Chapter3 Futures and Options on Foreign Exchange

金融专业英语阅读（答案）Chapter OneMonetary Policy(货币政策) …………………………………Chapter TwoForeign Exchange Risk andWhy It Should Be Managed(外汇风险和进行外汇管理的原因)………………………………………Chapter ThreeTools and Techniques forThe Management of Foreign Exchange Risk(控制外汇风险的工具和方法) …………………………………Chapter FourU.S. Foreign ExchangeIntervention(美国对外汇交易的干预) …………………………………Chapter FiveHistory of Accounting(会计的历史起源) …………………………………Chapter SixAccounting and Bookkeeping(会计和簿记) …………………………………Chapter SevenFinancial Markets and Intermediaries(金融市场和中间业务) …………………………………Chapter EightHistory of Insurance(保险的历史起源) …………………………………Chapter NineInsurance Policy(保险单) …………………………………Chapter TenBank for International Settlements(国际清算银行) …………………………………Chapter ElevenCommercial Bank Lending(商业银行借贷) …………………………………Chapter TwelveCredit Analysis(信贷分析) …………………………………Chapter ThirteenWhat Kind of Mortgage Loan Should You Get?(何种抵押贷款更适合你？) …………………………………Chapter FourteenMutual Fund(共同基金) …………………………………Chapter FifteenBonds(债券) …………………………………Chapter SixteenOptions(期权) …………………………………Chapter OneMonetary Policy货币政策Answers:Multiple choices1.D2.B3.C4.C5.ATrue or False1.F2.T3.F4.T5.F6.TRead the following text and choose the best sentences for A to E below to fill in each of the gaps in text1. E2. B3. D4. A5. CCloseEmployment, demand, fiscal policy tools, monetary policy, central bank, interest rates, "stable" prices, inflation, "federal funds" rate, open market operationsTranslation:Translate the following passage into Chinese1.紧缩性货币政策和扩张性货币政策都涉及到改变一个国家的货币供应量水平。

Lecture10(Chapter 07)Futures and Options on Foreign Exchange外汇期货与期权1. 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.TRUE2. A CME contract on €125,000 with Septe mber delivery 交货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.3. Yesterday, you entered into a futures contract to buy €62,500 at $1.50 per €. Suppose t he 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.4. In reference to the futures market, a "speculator"A. attempts to profit from a change in the futures priceB. 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 contractC. stands ready to buy or sell contracts in unlimited quantityD. both b) and c)5. Comparing "forward" and "futures" exchange contracts, we can say thatA. 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. both b) and c)Topic: Futures Contracts: Some Preliminaries6. Comparing "forward"远期合约 and "futures"期货合约 exchange contracts, we can say thatA. 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. both a) and b)E. both a) and c)7. In which market does a clearinghouse serve as a third party to all transactions?A. FuturesB. ForwardsC. SwapsD. None of the above8. In the event of a default on one side of a futures trade,A. the clearing member stands in for the defaulting party. 结算会员代表为违约方B. the clearing member will seek restitution for the defaulting party.寻求赔偿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. both a) and b)9. 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? 题目的意思是，初始保证金余额１５００，维持保证金水平为５００，当汇率在哪个水平上，客户需要追加保证金？,A.$1.5160 per €.B.$1.208 per €.C.$1.1920 per €.D.$1.4840 per €.10. 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 €.11. 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/€６２５００×（１．５－？）＝３７５０－２０００B.$1.5280/€C.$1.500/€D. None of the above12. 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 $2,500B.Made $0.04 per € or $2,500C.Lost $0.06 per € or $3,750D. None of the above13. 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 空头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 日元贬值，赚钱A. $1,425.B. $2,000.C. $2,325.＝（０．８０１１－０．７９８５）×１２５０００＋２０００D. $3,425.14. 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 多头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 日元贬值，亏钱A. $1,425.B. $1,675.C. $2,000.D. $3,425.Topic: Currency Futures Markets15. 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.16. What paradigm is used to define the futures price?A. IRP利率平价B. Hedge RatioC. Black ScholesD. Risk Neutral Valuation17. 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. $159.22Ｆ＝１．４５×１．０４／１．０３＝１．４６４１B. $153.10（１．４８－１．４６４１）×１００００＝４５９C. $439.42D. None of the aboveThe futures price of $1.48/€ is above the IRP futures price of $1.4641/€, so we want to sel l (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 investme nt 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 - $14,640.7818. Which equation is used to define the futures price?A.B.C.D.19. Which equation is used to define the futures price? A.B.C.D.E.Topic: Currency Futures Markets20. If a currency futures contract (direct quote) is priced below the price implied by Interest Rate Parity (IRP), arbitrageurs could take advantage of the mispricing by simultaneouslyA. going short in the futures contract, borrowing in the domestic currency, and going long in the foreign currency in the spot market.B. going short in the futures contract, lending in the domestic currency, and going long in the foreign currency in the spot market.C. going long in the futures contract, borrowing in the domestic currency, and going short in the foreign currency in the spot market.D. going long in the futures contract, borrowing in the foreign currency, and going long in the domestic currency, investing the proceeds at the local rate of interest.21. Open interest in currency futures contractsA. 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. both a) and c)22. The "open interest" shown in currency futures quotations isA. 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.23. If you think that the dollar is going to appreciate against the euro, you shouldA. buy put options on the euro.B. sell call options on the euro.卖出欧元看涨权C. buy call options on the euro.D. none of the above24. From the perspective of the writer 卖家of a put option 看跌期权written on €62,500. If the s trike price执行价格 i s $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 above25. A European option is different from an American option in thatA. 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.26. An "option" isA. 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.27. 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 optionA. (i), (ii), and (iii)B. (i), (ii), and (iv)C. (i), (iv), and (v)D. (ii) and (iii)28. Most exchange traded currency optionsA. 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.29. The volume of OTC currency options trading isA. 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 above30. 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)31. With currency futures options the underlying asset isA. foreign currency.B. a call or put option written on foreign currency.C. a futures contract on the foreign currency.D. none of the above32. Exercise of a currency futures option results inA. 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.33. 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. 标的资产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 above34. The current spot exchange rate目前即期汇率is $1.55 = €1.00 and the three-month forward rate is $1.60 = €1.00. Consi der a three-month American call option on €62,500. For this option to be considered at-the-money, the strike price must beA.$1.60 = €1.00B.$1.55 = €1.00C. $1.55 ⨯ (1+i$)3/12= €1.00 ⨯ (1+i€)3/12D. none of the above35. 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 ofA. $6,125B. $6,125/(1+i$)3/12C. negative profit, so exercise would not occurD. $3,12536. 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 = €1.00B.$1.62 = €1.00C.$1.50 = €1.00D.$1.68 = €1.0037. 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 = $1.55B. A = -€3,750 (or -€.06 depend ing on your scale); B = $1.50; C = $1.55C. A = -$.05; B = $1.55; C = $1.60D. none of the above38. 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. AB. BC. CD. D39. 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 = $3,125B. $3,125/1.02 = $3,063.73C. $0.00D. none of the above40. 