《期权期货习题》PPT课件.ppt

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1、Future Option and other derivatives,exercises,1.Whats the difference between entering into a long forward contact when the forward price is$50 and taking a long position in a call with a strike price of$50?,2.An investor enters into a short forward contract to sell 100,000British pounds for US dolla

2、rs at an exchange rate of 1.5000US dollars per pound.How much does the investor gain or lose if the exchange rate at the end of the contract is 1.4900 and 1.5200?,3.You would like to speculate on a rise in the price of a certain stock.The current stock price is$29,and a 3-month call with a strike pr

3、ice of$30 costs$2.90.You have$5,800 to invest.Identify two alternative investment strategies,one in the stock and the other in an option on the stock.What are the potential gains and losses from each?,4.Suppose that a March call option to buy a share for$50 costs$2.5 and is held until March.Under wh

4、at circumstances will the holder of the option make a profit?Under what circumstances will the option be exercised?Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.,5.Explain why a forward contract can be used for eith

5、er speculation or hedging.,6.Suppose that a June put option to sell a share for$60 costs$4 and is held until June.Under what circumstances will the option be exercised?Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.

6、,7.It is May and a trader writes a September call option with a strike price of$20.The stock price is$18 and the option price is$2.Describe the traders cash flows if the option is held until September and the stock price is$25 at that time.,8.A trader writes a December put option with a strike price

7、 of$30.The price of the option is$4.Under what circumstances does the trader make a gain?,9.A company knows that it is due to receive a certain amount of a foreign currency in 4 months.What type of option contract is appropriate for hedging?,10.The price of gold is currently$500 per ounce.The forwar

8、d price for delivery in 1 year is$700.An arbitrageur can borrow money at 10%per annum.What should the arbitrageur do?Assume that the cost of storing gold is zero and that gold provides no income.,11.Suppose that you enter into a short futures contract to sell July silver for$5.20 per ounce on the Ne

9、w York Commodity Exchange.The size of the contract is 5,000 ounces.The initial margin is$4,000,and the maintenance margin is$3,000.What change in futures price will lead to a margin call?What happens if you do not meet the margin call?,12.An investor enters into two long July futures contracts on or

10、ange juice.Each contract is for the delivery of 15,000 pounds.The current futures price is 160 cents per pound,the initial margin is$6,000 per contract,and the maintenance margin is$4,500 per contract.What price change would lead to a margin call?Under what circumstances could$2,000 be withdrawn fro

11、m the margin account?,13.At the end of one day a clearinghouse member is long 100 contracts,and the settlement price is$50,000 per contract.The original margin is$2,000 per contract.On the following day the member becomes responsible for clearing an additional 20 long contracts,entered into at a pri

12、ce of$51,000 per contract.The settlement price at the end of this day is$50,200.How much does the member have to add to its margin account with the exchange clearinghouse?,14.Describe the profit from the following portfolio:a long forward contract on an asset and a long European put option on the as

13、set with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up.,15.The current Price of a stock is$94，and3-month European call options with a strike price of$95 currently sell for$4.70.An investor who feels th

14、at the Price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options(=20 contracts).Both strategies involve an investment of$9,400.What advice would you give?How high does the stock price have to rise for the option strategy to be more profitable?,16.Su

15、ppose that the standard deviation of quarterly changes in the prices of a commodity is$0.65,the standard deviation of quarterly changes in a futures price on the commodity is$0.81,and the coefficient of correlation between the two changes is 0.8.What is the optimal hedge ratio for a 3-month contract

16、?What does it mean?,17.“If the minimum variance hedge ratio is calculated as 1.0,the hedge must be perfect.”Is this statement true?Explain your answer.,18.The standard deviation of monthly changes in the spot price of live cattle is(in cents per pound)1.2.The standard deviation of monthly changes in

17、 the futures price of live cattle for the closest contract is 1.4.The correlation between the futures price changes and the spot price changes is 0.7.It is now October 15.A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15.The producer wants to use the December li

18、ve cattle futures contracts to hedge its risk.Each contract is for the delivery of 40,000 pounds of cattle.What strategy should the beef producer follow?,19.A long forward contract on a non-dividend-paying stock was entered into some time ago.It currently has 6 months to maturity.The risk-free rate

