Ch.6 Test Bank Docx Currency Options And Options Markets

Chapter 6 Currency Options and Options Markets

Notes to instructors:

Answers to non-numeric multiple choice questions are arranged alphabetically, so that answers are randomly assigned to the five outcomes.

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1. In option contracts, one side has the obligation to perform if the other side forces the exchange. In futures contracts, both sides have the obligation to perform.

2. A currency put option is the right to sell the underlying currency at a specified price and within a specified period.

3. A currency call option is the right to sell the underlying currency at a specified price and within a specified period.

It is the right to buy.

4. When you sell a put option on euros, you incur an obligation to buy euros at the option of the purchaser of the contract.

5. A short put on pounds (for dollars) is equivalent to a long call on dollars (for pounds).

The option writer has an obligation to sell pounds and to buy dollars.

6. A foreign currency put option writer has the obligation to sell the underlying currency to the put option holder should the option be exercised.

The writer has the obligation to buy from the put option holder.

7. The holder of a currency call option has the right to buy one currency with another currency at the contract’s exercise price.

8. An option to buy pounds at a price of K^$/£ is equivalent to an option to sell dollars at K^£/$ = 1/K^$/£.

9. Currency options are traded only at organized options exchanges, such as the International Monetary Market of the Chicago Mercantile Exchange.

Over-the-counter options are also traded through commercial and investment banks.

10. Over-the-counter currency options are standardized to provide added liquidity.

They are often customized to fit the needs of a particular client.

11. There is an active over-the-counter market in currency options operated by large commercial and investment banks.

12. The deliverable asset of a currency option is the currency being bought or sold.

13. Currency options on spot and on futures prices are essentially equivalent in their ability to hedge currency risk.

14. Volatility on spot exchange rates is much less than volatility on forward exchange rates.

Volatilities on spot and forward currencies are similar.

15. There is little relation between currency spot and futures price volatilities.

Spot and futures price volatilities are similar.

16. American options are exercisable any time until expiration.

17. European options are exercisable any time until expiration.

They can be exercised only at expiration.

18. There is often an imbalance between the number of currency option contracts that are bought and sold on currency option exchanges.

The number of contracts bought must equal the number sold.

19. A currency call option is in the money when the exercise price is less than the underlying exchange rate.

20. A currency put option is in the money when the exercise price is greater than the underlying exchange rate.

21. A currency put option is out of the money when the underlying exchange rate is below the exercise price.

It is in the money.

22. Currency options are asymmetric in that, when an option holder gains, the option writer does not necessarily lose.

Currency option contracts are zero-sum games.

23. A synthetic forward contract can be constructed by combining a long call with a short put on the same currency with exercise prices equal to the forward rate of exchange.

24. The value of a call option increases as time to expiration increases, all else constant.

25. American call and put option values increase as time to expiration increases, all else constant.

26. American call and put option values increase as volatility in the underlying asset increases, all else constant.

27. Put values increase as the underlying asset value increases, all else constant.

Put options decrease in value with increases in the value of the underlying asset.

28. The intrinsic value of an option is the value of the option if exercised today.

29. An option’s time value is the difference between its market value and its intrinsic value.

30. The time value of an option is the value of the option prior to exercise.

Time value is the difference between market value and intrinsic value.

31. The systematic risk of the underlying asset is an important determinant of option value.

Systematic risk has no place in most option pricing models.

32. Historical volatility is the actual volatility realized over some historical period.

33. The implied volatility of an option is the volatility implied by the option price and the observable determinants of option value.

34. One advantage of currency options traded on organized exchanges is that there are no margin requirements.

Options traded on financial futures exchanges require initial and maintenance margins.

35. Exchange rate volatility measured in continuously compounded returns depends on the currency of reference.

With continuously compounded returns, increases in the value of one currency are offset by decreases of the same magnitude in the value of the other currency.

Multiple Choice Select the BEST ANSWER

1. An option cannot be attached to ____.

a. corporate bonds

b. corporate investments

c. currency futures contracts

d. Eurodollar floating rate notes (FRNs)

e. Each of the above can have an option component.