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 putsB. Buying calls and buying putsC. Buying calls and selling putsD. None of the aboveTopic: American Option-Pricing Relationships41. American call and put premiumsA. should be at least as large as their intrinsic value. 内在价值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.42. Which of the following is correct?A. Time value = intrinsic value + option premiumB. Intrinsic value = option premium + time valueC. Option premium = intrinsic value - time valueD. Option premium = intrinsic value + time value43. 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 above44. Assume that the dollar-euro spot rate is $1.28 and the six-month forward rateis . 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 $1.25 should sell for in a rational market isA. 0 centsB. 3.47 centsC. 3.55 centsD. 3 cents45. For European options, what of the effect of an increase in S t?A. Decrease the value of calls and puts ceteris paribusB. Increase the value of calls and puts ceteris paribusC. Decrease the value of calls, increase the value of puts ceteris paribusD. Increase the value of calls, decrease the value of puts ceteris paribus46. For an American call option, A and B in the graph areA. time value and intrinsic value.B. intrinsic value and time value.C. in-the-money and out-of-the money.D. none of the above47. For European options, what of the effect of an increase in the strike price E?A. Decrease the value of calls and puts ceteris paribusB. Increase the value of calls and puts ceteris paribusC. Decrease the value of calls, increase the value of puts ceteris paribusD. Increase the value of calls, decrease the value of puts ceteris paribus48. For European currency options written on euro with a strike price in dollars, what of the effect of an increase in r$ relative to r€?A. Decrease the value of calls and puts ceteris paribusB. Increase the value of calls and puts ceteris paribusC. Decrease the value of calls, increase the value of puts ceteris paribusD. Increase the value of calls, decrease the value of puts ceteris paribus49. For European currency options written on euro with a strike price in dollars, what of the effect of an increase in r$?A. Decrease the value of calls and puts ceteris paribusB. Increase the value of calls and puts ceteris paribusC. Decrease the value of calls, increase the value of puts ceteris paribusD. Increase the value of calls, decrease the value of puts ceteris paribusTopic: European Option-Pricing Relationships50. For European currency options written on euro with a strike price in dollars, what of the effect of an increase r€?A. Decrease the value of calls and puts ceteris paribusB. Increase the value of calls and puts ceteris paribusC. Decrease the value of calls, increase the value of puts ceteris paribusD. Increase the value of calls, decrease the value of puts ceteris paribus51. For European currency options written on euro with a strike price in dollars, what of the effect of an increase in the exchange rate S($/€)?A. Decrease the value of calls and puts ceteris paribusB. Increase the value of calls and puts ceteris paribusC. Decrease the value of calls, increase the value of puts ceteris paribusD. Increase the value of calls, decrease the value of puts ceteris paribus52. 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 paribusB. Increase the value of calls and puts ceteris paribusC. Decrease the value of calls, increase the value of puts ceteris paribusD. Increase the value of calls, decrease the value of puts ceteris paribus53. The hedge ratioA. 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 amount of the underlying asset.D. All of the above54. 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 dollar depreciation is 2/3 and the risk-neutral probability of the dollar strengthening is 1/3.A. $9.5238B. $0.0952C. $0D. $3.174655. 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.€3,275B.€2,500C.€3,373D.€3,24356. 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. 5/9B. 8/13C. 2/3D. 3/8E. None of the above57. 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 workF. None of the above58. 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 above59. 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 above60. 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. -15/49B. 5/13C. 3/2D. 15/4961. 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. -15/49B. 8/13C. -5/13D. 15/4962. Find the dollar value today of a 1-period at-the-money call option on €10,000. The spot exchange rate is €1.00 = $1.25. In the next period, the euro can increase in dollar value to $2.00 or fall to $1.00. The interest rate in dollars is i$ = 27.50%; the interest rate in euro is i€ = 2%.A. $3,308.82B. $0C. $3,294.12D. $4,218.7563. 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 a short position in 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 i n 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 above64. Find the value of a one-year put option on $15,000 with a strike price of €10,000. I n one year the exchange rate (currently S0($/€) = $1.50/€) can increase by 60% or decrease by 37.5% (i.e. u = 1.6 and d = 0.625). The current one-year interest rate in the U.S. is i$ = 4% and the current one-year interest rate in the euro zone is i€ = 4%.A.€1,525.52B. $3,328.40C. $4,992.60D.€2,218.94E. None of the above65. 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.€1,525.52B. $3,328.40C. $4,992.60D.€2,218.94E. None of the above66. 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. £6,666.67B. £6,349.21C. $12,698.41D. $20,000E. None of the above67. 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. $6,349.21B.C.D. None of the aboveTopic: Binomial Option-Pricing Model68. 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 £5,000.69. 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 = 0.103915B.d1 = 2.9871C.d1 = -0.0283D. none of the above70. 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 = 0.074246B.d1 = 0.005982C.d1 = $0.006137/¥D. None of the above71. The Black-Scholes option pricing formulaeA. 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 above72. 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 is10.7 percent.A.C e = $0.63577B.C e = $0.0998C.C e = $1.6331D. none of the aboveINSTRUCTOR NOTE: YOU WILL HAVE TO PROVIDE YOUR STUDENTS WITH A TABLE OF THE NORMAL DISTRIBUTION.。

Fundamentals of Futures and Options Markets, 8e (Hull)Chapter 6 Interest Rate Futures1) Which of the following is applicable to corporate bonds in the United States?A) Actual/360B) Actual/ActualC) 30/360D) Actual/365Answer: C2) It is May 1. The quoted price of a bond with an Actual/Actual (in period) day count and 12% per annum coupon in the United States is 105. It has a face value of 100 and pays coupons on April 1 and October 1. What is the cash price?A) 106.00B) 106.02C) 105.98D) 106.04Answer: C3) It is May 1. The quoted price of a bond with a 30/360 day count and 12% per annum coupon in the United States is 105. It has a face value of 100 and pays coupons on April 1 and October 1. What is the cash price?A) 106.00B) 106.02C) 105.98D) 106.04Answer: A4) The most recent settlement bond futures price is 103.5. Which of the following four bonds is cheapest to deliver?A) Quoted bond price = 110; conversion factor = 1.0400B) Quoted bond price = 160; conversion factor = 1.5200C) Quoted bond price = 131; conversion factor = 1.2500D) Quoted bond price = 143; conversion factor = 1.3500Answer: C5) Which of the following is NOT an option open to the party with a short position in the Treasury bond futures contract?A) The ability to deliver any of a number of different bondsB) The wild card playC) The fact that delivery can be made any time during the delivery monthD) The interest rate used in the calculation of the conversion factorAnswer: D6) A trader enters into a long position in one Eurodollar futures contract. How much does the trader gain when the futures price quote increases by 6 basis points?A) $6B) $150C) $60D) $600Answer: B7) A company invests $1,000 in a five-year