19、of interest(with continuous compounding)is 10%per annum,the stock price is$25,and the delivery price is$24.,20.Consider a 3-month futures contract on the S&P500.Suppose that the stocks underlying the index provide a dividend yield of 1%per annum,that the current value of the index is 800,and that th

20、e continuously compounded risk-free interest rate is 6%per annum.,21.Suppose that you enter into a 6-month forward contract on a non-dividend-paying stock when the stock price is$30and the risk-free interest rate(with continuous compounding)is 12%per annum.What is the forward price?,22.A 1-year long

21、 forward contract on a non-dividend-paying stock is entered into when the stock Price is$40 and the risk-free rate of interest is 10%per annum with continuous compounding.(a)What are the forward price and the initial value of the forward contract?(b)Six months later,the price of the stock is$45 and

22、the risk-free interest rate is still 10%What are the forward price and the value of the forward contract?,23.Suppose that the risk-free interest rate is 10%per annum with continuous compounding and that the dividend yield on a stock index is 4%per annum.The index is standing at 400，and the futures p

23、rice for a contract deliverable in four months is 405.What arbitrage opportunities does this create?,24.Assume that the risk-free interest rate is 9%per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year.In February，May，August，and November，divid

24、ends are paid at a rate of 5%per annum.In other months，dividends are paid at a rate of 2%per annum.Suppose that the value of the index on July 31，2006，is 300.What is the futures price for a contract deliverable on December 31，2006?,25.The 2-month interest rates in Switzerland and the United States a

25、re,respectively,3%and 8%per annum with continuous compounding.The spot price of the Swiss franc is$0.6500.The futures price for a contract deliverabe in 2 months is$0.6600.What arbitrage opportunities does this create?,26.The spot price of silver is$9 per ounce.The-storage costs are$0.24 per ounce;p

26、er year payable quarterly in advance.Assuming that interest rates are 10%per annum for all maturities,calculate the futures price of silver for delivery in 9 months.,27.Suppose that the Treasury bond futures price is 101-12.Which of the following four bonds is cheapest to deliver?,28.The price of a

27、90-day Treasury bill is quoted as 10.00.What continuously compounded return does an investor earn on the Treasury bill for the 90-day period?,29.It is May 5，2005.The quoted price of a government bond with a 12%coupon that matures on July 27，2011，is 110-17.What is the cash price?,30.Suppose that the

28、9-month LIBOR interest rate is 8%per annum and the 6-month LIBOR interest rate is 7.5%per annum(both with actual/365 and continuous compounding).Estimate the 3-month Eurodollar futures price quote for a contract maturing in 6 months.,31.Suppose that,in a Treasury bond futures contract,it is known th

29、at the cheapest-to-deliver bond will be a 12%coupon bond with a conversion factor of 1.4000.Suppose also that it is known that delivery will take place in 270days.Coupons are payable semiannually on the bond.As illustrated in Figure,the last coupon date was 60days ago,the next coupon date is in 122d

30、ays,and the coupon date thereafter is in 305days.The term structure is flat,and the rate of interest(with continuous compounding)is 10%per annum.Assume the current quoted bond price the proportion of the next coupon payment that accrues to the holder.,Figure.Time chart for Example 31,Coupon Current

31、Coupon Maturity CouponPayment time payment of payment futures contract,60days,122days,148days,35days,A number of factors determine the cheapest-to-deliver bond.When bond yields are in excess 6%,the conversion factor system tends to favor the delivery of bonds.,32Its July 30,2005.The cheapest-to-deli

32、ver bond in a September 2005 Treasury bond futures contract is a 13%coupon bond,and delivery is expected to be made on September 30,2005.Coupon payments on the bond are made on February 4 and August 4 each year.The term structure is flat,and the rate of interest with semiannual compounding is 12%per

33、 annum.The conversion factor for the bond is 1.5.The current quoted bond price is$110.Calculate the quoted futures price for the contract.,33.Assume that a bank can borrow or lend money at the same interest rate in the LIBOR market.The 90-day rate is 10%per annum,and the 180-day rate is 10.2%per ann

34、um both expressed with continuous compounding and actual/actual day count.The Eurodollar futures price for a contract maturing in 90days is quoted as 89.5.What arbitrage opportunities are open to the bank?,34.It is January 30，You are managing a bond portfolio worth$6 million.The duration of the port