2. Which of the following is an inappropriate pair when applied to currency options?

a. American option ≡ early exercise

b. call option ≡ put option

c. exercise price ≡ strike price

d. long position ≡ short position

e. option writer ≡ option seller

3. Exchange-traded currency options do not have ____.

a. contractually determined contract sizes

b. contractually determined exercise prices

c. contractually determined market prices

d. contractually determined underlying assets

e. more than one of the above

4. Over-the-counter currency options traded by commercial and investment banks ____.

a. are customized to fit the needs of the banks’ customers

b. have expiration dates and contract amounts that are specified by the banks

c. have standardized commissions

d. typically give the short side of the contract to the customer

e. none of the above

5. Exchange-traded currency options are traded on ____.

a. currency forward prices

b. currency spot or futures prices

c. interest rates

d. oil prices

e. wheat prices

6. A currency option quote from a financial newspaper identifies ____.

a. the exchange on which the option is traded

b. the exercise price

c. the expiration date

d. Three of the above

e. b and c only

7. Consider a “C$ Dec 6000 call” selling on the Chicago Mercantile Exchange (CME) at a price of $0.0180/C$. Each CME C$ contract is worth C$125,000. What would be the profit on an investment in this option if the spot rate at expiration is $0.5930/C$?

a. –$2,250

b. $0

c. $1,750

d. $2,250

e. $4,000

8. Consider a “SFr Dec 7000 call” selling on the Chicago Mercantile Exchange (CME) at a price of $0.0180/SFr. Each CME Swiss franc contract is worth SFr125,000. What would be the profit on an investment in this option if the spot rate at expiration is $0.7320/SFr?

a. –$2,250

b. $0

c. $1,750

d. $2,250

e. $4,000

9. Consider a “C$ Dec 7000 put” selling on the Chicago Mercantile Exchange (CME) at a price of $0.0120/C$. Each CME C$ contract is worth C$125,000. What would be the profit on an investment in this option if the spot rate at expiration is $0.6760/C$?

a. –$1,500

b. $0

c. $1,500

d. $3,000

e. none of the above

10. Consider a “SFr Dec 7000 put” selling on the Chicago Mercantile Exchange (CME) at a price of $0.0120/SFr. Each CME C$ contract is worth SFr125,000. What would be the profit on an investment in this option if the spot rate at expiration is $0.7120/SFr?

a. –$1,500

b. $0

c. $1,500

d. $3,000

e. none of the above

11. A long put option to sell pounds for dollars is identical to ____.

a. a long call option to buy dollars with pounds

b. a long call option to buy pounds for dollars

c. a short put option to sell dollars for pounds

d. a short put option to sell pounds for dollars

e. none of the above

12. A long put on pound sterling with a strike price of K^$/£ = $1.25/£ is ____.

a. an option to buy pound sterling with dollars

b. equivalent to a long call on dollars with a strike price of K^£/$ = £0.80/$

c. equivalent to a short call on dollars with a strike price of K^£/$ = £0.80/$

d. unlikely to have a positive market value

e. none of the above

13. A portfolio of a long dollar call and a short dollar put at an exercise price K^€/$ is equivalent to ____.

a. a long euro call and a short euro put

b. a long forward contract to buy dollars

c. a long forward contract to sell dollars

d. a short dollar call and a long dollar put

e. a headache waiting to happen

14. An option writer ____ the currency underlying the exercise price of a call option and ____ the currency underlying the exercise price of a put option.

a. pays … pays

b. pays … receives

c. receives … pays

d. receives … receives

e. none of the above

15. Which of the following is most accurate?

a. Put-call parity relates call values to put values.

b. Put-call parity relates call and put values to the value of a forward contract.

c. Put-call parity relates call and put values to the value of a forward contract after adjusting for the present value of the exercise price.

d. Put-call parity relates call and put values to the value of a forward contract after adjusting for the present value of the exercise price and the systematic risk of the underlying asset.

e. none of the above is accurate.

16. You form a long option straddle (a combination of a long call and a long put with the same exercise price) on the Mexican peso. Which of (a) through (c) results in a profit on your position?

a. a large decrease in the value of the Mexican peso

b. a large increase in the value of the Mexican peso

c. no change in the value of the Mexican peso

d. more than one of the above

e. none of the above

17. Consider a “SFr Dec 7000 call” selling on the Chicago Mercantile Exchange (CME) at a price of $0.0120/SFr. The current spot rate is $0.7090/SFr. Which of the following is ?

a. intrinsic value = $0.0000/SFr and time value = $0.0090/SFr

b. intrinsic value = $0.0000/SFr and time value = $0.0120/SFr

c. intrinsic value = $0.0090/SFr and time value = $0.0000/SFr

d. intrinsic value = $0.0090/SFr and time value = $0.0030/SFr

e. intrinsic value = $0.1200/SFr and time value = $0.0090/SFr

18. Which of the following is ?

a. Both call and put options lose more in value from spot rate decreases than they gain in value from spot rate increases of the same magnitude.

b. Both call and put options gain more in value from spot rate decreases than they lose in value from spot rate increases of the same magnitude.

c. Call options gain more in value from spot rate decreases than they lose in value from spot rate increases of the same magnitude.

d. Put options gain more in value from spot rate decreases than they lose in value from spot rate increases of the same magnitude.

e. None of the above are

19. Which of the following is ?

a. As volatility increases, call values increase and put values decrease.

b. As volatility increases, call values decrease and put values increase.

c. As volatility increases, the values of both call and put options decrease.

d. As volatility increases, the values of both call and put options increase.

e. Call and put values are independent of volatility.