zero-coupon bond and $4,000 in aten-year zero-coupon bond. What is the duration of the portfolio?A) 6 yearsB) 7 yearsC) 8 yearsD) 9 yearsAnswer: D8) The modified duration of a bond portfolio worth $1 million is 5 years. By approximately how much does the value of the portfolio change if all yields increase by 5 basis points?A) Increase of $2,500B) Decrease of $2,500C) Increase of $25,000D) Decrease of $25,000Answer: B9) A portfolio is worth $24,000,000. The futures price for a Treasury note futures contract is 110 and each contract is for the delivery of bonds with a face value of $100,000. On the delivery date the duration of the bond that is expected to be cheapest to deliver is 6 years and the duration of the portfolio will be 5.5 years. How many contracts are necessary for hedging the portfolio?A) 100B) 200C) 300D) 400Answer: B10) Which of the following is true?A) The futures rates calculated from a Eurodollar futures quote are always less than the corresponding forward rateB) The futures rates calculated from a Eurodollar futures quote are always greater than the corresponding forward rateC) The futures rates calculated from a Eurodollar futures quote should equal the corresponding forward rateD) The futures rates calculated from a Eurodollar futures quote are sometimes greater than and sometimes less than the corresponding forward rateAnswer: B11) How much is a basis point?A) 1.0%B) 0.1%C) 0.01%D) 0.001%Answer: C12) Which of the following day count conventions applies to a US Treasury bond?A) Actual/360B) Actual/Actual (in period)C) 30/360D) Actual/365Answer: B13) What is the quoted discount rate on a money market instrument?A) The interest rate earned as a percentage of the final face value of a bondB) The interest rate earned as a percentage of the initial price of a bondC) The interest rate earned as a percentage of the average price of a bondD) The risk-free rate used to calculate the present value of future cash flows from a bondAnswer: A14) Which of the following is closest to the duration of a 2-year bond that pays a coupon of 8% per annum semiannually? The yield on the bond is 10% per annum with continuous compounding.A) 1.82B) 1.85C) 1.88D) 1.92Answer: C15) Which of the following is NOT true about duration?A) It equals the years-to-maturity for a zero coupon bondB) It equals the weighted average of payment times for a bond, where weights are proportional to the present value of paymentsC) Equals the weighted average of individual bond durations for a portfolio, where weights are proportional to the present value of bond pricesD) The prices of two bonds with the same duration change by the same percentage amount when interest rate move up by 100 basis pointsAnswer: D16) The conversion factor for a bond is approximatelyA) The price it would have if all cash flows were discounted at 6% per annumB) The price it would have if it paid coupons at 6% per annumC) The price it would have if all cash flows were discounted at 8% per annumD) The price it would have if it paid coupons at 8% per annumAnswer: A17) The time-to-maturity of a Eurodollars futures contract is 4 years, and thetime-to-maturity of the rate underlying the futures contract is 4.25 years. The standard deviation of the change in the short term interest rate, σ = 0.011. What is the difference between the futures and the forward interest rate?A) 0.105%B) 0.103%C) 0.098%D) 0.093%Answer: B18) A trader uses 3-month Eurodollar futures to lock in a rate on $5 million for six months. How many contracts are required?A) 5B) 10C) 15D) 20Answer: B19) In the U.S. what is the longest maturity for 3-month Eurodollar futures contracts?A) 2 yearsB) 5 yearsC) 10 yearsD) 20 yearsAnswer: C20) Duration matching immunizes a portfolio againstA) Any parallel shift in the yield curveB) All shifts in the yield curveC) Changes in the steepness of the yield curveD) Small parallel shifts in the yield curve Answer: D。

金融英语第十三章答案Chapter13 (exercises)I .Answer the following questions in English.1.Carefully describe a futures contract.A future contract is a blinding agreement between a seller and a buyer to make and to take delivery of the underlying commodity at a specified future date with agreed upon payment terms.Futures contracts are standardized with respect to the delivery month.2.Explain how futures contracts are valued daily,It is possible to calculate a theoretical fair value for a futures contract.The fair value of a futures contract should approximately equal the current value of the underlying shares or index,plus an amount referred to as the “cost of carry”.The full value of the contract is not paid or received when the contract is established-instead both buyer and seller pay a small initialmargin.3.Describe the role of the clearinghouse in futures trading.The clearinghouse,an agency or separate corporation of a futures exchange.The clearinghouse becomes the buyer to each seller and assumes responsibility for protecting buyers and sellers from financial loss by assuring performance on each contract.4. Explain the differences between a hedger and a speculator.The difference between hedgers an speculators is the risk.Hedgers are parties at risk with a commodity or an asset,but speculators trads futures with the objective of making a profit by being on the right side of a price move.5. Give a brief description of the history of futures.Both the histories of futures are focused on that how people have tried to improve the effectiveness of the commercial marketplace. 6. What is key difference between forward and futures?Forward contracts and futures comparison: the former is a standardized contract, OTC, flexible and high transaction cost, risk is big. The latter are standardized contracts, exchange as a medium, investors and unlike forward contracts as the direct trading, risk is small.Options and futures comparison: futures trading both sides has rights and obligations. While the option buyer the right to sell only, only obligation. In addition from the gains and losses, the futures of profit and loss is uncertain, but the option buyer 's loss is the option premium.Ⅱ. Fill in the e ach blank with an appropriate word or expression.1. Futures are binding agreements made between two partiesthrough a regulated futures exchange. Each futures contract specifies the quantity and quality of the item, expirationmonth, the time of delivery and virtually all the detailsof the transaction except price , which the two partiesnegotiate based on current market conditions.2. The clearinghouse, an agency or separate corporation of afutures exchange, is responsible for settlingtrading accounts, collecting and margin monies,regulating delivery and reporting trade data.3. A futures contract is an agreement to purchase or sell acommodity for delivery in the future: ( 1 ) at a price thatis determined at initiation of the contract; (2) whichobligates each party to the contract to the contract at thespecified price; (3) which is used to assume or shift pricerisk ; and(4) which may be satisfied by delivery or offset４. The key to any hedge is that a futures position is taken opposite to the position in the cash market. That is, the nature of cash market position determines the hedge in the futures market.5. Currency futures are standardized contracts that tradelike conventional commodity futures on the floor of a futures exchange.6. These orders,from companies,individuals,and evenmarket-making commercial banks, are happened to the floor ofthe futures exchange.Ⅲ. Translate the following sentences into English.1．商品生产者和经营者在生产和经营过程中，时刻面临着价格波动的风险。

