash flow (in dollars) at maturity if the exchange rate increases? Hint: H = ⅔.
A. £6,666.67
B.
C.
D. None of the above
The hedge ratio is ⅔, so to hedge 1 written call you should buy the present value of £6,666.67. If at maturity the exchange rate is $4/£ then the option will be exercised and you will receive $20,000. You have to deliver £10,000, as you already own £6,666.67 you will have to buy an additional £3,333.33 at $4/£.
Net cash flow = $20,000 – $13,333.33 = $6,666.67

N(d) was calculated using NORMSDIST in excel
INSTRUCTOR NOTE: YOU WILL HAVE TO PROVIDE YOUR STUDENTS WITH A TABLE OF THE NORMAL DISTRIBUTION.

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