20. Which of the following is not a determinant of currency option values?

a. interest rates

b. the exercise price

c. the systematic risk of the underlying currency value

d. the underlying exchange rate

e. volatility in the underlying exchange rate

21. The sensitivity of option value to change in the underlying asset value is called the ____.

a. option delta

b. option gamma

c. option sigma

d. option theta

e. option vega

22. The ______ is the number of options required to offset one unit of the underlying asset.

a. hedge ratio

b. implied volatility

c. option volatility

d. stationary series

e. none of the above

23. Exchange rate volatility over a future period can be estimated with ____.

a. implied volatility

b. reciprocal volatility

c. virtual volatility

d. more than one of the above

e. none of the above

24. The standard deviation of continuously compounded changes in the £/$ spot rate is estimated to be σ = 0.0082 = 0.82% per trading day. There are 252 business days in a year. Assuming zero volatility on nontrading days (weekends and holidays), what is the annual standard deviation of continuously compounded changes in the £/$ spot rate?

a. 9.38%

b. 13.02%

c. 15.11%

d. 20.64%

e. 28.20%

25. The current spot rate of the HK$ against the pound is S₀^£/HK$ = £0.10/HK$. The standard deviation of continuously compounded annual changes is estimated to be 10 percent. What price is two standard deviations above the current exchange rate?

a. £0.1020/HK$

b. £0.1100/HK$

c. £0.1200/HK$

d. £0.1221/HK$

e. The price cannot be determined from the information given.

26. The current spot rate of the Hong Kong dollar against the pound is S₀^£/HK$ = £0.10/HK$. The standard deviation of continuously compounded annual changes is estimated to be 10 percent. What price is two standard deviations below the current exchange rate?

a. £0.0778/HK$

b. £0.0800/HK$

c. £0.0819/HK$

d. £0.0900/HK$

e. The price cannot be determined from the information given.

27. Option prices can be used to calculate which of the following volatility estimates?

a. autoregressive volatility

b conditional volatility

c. historical volatility

d. implied volatility

e. RiskMetrics volatility

Problems (Some of these can be converted into Multiple Choice questions.)

1. You own an option to buy 1 million Argentinian pesos with an exercise price of $0.3649/ARS. What is the value of the option if the spot rate at expiration is $0.3824/ARS?

2. You buy a HK$1 million call option on Hong Kong dollars with an exercise price of $0.1667/HK$. The spot rate at expiration is $0.1685/HK$. What is the value of your option at expiration?

3. You buy a $1 million call option on U.S. dollars with an exercise price of $0.1667/HK$. The spot price at expiration is $0.1685/HK$. What is the value of your option at expiration?

4. You buy a call option on SFr with a strike price of $0.6573/SFr. You pay a premium of $0.0010/SFr to buy the option. The contract size is SFr125,000. If the option expires when the spot price is $0.6682/SFr, what is your net profit on this transaction? (For simplicity, ignore the time value of money.)

5. You buy a put option on SFr with a strike price of $0.6573/SFr. You pay a premium of $0.0010/SFr to buy the option. The contract size is SFr125,000. If the option expires when the spot price is $0.6682/SFr, what is your net profit on this transaction?

6. You write a call option on pounds and give it to Scrooge McDuck to compensate him for some consulting work. The contract size is £125,000 and the exercise price is £0.6344/$. If the option expires when the spot rate is £0.6285/$, will Scrooge’s treasure chest of dollars grow larger or smaller? By how much? (Scrooge takes his profit or loss in dollars). What is your profit or loss on this transaction?

7. You grow mesquite trees on your farm in Texas. Whenever a tornado strikes, you collect the fallen branches and sell the wood to Switzerland for use in bratwurst barbecues. You expect a payment of SFr62,500 in two months. In order to hedge, you buy a put option on francs that expires in two months with an exercise price of $0.7145/SFr. Draw the payoff profile of the currency put option. Calculate the dollar value of the option at closing spot rates of $0.7023/SFr, $0.7145/SFr, and $0.7234/SFr.

8. What is the advantage of a currency option hedge relative to a currency forward or futures hedge? What is the disadvantage of a currency option?