Chapter12.Forwards,Futures,and SwapsPricing PrinciplesSuppose that your uncle promises that he will give you an ounce of gold1year from now,which is worth$1,000today.How should you evaluate this promised gift?Pricing principles:•Use the market.The gold market may befluctuating,but one can purchase the gold and give it to you next year.So using the market,its value today is$1,000.•Discounting certain cash at the current rate of interest.Suppose your uncle promises to give you$1,000next year,and the interest rate is10%.Then,the value of the cash is$909.•If asset A has value V A,and B has value V B,then the value of a units of A and b units of B is aV A+bV B.Forward Contracts•A forward contract on a commodity is a contract to purchase or sell a specific amount of the commodity at a specific price and at a specific time in the future.•Long position:buyer.•Short position:seller.•Spot market.•Forward market.Forward interest rateExample12.1.Suppose that you wish to arrange to loan money for6 months beginning3months from now.Suppose that the forward rate for that period is10%.A suitable contract that implements this loan would be an agreement for a bank to deliver to you,3months from now,a6-month Treasury bill.The price would be agreed upon today for this delivery,and the Treasury bill would pay its face value of,say $1000,at maturity.The value of the T-bill would be$1000/1.05=$952.38.This is the price you would agree to pay in3 months when the T-bill is delivered to you.Six months later you receive the$1000face value.Forward prices•Forward price F.•Current value of a forward contract.•Delivery time T.•Spot market price S.Forward price formula.Suppose an asset can be stored at no cost and also sold short.The theoretical forward price isF=S/d(0,T).Proof of forward price formula:One of the following two strategies will provide an arbitrage opportunity if the formula did not hold:t=0initial costfinal receiptborrow$S−S−S/d(0,T)buy1unit and store S0short1forward0FTotal:0F−S/d(0,T)t=0initial costfinal receiptshort1unit−S0lend$S S S/d(0,T)go long1forward0−FTotal:0S/d(0,T)−FCosts of CarryForward price formula with carrying costs.Suppose that an asset has a holding cost of c(k)per unit in period k,and the asset can be sold short.Suppose the initial spot price is S.Then the theoretical forward price isF=Sd(0,M)+M−1∑k=0c(k)d(k,M),where d(k,M)is the discount factor from k to M.EquivalentlyS=−M−1∑k=0d(0,k)c(k)+d(0,M)F.t =0time 0costtime k costreceipt at time Mshort 1unit 00F borrow $S −S 0−S/d (0,M )buy 1unit spot S 00borrow c (k )’s forward −c (0)−c (k )−∑M −1k =0c (k )d (k,M )pay storage c (0)c (k )0Total :F −S d (0,M )−∑M −1k =0c (k )d (k,M )Example12.4.The current price of sugar is12cents per pound.We wish tofind the forward price of sugar to be delivered in5months. The carrying cost of sugar is0.1cent per pound per month,to be paid at the beginning of the month,and the interest rate is constant at9% per annum.The monthly interest rate is0.09/12=0.75%.The reciprocal of the1-month discount rate is1.0075.Therefore,F=1.00755×0.12+(1.00755+1.00754+1.00753+1.00752+1.00751)×0.001 =0.1295=12.95cents.IE544110Tight MarketAccording to the above analysis,the forward prices should beincreasing with M.However,it may not necessarily be the case inpractice.The main reason for this is that it is difficult or evenimpossible to reverse the positions:short-selling with the spot priceespecially when the market on the commodity is tight,and charge the storage costs to someone else.Hence,we will only be able to establishF≤Sd(0,M)+M−1∑k=0c(k)d(k,M).The so-called convenience yield y is the slack to make the above an equality:F=Sd(0,M)+M−1∑k=0c(k)d(k,M)−M−1∑k=0yd(k,M).Investment AssetsWe can roughly distinguish the commodities by their nature:(1) consumption assets(such as food,cotton,oil,...);(2)investment assets(such as gold,silver,or other precious metals).The maindifference is that many people are holding investment assets for profit, and so the market is less likely to be tight.The construction of an arbitrage such as the following is more likely:t=0initial costfinal receiptshort1unit−S0lend$S S S/d(0,T)go long1forward0−FTotal:0S/d(0,T)−FHence,the equation F=S/d(0,T)is more likely;or,the convenience yield for investment assets is small.The value of a forward contractThe value of a forward contract.Suppose a forward contract for delivery at time T in the future has a delivery price F0and a current forward price F t.The value of the contract isf t=(F t−F0)d(t,T),where d(t,T)is the risk-free discount factor from t to T.Proof.Form the following portfolio at time t:one unit long of a new forward contract with delivery price F t maturing at time T,and one unit short of the old contract with delivery price F0.The initial cashflow of this portfolio is f t.Thefinal cashflow at time T is F0−F t.The present value of the portfolio is f t+(F0−F t)d(t,T), which must be zero.2SwapsA swap is an agreement to exchange one cashflow stream for another. Consider an electric power company that must purchase oil every month for its power generation facility.Value of a commodity swap.Consider an agreement where party A receives spot price for N units of a commodity each period while paying afixed amount X per unit for N units.If the agreement is made for M periods,the net cashflow received by A is(S1−X,S2−X,···,S M−X)multiplied by N,where S i is the spot price at time i.The current value of receiving S i at time i is d(0,i)F i.Hence,the total value of the stream isV=M∑i=1d(0,i)(F i−X)N.Example12.6.Consider an agreement by an electronicfirm to receive spot value for gold in return forfixed payments.We assume that gold is in ample supply and can be stored without cost;in that case we know that the forward price is F i=S0/d(0,i).ThereforeV=[MS0−M∑i=0d(0,i)X]N.Suppose the price of a bond of maturity M,face value F,coupon C per period is B(M,C).Then,V={MS0−XC[B(M,C)−F d(0,M)]}N.Value of an interest rate swap.Party A agrees to make payments of a fixed rate r of interest on principal N while receivingfloating rate payments on the same notional principal for M periods.The cashflow stream received by A is(c0−r,c1−r,···,c M−r)×N where c i is the floating rate in period i.The initial value of afloating rate bond is par.The value of thefloating rate portion of the swap is par minus the present value of the principal received at M.Hence,the value of thefloating rate portion of the swap is N−d(0,M)N.The overall value of the swap isV=[1−d(0,M)−rM∑i=1d(0,i)]N.Basics of futures contracts•Futures market.•Marking to market.•Margin account.•Margin call.Example12.7(Margin).Mr.Smith takes a long position of one contract of corn(5,000bushels)for March delivery at a price of$2.10 per bushel.The broker requires margin of$800with a maintenance margin of$600.The next day the price drops to$2.07,representing a loss of0.03×5,000=$150.The broker takes this amount from the margin account,leaving a balance of$650.The following day it further drops to$2.05,representing an additional loss of$100.At this point the broker calls Mr.Smith telling him that he must deposit at least$50in his margin account,or his position will be closed out.Futures pricesFutures-forward equivalence.Suppose that the interest rates are known to follow expectation dynamics.Then the theoretical futures and forward prices of corresponding contracts areidentical.Let F0be the initial futures price.Let G0be the forward price(to be paid at delivery).Consider the following two strategies:Strategy A:•Time0:Go long d(1,T)futures.•Time1:Increase position to d(2,T).•···•Time k:Increase position to d(k+1,T).