35、folio in 6 months will be 8.2 years.The September Treasure bond futures price is currently 108-15，and the cheapest-to-deliver bond will have a duration of 7.6 years in September.How should you hedge against changes in interest rates over the next 6 months?,35.Explain why brokers require margins when

36、 clients write options but not when they buy options.,36.A company declares a 2-to-1 stock split.Explain how the terms change for a call option with a strike price of$60.,37.Consider an exchange-traded call option contract to buy 500 shares with a strike price of$40 and maturity in 4 months.Explain

37、how the terms of the option contract change when there is:1)a 10%stock dividend;2)a 10%cash dividend;3)a 4-to-1 stock split.,38.A United States investor writes five naked call option contracts.The option price is$3.50,the strike price is$60.00,and the stock price is$57.00.What is the initial margin

38、requirement?,39.An investor writes four naked call option contracts on a stock.The option price is$5,the strike price is$40,and the stock price is$38.Because the option is$2 out of the money.If the option had been a put,it would be$2 in the money and the margin requirement would be?,40.What is a low

39、er bound for the price of a 4-month call option on a non-dividend-paying stock when the stock price is$28,the strike price is$25,and the risk-free interest rate is 8%per annum?What is a lower bound for the price of a 1-month European put option on a non-dividend-paying stock when the stock price is$

40、12,the strike price is$15,and the risk-free interest rate is 6%per annum?,41.A 1-month European put option on a non-dividend-paying stock is currently selling for$2.5.The stock price is$47,the strike price is$50,and the risk-free interest rate is 6%per annum.What opportunities are there for an arbit

41、rageur?,42.A European call option and put option on a stock both have a strike price of$20 and an expiration date in 3 months.Both sell for$3.The risk-free interest rate is 10%per annum,the current stock price is$19,and a$1 dividend is in 1 month.Identify the arbitrage opportunity open to a trader.,

42、43.The price of a European call that expires in 6months and has a strike price of$30 is$2.The underlying stock price is$29,and a dividend of$0.50 is expected in 2 months and again in 5months.The term structure is flat,with all risk-free interest rates being 10%.What is the price of a European put op

43、tion that expires in 6months and has a strike price of$30?Explain carefully the arbitrage opportunities in problem 8.4 if the European put price is$3.,44.Suppose that are the prices of European call options with strike prices respectively,where and All options have the same maturity.Show that What i

44、s the result corresponding to that in Problem 8.5 for European put options?,45.The price of an American call on a non-dividend-paying stock is$4.The stock price is$31,the strike price is$30,and the expiration date is in 3 months.The risk-free interest rate is 8%.Derive upper and lower bounds for the

45、 price of an American put on the same stock with the same strike price and expiration date.Explain carefully the arbitrage opportunities in Problem45 if the American put price is greater than the calculated upper bound.,46.Suppose that put option on a stock with strike prices$30 and$35 cost$4 and$7，

46、respectively.How can the options be used to create(a)a bull spread and(b)a bear spread?Construct a table that shows the profit and payoff for both spreads.,47.Use put-call parity to show that the cost of a butterfly spread created from European puts is identical to the cost of a butterfly spread cre

47、ated from European calls.,48.Call options on a stock are available with strike prices of$15，$17.5，and$20，and expiration dates in 3 months.Their prices are$4，$2，and$0.5，respectively.Explain how the options can be used to create a butterfly spread.Construct a table showing how profit varies with stock

48、 price for the butterfly spread.,49.A call with a strike price of$60 costs$6.A put with the same strike price and expiration date costs$4.Construct a table that shows the profit from a straddle.For what range of stock prices would the straddle lead to a loss?,50.A stock price is currently$40.It is k

49、nown that at the end of 1 month it will be either$42 or$38.The risk-free interest rate is 8%per annum with continuous compounding.What is the value of a 1-month European call option with a strike price of$39?,51.A stock price is currently$50.It is known that at the end of 6months it will be either$4

50、5or$55.The risk-free interest rate is 10%per annum with continuous compounding.What is the value of a 6-month European put option with a strike price of$50?,52.A stock price is currently$100.Over each of the next two 6-month periods it is expected to go up by 10%or down by 10%.The risk-free interest