9. You own a put option to sell Swiss francs for U.S. dollars. Draw the following:

a. The value of the put option against the underlying spot rate (S^$/SFr). Identify the exercise price K^$/SFr on the graph.

b. Change in option value (V^$/SFr) against change in the underlying spot rate (S^$/SFr).

10. Using both words and graphs, demonstrate that a long (¥/$) call option on dollars is equivalent to a long ($/¥) put option on yen.

11. Gretchen Van Damme is considering buying call options on Swiss francs on the International Monetary Market of the Chicago Mercantile Exchange with a March expiration date and a strike price of $0.77/SF. The current spot rate of exchange is $0.77/SF. Gretchen believes that the spot rate in March will be between $0.74/SF and $0.81/SF, with a most likely value of $0.77/SF.

a. Calculate Gretchen’s gain or loss at closing spot rates of $0.74/SF, $0.77/SF, and $0.81/SF.

b. Diagram the value of Gretchen’s Swiss franc call option at expiration.

c. Suppose the price of a call option on Swiss francs is $0.02/SF. Diagram the profit or loss on Gretchen’s Swiss franc call option at expiration as a function of the underlying S^$/SF exchange rate.

12. Dubious Value, Inc. is scheduled to receive a 144 million cruzados dividend from its affiliate in Companis, Brazil, in three months. Name and briefly describe several different financial market hedges of Dubious’ exposure to currency risk.

13. Option payoff profiles:

a. Construct an option position (a combination of calls and/or puts) with the same risk profile (v^$/SFr versus s^$/SFr) as a forward contract to buy SFr for dollars at an agreed-upon future date. Identify the underlying asset, whether you are using puts or calls, and whether you are short or long.

b. Construct an option position that is identical to selling SFr forward. Clearly identify the asset underlying the option(s), whether you are using puts or calls, and whether you are short or long.

Problem Solutions

1. The gain is ($0.3824/ARS – $0.3649/ARS)(ARS1,000,000) = $17,500.

2. Buy HK$ at $0.1667/HK$ and sell them at $0.1685/HK$ for a gain of $0.0018/HK$

⇒ (HK$1,000,000)($0.0018/HK$) = $1,800.

3. Because the option is on dollars, it is convenient to state these quotes with the U.S. dollar in the denominator. The call option is an option to buy dollars at ($0.1667/HK$), or HK$6.000/$. The value of the dollar at expiration is 1/($0.1685/HK$) = HK$5.935/$. The exercise price of HK$6/$ is greater than the spot price of HK$5.935/$, so the call option is worthless.

4. The option is worth ($0.6682/SFr – $0.6573/SFr)(SFr125,000) = $1,362.50. You have paid (SFr125,000)($0.001/SFr) = $125. You have a $1,362.50– $125 = $1,237.50 gain.

5. The put option is an option to sell. The option expires out of the money because the exercise price is above the spot rate at expiration. The option premium of (SFr125,000)($0.001/SFr) = $125 is lost.

6. This is an option on pounds, so it is convenient to use the dollar price of the pound. Scrooge’s call is an option to buy pounds at (£0.6344/$)^1 = $1.5763/£. The spot rate at expiration is (£0.6285/$)^1 = $1.5911/£. Scrooge’s gain at expiration is ($1.5911/£ – $1.5763/£) = $0.0148/£, or (£125,000)($0.0148/£) = $1,850. Scrooge’s gain is your loss.

7.

At $0.7023/SF: option is out of the money and worthless.

At $0.7145/SF: option is at the money and worthless.

At $0.7234/SF: value = ($0.7234/SF – $0.7145/SF)(SF125,000) = $556.25.

8. In an option hedge, you benefit on the upside but do not lose on the downside. Of course, you must pay the option premium to buy the option. If the option expires out of the money, you’ll lose the premium with nothing (except the hedge) in return. Futures and forward hedges differ from option hedges in that their payoff profiles are symmetric.

9.

10. An option to buy dollars with yen is equivalent to an option to sell yen for dollars. The long call on dollars is in the money when S^¥/$ > K^¥/$. The long put is in the money when S^$/¥ < K^$/¥. These are equivalent because S^¥/$ > K^¥/$ is the same as S^$/¥ < K^$/¥.

11. a. If S^$/SF is $0.74/SF, Gretchen would rather purchase Swiss francs on the spot market at $0.74/SF than at the option exercise price of $0.77/SF. The option is out of the money and has no value at expiration.

If S^$/SF is $0.77/SF, Gretchen would be indifferent between purchasing Swiss francs at the $0.77/SF market price or at the $0.77/SF exercise price of the option. The option is at the money and has no value at expiration.