•···•Time T−1:Increase position to1.The profit at time k+1from the previous period is(F k+1−F k)d(k+1,T).This amounts to thefinal payment(F k+1−F k)d(k+1,T)=F k+1−F k.d(k+1,T)IE544120Therefore,the totalfinal settlement is:∑T−1(F k+1−F k)=F T−F0=S T−F0.k=0Strategy B:Take a long position in one forward contract.This requires no initial payment and thefinal settlement will beS T−G0.Now,let us consider a new strategy:A−B.This new strategy requires no cashflow until T,when the value is:G0−F0.According to the no-arbitrage principle,we must haveG0=F0.We have shown that the initial futures price must be equal to theforward contract value to be delivered in the end.The perfect hedgeExample12.10.A U.S.electronicsfirm has received an order to sell equipment to a German customer in90days.The price of the order is specified as500,000euros,which will be paid upon delivery.The U.S.firm faces the exchange risk.Thefirm can hedge this exchange rate risk with four euros’contracts (125,000per contract)with a90-day maturity date.Effectively,thefirm hedges the risk by taking a short position on four contracts.The minimum-variance hedgeSometimes it is not possible to hedge the risk perfectly.The lack of hedging perfection can be measured by the so-called basis:basis=spot price of asset to be hedged-futures price of contract used.Suppose x to be the cash to occur at T,h to be the futures position taken.Then,the cashflow at T isy=x+(F T−F0)h,with var(y)=var(x)+2cov(x,F T)h+var(F T)h2.Theminimum-variance hedging formula:h=−cov(x,F T) var(F T)var(y)=var(x)−cov(x,F T)2 var(F T).Optimal HedgingIf a utility function U is available,then it is appropriate to solvemaxhE[U(x+h(F T−F0))].Suppose the utility function is a quadratic function.Then,the objective becomes E[x+h(F T−F0)]−r var(x+hF T).The optimalsolution ish=E[F T]−F02r var(F T)−cov(x,F T)var(F T).Example 12.15.In January a large producer of commercial flour andbread wishes to lock in the price for a large order of wheat.Theproducer would like to buy 500,000bushels of wheat forward for Maydelivery.The current futures price for May delivery is $3.30perbushel.Suppose this producer expects the price of wheat to increaseby 5%in 3months,and the wheat market has approximately 30%volatility per year,so the producer assigns a 15%volatility to the 3-month forecast (15%=30%/√4).Using x =500,000F T ,we haveh =−500,000+E [F T ]−F 02r var (F T )=−500,000+E [F T ]F 0−12rF 0var (F T /F 0)=−500,000+0.052r ×3.3×0.152=−500,000+0.336r.Suppose r =1/1,000,000,we have h =−164,000.Hedging Nonlinear RiskExample12.16(A corn farmer case).The amount of corn harvested by every farmer depends on the weather,and the price of corn per bushel is determined by the equation P=10−D/100,000where D is the total supply.We assume the amount of corn grown on each farm is C and varies between0to6,000bushels with E[C]=3,000.There are a total of100farms,and so D=100C.The revenue of a farmer will beR=P C=10C−C2 1,000.Suppose$7per bushel is the current futures price.Let h be the futures market position.The farmer’s revenue will then beP C+h(P−P0)=10C−C21,000+E[C]−C1,000h.One may wish tofind h by maximizing E[U(10C−C21,000+E[C]−C1,000h)].。

CHAPTER 7 Futures and Options on Foreign ExchangeFutures Contracts: Some PreliminariesCurrency Futures MarketsInternational Finance in Practice: CME Ramping Up FOREX Support, Targets OTC Business Basic Currency Futures RelationshipsEurodollar Interest Rate Futures ContractsOptions Contracts: Some PreliminariesCurrency Options MarketsCurrency Futures OptionsBasic Option-Pricing Relationships at ExpirationAmerican Option-Pricing RelationshipsEuropean Option-Pricing RelationshipsBinomial Option-Pricing ModelEuropean Option-Pricing FormulaEmpirical Tests of Currency OptionsSummaryMINI CASE: The Options SpeculatorFutures Contracts: Some Preliminaries1 A CME contract on €125,000 with September deliverya)Is an example of a forward contractb)Is an example of a futures contractc)Is an example of a put optiond)Is an example of a call optionAnswer: b)Rationale: options trade on the CBOE2Yesterday, you entered into a futures contract to buy €62,500 at $1.20 per €. Suppose that the futures price closes today at $1.16. How much have you made/lost?a)Depends on your margin balanceb)You have made $2,500.00c)You have lost $2,500.00d)You have neither made nor lost money, yet.Answer: c)Rationale: You have lost $0.04, 62,500 times for a total loss of $2,500 = $0.04/€ × €62,5003In reference to the futures market, a “speculator”a)attempts to profit from a change in the futures priceb)wants to avoid price variation by locking in a purchase price of the underlyingasset through a long position in the futures contract or a sales price through ashort position in the futures contractc)stands ready to buy or sell contracts in unlimited quantityd)b) and c)Answer: a)4Comparing “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 futurepurchase or sale: futures settle daily and forwards settle at maturity.c) A futures contract is negotiated by open outcry between floor brokers or tradersand 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)Answer: d)5Comparing “forward” and “futures” exchange contracts, we can say thata)Delivery of the underlying asset is seldom made in futures contractsb)Delivery of the underlying asset is usually made in forward contractsc)Delivery of the underlying asset is seldom made in either contract—they aretypically cash settled at maturity.d)a) and b)e)a) and c).Answer: d)6In which market does a clearinghouse serve as a third party to all transactions?a)Futuresb)Forwardsc)Swapsd)None of the aboveAnswer: a)7In the event of a default on one side of a futures trade,a)The clearing member stands in for the defaulting partyb)The clearing member will seek restitution for the defaulting partyc)If the default is on the short side, a randomly selected long contract will not getpaid. That party will then have standing to initiate a civil suit against thedefaulting short.d)a) and b)Answer: d)8Yesterday, you entered into a futures contract to buy €62,500 at $1.20 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)$1.2160 per €.b)$1.208 per €.c)$1.1920 per €.d)$1.1840 per €.Answer: d)Rationale: To get a margin call, you have to lose $1,000. That will happen when the price FALLS (since you’re buying euro) to $1.1840 per €:[$1.20/ € – $1.1840 per €] × €62,500 = $1,000.9Yesterday, you entered into a futures contract to sell €62,500 at $1.20 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)$1.2160 per €.b)$1.208 per €.c)$1.1920 per €.d)$1.1840 per €.Answer: a)Rationale: To get a margin call, you have to lose $1,000. That will happen when the price RISES (since you’re selling euro at $1.20 per €.) to $1.2160 per €:[$1.2160/ € – $1.20 per €] × €62,500 = $1,000.10Three days ago, you entered into a futures contract to sell €62,500 at $1.20 per €.Over the past three days the contract has settled at $1.20, $1.22, and $1.24. Howmuch have you made or lost?a)Lost $0.04 per € or $2,500b)Made $0.04 per € or $2,500c)Lost $0.06 per € or $3,750d)None of the aboveAnswer: a)Rationale: Losses will happen when the price RISES (since you’re selling euro at $1.20 per €.) Total loss[$1.20/ € – $1.24 per €] × €62,500 = –$2,500Currency Futures Markets11Today’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 bea)$1,425b)$2,000c)$2,325d)$3,425Answer: c) not unlike Problem 1 at the end-of-chapter exercisesRationale: $2,325 = $2,000 +¥12,500,000×[(0.008011 – 0.008057) + (0.008057 – 0.007996) + (0.007996 – 0.007985)] Please note that $0.8011/¥100 = $0.008011/¥ and $0.8057/¥100 = $0.008057/¥, etc.12Today’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)$1,425b)$1,675c)$2,000d)$3,425Answer: b) not unlike Problem 1 at the end-of-chapter exercisesRationale: $1,675 = $2,000 +¥12,500,000×[(0.008057 - 0.008011) + (0.007996 – 0.008057) + (0.007985 – 0.007996)] Please note that $0.8011/¥100 = $0.008011/¥ and $0.8057/¥100 = $0.008057/¥, etc. Basic Currency Futures Relationships13Open interest in currency futures contractsa)Tends to be greatest for the near-term contractsb)Tends to be greatest for the longer-term contractsc)Typically decreases with the term to maturity of most futures contractsd)a) and c)Answer: a)14The “open interest” shown in currency futures quotations is:a)the total number of people indicating interest in buying the contracts in the nearfutureb)the total number of people indicating interest in selling the contracts in the nearfuturec)the total number of people indicating interest in buying or selling the contracts inthe near futured)the total number of long or short contracts outstanding for the particular deliverymonthAnswer: d)Eurodollar Interest Rate Futures Contracts15The most widely used futures contract for hedging short-term U.S. dollar interest rate risk is:a)The Eurodollar contractb)The Euroyen contractc)The EURIBOR contractd)None of the aboveAnswer: a)16Consider 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 marketb)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 Answer: b)17A DECREASE in the implied three-month LIBOR yield causes Eurodollar futurespricea)To increase b)To decreasec)There is no direct or indirect relationship d)None of the above Answer: a)Options Contracts: Some Preliminaries18If you think that the dollar is going to appreciate against the euroa)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 Answer: c)19From the perspective of the writer of a put option written on €62,500. If the strikeprice is $1.25/€, and the option premium is $1,875, at what exchange rate do you start to lose money?a)$1.22/€b)$1.25/€c)$1.28/€d)None of the above Answer: a)Rationale: Per euro, the option premium is. Since it’s a put option, $1,875$0.03/€€62,500the writer loses money when the price goes down, thus he breaks even at $1.25/€ – $0.03/€ = $1.22/€20A European option is different from an American option in that a)One is traded in Europe and one in traded in the United Statesb)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 isset at the average price of the underlying asset during the life of the option.Answer: b)卷调整试验；通电检查所21An “option” is:a) a contract giving the seller (writer) the right, but not the obligation, to buy or sella given quantity of an asset at a specified price at some time in the futureb) a contract giving the owner (buyer) the right, but not the obligation, to buy or sella given quantity of an asset at a specified price at some time in the futurec)not a derivative, nor a contingent claim, securityd)unlike a futures or forward contractAnswer: b)22An 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 optiona)(i), (ii), and (iii)b)(i), (ii), and (iv)c)(i), (iv), and (v)d)(ii) and (iii)Answer: c)Currency Options Markets23Most exchange traded currency optionsa)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 resettlementAnswer: c)24The volume of OTC currency options trading isa)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 theircustomersd)None of the aboveAnswer: b)25In the CURRENCY TRADING section of The Wall Street Journal, the following appeared under the heading OPTIONS:Philadelphia ExchangePutsSwiss Franc69.3362,500 Swiss Francs-cents per unit st68 May 12 0.3069 May 50 0.50Which combination of the following statements are true?(i)- The time values of the 68 May and 69 May put options are respectively .30cents 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)Answer: a)Rationale: Premium - Intrinsic Value = Time Value68 May Put: 0.30 – Max[68 - 69.33, 0] = 0.30 cents69 May Put: 0.50 – Max[69 - 69.33, 0] = 0.50 centsCurrency Futures Options26With currency futures options the underlying asset isa)Foreign currencyb) A call or put option written on foreign currencyc) A futures contract on the foreign currencyd)None of the aboveAnswer: c)27Exercise of a currency futures option results ina) A long futures position for the call buyer or put writerb) A short futures position for the call buyer or put writerc) A long futures position for the put buyer or call writerd) A short futures position for the call buyer or put buyerAnswer: a)28A currency futures option amounts to a derivative on a derivative. Why wouldsomething like that exist?a)For some assets, the futures contract can have lower transactions costs and greaterliquidity than the underlying assetb)Tax consequences matter as well, and for some users an option contract on afuture is more tax efficientc)Transactions costs and liquidity.d)All of the aboveAnswer: d)Basic Option-Pricing Relationships at Expiration29The current spot exchange rate is $1.25 = €1.00 and the three-month forward rate is $1.30 = €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)$1.30 = €1.00b)$1.25 = €1.00c)$1.25 × (1+i$)3/12= €1.00 × (1+i€)3/12d)none of the aboveAnswer: b)30The current spot exchange rate is $1.25 = €1.00 and the three-month forward rate is $1.30 = €1.00. Consider a three-month American call option on €62,500 with a strike price of $1.20 = €1.00. Immediate exercise of this option will generate a profit ofa)$6,125b)$6,125/(1+i$)3/12c)negative profit, so exercise would not occurd)$3,125Answer: d)Rationale: with early exercise, you can pay $1.20 for something worth $1.25. So you make a nickel. Make a nickel 62,500 times and you’ve made $3,125.31The current spot exchange rate is $1.25 = €1.00 and the three-month forward rate is $1.30 = €1.00. Consider a three-month American call option on €62,500 with a strike price of $1.20 = €1.00. If you pay an option premium of $5,000 to buy this call, at what exchange rate will you break-even?a)$1.28 = €1.00b)$1.32 = €1.00c)$1.20 = €1.00d)$1.38 = €1.00Answer: a)Rationale: A $5,000 option premium on €62,500 amounts to $0.08 per euro. With a strike price of $1.20 = €1.00 the exchange rate has to go to $1.28 = €1.00 for you to break even.shown at right. The option is a three-month American call option on€62,500 with a strike price of $1.20 =€1.00 and an option premium of$3,125. What are the values of A, B,and C, respectively?a) A = –$3,125 (or –$.05depending on your scale);B = $1.20;C = $1.25b) A = –€3,750 (or –€.06depending on your scale);B = $1.20;C = $1.25c) A = –$.05; B = $1.25; C =$1.30d)none of the aboveAnswer: a)33Which of the lines is a graph of theprofit at maturity of writing a calloption on €62,500 with a strike priceof $1.20 = €1.00 and an optionpremium of $3,125?a)Ab)Bc)Cd)DAnswer: b)American Option-Pricing Relationships34The current spot exchange rate is $1.25 = €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 $1.20 = €1.00. What is the least that this option should sell for?a)$0.05×62,500 = $3,125b)$3,125/1.02 = $3,063.73c)$0.00d)none of the aboveAnswer: a)35Which of the follow options strategies are consistent in their belief about the futurebehavior 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 Answer: c)36American call and put premiumsa)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 Answer: a)37Which 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 Answer: d)European Option-Pricing Relationships38Assume 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 $€().01.5$1.28$1.2864r r T T t F S e e -⨯===Eurodollar rate is 4%. The minimum price that a six-month American call option with a striking price of $1.25 should sell for in a rational market is:a)0 cents b) 3.47 cents c) 3.55 cents d) 3 centsAnswer: c) footnote 3$€().01.5$1.28$1.2864r r T T t F S e e -⨯===Rationale: C a ≥ Max[(S t - E ), (F - E )/(1+r $), 0],C a ≥ Max[($1.28 – $1.25), ($1.2864 – $1.25)/1.05½ , 0] = 3.55 cents 11 You might consider partial credit for answer b), it is found byC a ≥ Max[($1.28 – $1.25), ($1.2864 – $1.25)/1.05 , 0] = 3.47 cents39For European options, what of the effect of an increase in S t?a)Decrease the value of calls and puts ceteris paribusb)Increase the value of calls and puts ceteris paribusc)Decrease the value of calls, increase the value of puts ceteris paribusd)Increase the value of calls, decrease the value of puts ceteris paribusAnswer: d)the graph area)Time value and intrinsic valueb)Intrinsic value and time valuec)In-the-money and out-of-the moneyd)None of the aboveAnswer: b)Rationale: Exhibit 7.1041a)Decrease the value of calls and puts ceteris paribusb)Increase the value of calls and puts ceteris paribusc)Decrease the value of calls, increase the value of puts ceteris paribusd)Increase the value of calls, decrease the value of puts ceteris paribusAnswer: c)42For European currency options written on euro with a strike price in dollars, what of the effect of an increase in r$ relative to r€?a)Decrease the value of calls and puts ceteris paribusb)Increase the value of calls and puts ceteris paribusc)Decrease the value of calls, increase the value of puts ceteris paribusd)Increase the value of