If S^$/SF is $0.81/SF, Gretchen would purchase Swiss francs at the option’s strike price of $0.77/SF, gaining $0.04/SF over what the spot would have cost her.

b.

c. If the option expires out of the money, Gretchen loses the $0.02/SF option premium. Gretchen begins to recoup her investment if the spot rate closes above $0.77/SF. Gretchen will earn a profit (ignoring the time value of the option premium) if the spot price closes above $0.79/SF. At a spot rate of $0.81/SF, Gretchen earns $0.02/SF.

12. Dubious can hedge its transaction exposure in any of the following ways: (a) a currency futures hedge, (b) a currency forward hedge, (c) a money market hedge (replicate the payoff on a forward market hedge by borrowing cruzados, lending the domestic currency, and converting at the spot exchange rate), or (d) or a currency option hedge.

13. a.

b.

Appendix 6A Currency Option Valuation

Problem

1. You work for SABMiller plc in London. You have an accounts payable balance of 10 million Chinese new yuan (CNY) that is due in one year to a Chinese supplier. HSBC is offering a European call option on 10 million yuan with an exercise price of K^£/CNY = £0.10/CNY. The current spot rate is S₀^£/CNY = £0.0940/CNY. You estimate that the standard deviation of continuously compounded returns to the S_t^£/CNY exchange rate is σ = 20 percent per year. The continuously compounded risk-free rates of interest are i_F^£ = 2 percent in sterling and i_F^CNY = 3 percent in yuan.

a. How much would you be willing to pay for this call option assuming the Biger-Hull currency option pricing model is correct?

b. Holding everything else constant, would you be willing to pay more or less for this option given each of the following changes?

i. the exchange rate increases to £0.0950/CNY

ii. the exercise price is increased to K^£/CNY = £0.11/CNY

iii. the risk-free rate increases to i_F^£ = 2.1 percent in sterling

iv. the risk-free rate increases to i_F^CNY = 3.1 percent in yuan

v. the time to expiration increases from one to two years

vi. exchange rate volatility increases to σ = 40 percent per year

Describe the intuition behind each of these effects on the value of the currency call option?

c. Repeat steps (a) and (b) for a put option on yuan.

Problem solution

1. a. First, note that the forward rate is F_T^£/CNY = S₀^£/CNY e^(0.02--.03) = £0.0931/CNY. The values d₁ = [ln(S^£/CNY/K^£/CNY) + (i^£ – i^CNY + (σ²/2))T ]/(σ√T) = [ln(0.0940/0.10) + (0.02 – 0.03 + (0.20)²/2)] / (0.20) = –0.2594 and d₂ = (d₁ – σ√T) = –0.2594 – (0.20) = –0.4594. From the cumulative normal distribution function, the probability that the call will expire in the money is N(d₁) = 0.3977. Call value from Equation 6A.3is then Call^£/CNY = e^(–i£T) [ F_T^£/CNY N(d₁) – K^£/CNY N(d₂) ] = e^0.02[(£0.0931/CNY)(0.3977) – (£0.10/CNY)(0.3230)] = £0.0046/CNY.

b. i. A CNY appreciation to £0.0950/CNY increases call option value to £0.0050/CNY by increasing the probability and consequences of expiring in-the-money.

ii. A strike price increase to K^£/CNY = £0.11/CNY yields Call^£/CNY = £0.0022/CNY by moving the call farther out of the money, thereby decreasing the probability of expiring in the money.

iii. An increase in the pound risk-free rate to i_F^£ = 2.1 percent has little effect on option value; Call^£/CNY = £0.0046/CNY.

iv. An increase in the CNY risk-free rate to i_F^CNY = 3.1 percent also has little effect on option value; Call^£/CNY = £0.0046/CNY.

v. An increase in time to expiration two years yields Call^£/CNY = £0.0070/CNY because the time to expiration increases the variability of exchange rate outcomes.

vi. An increase in volatility to σ = 40 percent per year yields Call^£/CNY = £0.0118/CNY because the value of that part of the distribution that falls in-the-money increases.

c. Put^£/CNY = £0.0114/CNY at K^£/CNY = £0.10/CNY. Then:

i. S_t^£/CNY = £0.0950/CNY = > Put^£/CNY = £0.0108/CNY

ii. K^£/CNY = £0.11/CNY = > Put^£/CNY = £0.0188/CNY

iii. i_F^£ = 2.1 percent = > Put^£/CNY = £0.0113/CNY

iv. i_F^CNY = 3.1 percent = > Put^£/CNY = £0.0115/CNY

v. T = 2 = > Put^£/CNY = £0.0146/CNY

vi. σ = 40 percent = > Put^£/CNY = £0.0186/CNY