calls, decrease the value of puts ceteris paribusAnswer: d)43For 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 paribusb)Increase the value of calls and puts ceteris paribusc)Decrease the value of calls, increase the value of puts ceteris paribusd)Increase the value of calls, decrease the value of puts ceteris paribusAnswer: d)44For European currency options written on euro with a strike price in dollars, what ofthe effect of an increase r €?a)Decrease the value of calls and puts ceteris paribus b)Increase the value of calls and puts ceteris paribusc)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 Answer: c)Binomial Option-Pricing Model45The hedge ratioa)Is the size of the long (short) position the investor must have in the underlyingasset 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)0()uT dT C C S u d --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.Answer: d)Rationale: 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).46Find the value of a call option written on €100 with a strike price of $1.00 = €1.00. In one period there are only 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)$9.5238b)$0.0952c)$0d)$3.1746Answer: a)Rationale:Equation 9.10: 00$21$15$0(1)33max(,)$9.521 1.05uT dt qC q C C S E r ⨯+⨯+-=-==+European Option-Pricing Formula47Find the input d 1 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)d 1 = 0.103915b)d 1 = 2.9871c)d 1 = –0.0283d)none of the above Answer: a)Rationale: $€()$1.256266r r T T t F S e -==10.103915d ===48Find the Black-Scholes price of a six-month call option written on €100,000 with astrike 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)C e = $0.63577b)C e = $0.0998c)C e = $1.6331d)none of the above Answer: a)Rationale: $€()$1.256266r r T T t F S e -==$€12120120.1039150.028255()0.541382()0.51127()()0.63577r T r T t d d N d N d C S e N d Ee N d --=======-=NOTE THAT YOU WILL HAVE TO PROVIDE YOUR STUDENTS WITH A TABLE OF THE NORMAL DISTRIBUTION.49The Black-Scholes option pricing formulaa)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 timeto flog their calculator for five minutes on the trading floor.d)None of the above.Answer: a)Empirical Tests of Currency Options50Empirical tests of the Black-Scholes option pricing formulaa)Shows that binomial option pricing is used widely in practice, especially byinternational 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)Answer: d)。

CHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGESUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTERQUESTIONS AND PROBLEMSQUESTIONS1. 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 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 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, desires 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 transactions will occur. Thus, they are generally closed out in a reversing trade. In fact, the commission thatbuyers 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 cont racts 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 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, 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 t > E (E > S t) is referred to as trading in-the-money. If S t E the option is trading at-the-money. If S t< E (E < S t) the call (put) option is trading out-of-the-money.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 t, E, r i, r$, T andσ. When all else remains the same, the price of a European FX call (put) option will increase:1. the larger (smaller) is S,2. the smaller (larger) is E,3. the smaller (larger) is r i,4. the larger (smaller) is r$,5. the larger (smaller) r$ is relative to r i, and6. the greater is σ.When r$ and r i 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 r i, a European FX call will increase in price, but the put premium will decrease, when the option term-to-maturity increases. The opposite is true when r i is very much greater than r$. For American FX options 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.PROBLEMS1. 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 day s’ 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.Solution: $1,700 + [($1.3140 - $1.3126) + ($1.3126 - $1.3133)+ ($1.3133 - $1.3049)] x EUR125,000 = $2,837.50,where EUR125,000 is the contractual size of one EUR contract.2. Do problem 1 again assuming you have a long position in the futures contract.Solution: $1,700 + [($1.3126 - $1.3140) + ($1.3133 - $1.3126) + ($1.3049 - $1.3133)] x EUR125,000 = $562.50,where EUR125,000 is the contractual size of one EUR contract.With only $562.50 in your performance bond account, you would experience a margin call requesting that additional funds be added to your performance bond account to bring the balance back up to the initial performance bond level.3. Using the quotations in Exhibit 7.3, calculate the face value of the open interest in the June 2005 Swiss franc futures contract.Solution: 2,101 contracts x SF125,000 = SF262,625,000.where SF125,000 is the contractual size of one SF contract.4. Using the quotations in Exhibit 7.3, note that the June 2005 Mexican peso futures contract has a price of $0.08845. You believe the spot price in June will be $0.09500. 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?Solution: If you expect the Mexican peso to rise from $0.08845 to $0.09500, you would take a long position in futures since the futures price of $0.08845 is less than your expected spot price.Your anticipated profit from a long position in three contracts is: 3 x ($0.09500 - $0.08845) x MP500,000 = $9,825.00, where MP500,000 is the contractual size of one MP contract.If the futures price is an unbiased predictor of the expected spot price, the expected spot price is the futures price of $0.08845/MP. If this spot price materializes, you will not have any profits or losses from your short position in three futures contracts: 3 x ($0.08845 - $0.08845) x MP500,000 = 0.5. Do problem 4 again assuming you believe the June 2005 spot price will be $0.08500.Solution: If you expect the Mexican peso to depreciate from $0.08845 to $0.07500, you would take a short position in futures since the futures price of $0.08845 is greater than your expected spot price.Your anticipated profit from a short position in three contracts is: 3 x ($0.08845 - $0.07500) x MP500,000 = $20,175.00.If the futures price is an unbiased predictor of the future spot price and this price materializes, you will not profit or lose from your long futures position.6. George Johnson is considering a possible six-month $100 million LIBOR-based, floating-rate bank loan to fund a project at terms shown in the table below. Johnson fears a possible rise in the LIBOR rate by December and wants to use the December Eurodollar futures contract to hedge this risk. The contract expires December 20, 1999, has a US$ 1 million contract size, and a discount yield of7.3 percent.Johnson 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 in March.Loan TermsSeptember 20, 1999 December 20, 1999 March 20, 2000 • Borrow $100 million at • Pay interest for first three • Pay back principal September 20 LIBOR + 200 months plus interestbasis points (bps) • Roll loan over at• September 20 LIBOR = 7% December 20 LIBOR +200 bpsLoan First loan payment (9%) Second paymentinitiated and futures contract expires and principal↓↓↓•••9/20/99 12/20/99 3/20/00a. Formulate Johnson’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.Johnson is considering a 12-month loan as an alternative. This approach will result in two additional uncertain cash flows, as follows:Loan First Second Third Fourth payment initiated payment (9%) payment payment and principal ↓↓↓↓↓•••••9/20/99 12/20/99 3/20/00 6/20/00 9/20/00 b. Describe the strip hedge that Johnson could use and explain how it hedges the 12-month loan (specify number of contracts). No calculations are needed.CFA Guideline Answera. The basis point value (BPV) of a Eurodollar futures contract can be 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)= $25The number of contract, N, can be found by:N = (BPV spot) / (BPV futures)= ($2,500) / ($25)= 100ORN = (value of spot position) / (face value of each futures contract)= ($100 million) / ($1 million)= 100ORN = (value of spot position) / (value of futures position)= ($100,000,000) / ($981,750)where value of futures position = $1,000,000 x [1 – (0.073 / 4)]102 contractsTherefore on September 20, Johnson 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:= ($25 per basis point per contract) x 50 bp x 100 contracts= $125,000.However, the cash flow on the floating rate liability is:= -0.098 x ($100,000,000 / 4)= - $2,450,000.Combining the cash flow from the hedge with the cash flow from the loan results in a net outflow of $2,325,000, which translates into an annual rate of 9.3 percent:= ($2,325,000 x 4) / $100,000,000 = 0.093This is precisely the implied borrowing rate that Johnson locked in on September 20. Regardless of the LIBOR rate on December 20, the net cash outflow will be $2,325,000, which translates into an annualized rate of 9.3 percent. Consequently, the floating rate liability has been converted to a fixed rate liability in the sense that the interest rate uncertainty associated with the March 20 payment (using the December 20 contract) has been removed as of September 20.b. In a strip hedge, Johnson would sell 100 December futures (for the March payment), 100 March futures (for the June payment), and 100 June futures (for the September payment). The objective is to hedge each interest rate payment separately using the appropriate number of contracts. The problem is the same as in Part A except here three cash flows are subject to rising rates and a strip of futures is used to hedge this interest rate risk. This problem is simplified somewhat because the cash flow mismatch between thefutures and the loan payment is ignored. Therefore, in order to hedge each cash flow, Johnson simply sells 100 contracts for each payment. The strip hedge transforms the floating rate loan into a strip of fixed rate payments. As was done in Part A, the fixed rates are found by adding 200 basis points to the implied forward LIBOR rate indicated by the discount yield of the three different Eurodollar futures contracts. The fixed payments will be equal when the LIBOR term structure is flat for the first year.7. Jacob Bower has a liability that:• has a principal balance of $100 million on June 30, 1998,• accrues interest quarterly starting on June 30, 1998,• pays interest quarterly,• has a one-year term to maturity, and• calculates interest due based on 90-day LIBOR (the London Interbank OfferedRate).Bower wishes to hedge his remaining interest payments against changes in interest rates.Bower has correctly calculated that he needs to sell (short) 300 Eurodollar futures contracts to accomplish the hedge. He is considering the alternative hedging strategies outlined in the following table.Initial Position (6/30/98) in90-Day LIBOR Eurodollar ContractsStrategy A Strategy BContract Month (contracts) (contracts)September 1998 300 100December 1998 0 100March 1999 0 100a. Explain why strategy B is a more effective hedge than strategy A when the yield curveundergoes an instantaneous nonparallel shift.b. Discuss an interest rate scenario in which strategy A would be superior to strategy B.CFA Guideline Answera. Strategy B’s SuperiorityStrategy B is a strip hedge that is constructed by selling (shorting) 100 futures contracts maturing in each of the next three quarters. With the strip hedge in place, each quarter of the coming year is hedged against shifts in interest rates for that quarter. The reason Strategy B will be a more effective hedge than Strategy A for Jacob Bower is that Strategy B is likely to work well whether a parallel shift or a nonparallel shift occurs over the one-year term of Bower’s liability. That is, regardless of what happens to the term structure, Strategy B structures the futures hedge so that the rates reflected by the Eurodollar futures cash price match the applicable rates for the underlying liability-the 90day LIBOR-based rate on Bower’s liability. The same is not true for Strategy A. Because Jacob Bower’s liability carries a floating interest rate that resets quarterly, he needs a strategy that provides a series of three-month hedges. Strategy A will need to be restructured when the three-month September contract expires. In particular, if the yield curve twists upward (futures yields rise more for distant expirations than for near expirations), Strategy A will produce inferior hedge results.b. Scenario in Which Strategy A is SuperiorStrategy A is a stack hedge strategy that initially involves selling (shorting) 300 September contracts. Strategy A is rarely better than Strategy B as a hedging or risk-reduction strategy. Only from the perspective of favorable cash flows is Strategy A better than Strategy B. Such cash flows occur only in certain interest rate scenarios. For example Strategy A will work as well as Strategy B for Bower’s liability if interest rates (instantaneously) change in parallel fashion. Another interest rate scenario where Strategy A outperforms Strategy B is one in which the yield curve rises but with a twist so that futures yields rise more for near expirations than for distant expirations. Upon expiration of the September contract, Bower will have to roll out his hedge by selling 200 December contracts to hedge the remaining interest payments. This action will have the effect that the cash flow from Strategy A will be larger than the cash flow from Strategy B because the appreciation on the 300 short September futures contracts will be larger than the cumulative appreciation in the 300 contracts shorted in Strategy B (i.e., 100 September, 100 December, and 100 March). Consequently, the cash flow from Strategy A will more than offset the increase in the interest payment on the liability, whereas the cash flow from Strategy B will exactly offset the increase in the interest payment on the liability.8. Use the quotations in Exhibit 7.7 to calculate the intrinsic value and the time value of the 97 September Japanese yen American call and put options.Solution: Premium - Intrinsic Value = Time Value97 Sep Call 2.08 - Max[95.80 – 97.00 = - 1.20, 0] = 2.08 cents per 100 yen97 Sep Put 2.47 - Max[97.00 – 95.80 = 1.20, 0] = 1.27 cents per 100 yen9. 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.C a≥Max[(70 - 68), (69.50 - 68)/(1.0175), 0]≥Max[ 2, 1.47, 0] = 2 cents10. Do problem 9 again assuming an American put option instead of a call option.Solution: P a≥Max[(68 - 70), (68 - 69.50)/(1.0175), 0]≥Max[ -2, -1.47, 0] = 0 cents11. 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.Solution:d1 = [ln(69.50/68) + .5(.142)2(.50)]/(.142)√.50 = .2675d2 = d1 - .142√.50 = .2765 - .1004 = .1671N(d1) = .6055N(d2) = .5664N(-d1) = .3945N(-d2) = .4336C e = [69.50(.6055) - 68(.5664)]e-(.035)(.50) = 3.51 centsP e = [68(.4336) - 69.50(.3945)]e-(.035)(.50) = 2.03 cents12. 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.Solution: The spot rate at T will be either 77.39¢ = 70.00¢(1.1056) or 63.32¢ = 70.00¢(.9045), where u = e.142 .50 = 1.1056 and d = 1/u = .9045. At the exercise price of E = 68, the option will only be exercised at time T if the Swiss franc appreciates; its exercise value would be C uT= 9.39¢ = 77.39¢ - 68. If the Swiss franc depreciates it would not be rational to exercise the option; its value would be C dT = 0.The hedge ratio is h = (9.39 – 0)/(77.39 – 63.32) = .6674.Thus, the call premium is:C0 = Max{[69.50(.6674) – 68((70/68)(.6674 – 1) +1)]/(1.0175), 70 – 68}= Max[1.64, 2] = 2 cents per SF.MINI CASE: THE OPTIONS SPECULATORA 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:1.-2. (5 x ¥6,250,000) x [(100 - 96) - 1.35]/10000 = $8,281.25.3. Since the option expires out-of-the-money, the speculator will let the option expire worthless. He will only lose the option premium.4. S T = E + C = 96 + 1.35 = 97.35 cents per 100 yen.。