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options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

"If there is no basis risk, the minimum variance hedge ratio is always 1.0." Is this statement true?Explain your answer.
"If the minimum variance hedge ratio is calculated as 1.0, the hedge must be perfect." Is this statement true? Explain your answer.
How does the decision affect the way in which the hedge is implemented and the result?
Suppose that in Example 4.2 of Section 4.3 the company decides to use a hedge ratio of
Imagine you are the treasurer of a Japanese company exporting electronic equipment to the United States. Discuss how you would design a foreign exchange hedging strategy and the arguments you would
Explain why a short hedger's position improves when the basis strengthens unexpectedly and worsens when the basis weakens unexpectedly.
Does a perfect hedge always succeed in locking in the current spot price of an asset for a future transaction? Explain your answer.
In the Chicago JJoard of Trade's corn futures contract, the following delivery months are available: March, May, July, September, and December. State the contract that should be used for hedging when
It would like to use futures contracts on the S&P 500 to hedge its risk. The index is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that
A company has a $20 million portfolio with a beta of
What is the optimal hedge ratio for a three-month contract? What does it mean?
Suppose 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 S0.81, and the
Give three reasons that the treasurer of a company might not hedge the company's exposure to a particular risk.
Under what circumstances does a minimum variance hedge portfolio lead to no hedging at all?
Explain what is meant by a perfect hedge. Does a perfect hedge always lead to a better outcome than an imperfect hedge? Explain your answer.
Explain what is meant by basis risk when futures contracts are used for hedging.
Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?
A company enters into a forward contract with a bank to sell a foreign currency for K\ at time Tj.The exchange rate at time 7\ proves to be S\ (> K]). The company asks the bank if it can roll the
A foreign exchange trader working for a bank enters into a long forward contract to buy one million pounds sterling at an exchange rate of 1.6000 in three months. At the same time, another trader on
A company that is uncertain about the exact date when it will pay or receive a foreign currency may try to negotiate with its bank a forward contract that specifies a period during which delivery can
A bank offers a corporate client a choice between borrowing cash at 11% per annum and borrowing gold at 2% per annum. (If gold is borrowed, interest must be repaid in gold. Thus, 100 ounces borrowed
A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all
The Value Line Index is designed to reflect changes in the value of a portfolio of over 1,600 equally weighted stocks. Prior to March 9, 1988, the change in the index from one day to the next was
Show that equation (3.7) is true by considering an investment in the asset combined with a short position in a futures contract. Assume that all income from the asset is reinvested in the asset. Use
Show that the growth rate in an index futures price equals the excess return of the index over the risk-free rate. Assume that the risk-free interest rate and the dividend yield are constant.
When a known future cash outflow in a foreign currency is hedged by a company using a forward contract, there is no foreign exchange risk. When it is hedged using futures contracts, the
Suppose that Fl and F2 are two futures contracts on the same commodity with times to maturity, t\ and t2, where t2 > t\. Prove that F2
The current price of silver is $9 per ounce. The storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, calculate
The two-month interest rates in Switzerland and the United States are 3% and 8% per annum, respectively, with continuous compounding. The spot price of the Swiss franc is $0.6500. The futures price
Estimate the difference between short-term interest rates in Mexico and the United States on March 15, 2001, from the information in Table 3.3.
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 price
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,
The risk-free rate of interest is 7% per annum with continuous compounding, and the dividend yield on a stock index is 3.2% per annum. The current value of the index is 150. What is the sixmonth
A one-year long 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
A stock index currently stands at 350. The risk-free interest rate is 8% per annum (with continuous compounding) and the dividend yield on the index is 4% per annum. What should the futures price for
Suppose that you enter into a six-month forward contract on a non-dividend-paying stock when the stock price is $30 and the risk-free interest rate (with continuous compounding) is 12% per annum.
A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?
The author's Web page www.rotman.utoronto.ca/~hull contains daily closing prices for the December 2001 crude oil futures contract and the December 2001 gold futures contract. (Both contracts are
Suppose that corn can be stored for 20 cents per bushel per year and the risk-free interest rate is 5% per year. How could you make money in the corn market on March 15, 2001, by trading the May 2001
Explain carefully what is meant by the expected price of a commodity on a particular future date.
Suppose that on March 15, 2001, speculators tended to be short Sugar-World futures and hedgers tended to be long Sugar-World futures. What does the Keynes and Hicks argument imply about the expected
A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead
It is now July 2002. A mining company has just discovered a small deposit of gold. It will take six months to construct the mine. The gold will then be extracted on a more or less continuous basis
A cattle farmer expects to have 120,000 pounds of live cattle to sell in three months. The live-cattle futures contract on the Chicago Mercantile Exchange is for the delivery of 40,000 pounds of
Suppose that on October 24, 2002, you take a short position in an April 2003 live-cattle futures contract. You close out your position on January 21, 2003. The futures price (per pound) is 61.20
"When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one." Explain this statement.
What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?
Consider each of the following sections separately: grains and oilseeds, livestock and meat, food and fiber, and metals and petroleum.
Identify the contracts with the highest open interest in Table
The forward price on the Swiss franc for delivery in 45 days is quoted as 1.8204. The futures price for a contract that will be delivered in 45 days is 0.5479. Explain these two quotes. Which is more
On July 1, 2002, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2003. On September 1, 2002, it enters into a forward contract to sell 10 million Japanese yen on
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
Show that if the futures price of a commodity is greater than the spot price during the delivery period there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures price is
An investor enters into two long futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin
Explain how margins protect investors against the possibility of default.
The party with a short position in a futures contract sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on.
Suppose that in September 2002 you take a long position in a contract on May 2003 crude oil futures. You close out your position in March 2003. The futures price (per barrel) is $18.30 when you enter
Suppose that you enter into a short futures contract to sell July silver for $5.20 per ounce on the New York Commodity Exchange. The size of the contract is 5,000 ounces. The initial margin is$4,000,
What is the difference between a local and a commission broker!
Describe how foreign currency options can be used for hedging in the situation considered in Section 1.6 so that (a) ImportCo is guaranteed that its exchange rate will be less than 1.4600, and(b)
A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $250 per ounce and sell gold for $249 per ounce. The trader can borrow funds at 6% per year and invest
Use the DerivaGem software to calculate the value of the range forward contract considered in Section 1.7 on the assumption that the exchange rate volatility is 15% per annum. Adjust the upper end of
Show that the Standard Oil bond described in Section 1.7 is a combination of a regular bond, a long position in call options on oil with a strike price of $25, and a short position in call options on
The current price of a stock is $94, and three-month call options with a strike price of $95 currently sell for $4.70. An investor who feels that the price of the stock will increase is trying to
The price of gold is currently $500 per ounce. The forward price for delivery in one year is $700.An arbitrageur can borrow money at 10% per annum. What should the arbitrageur do? Assume that the
Suppose that sterling-USD spot and forward exchange rates are as follows:Spot 1.6080 90-day forward 1.6056 180-day forward 1.6018 What opportunities are open to an arbitrageur in the following
On July 1, 2002, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2003. On September 1, 2002, it enters into a forward contract to sell 10 million Japanese yen on
Show that a range forward contract such as the one described in Section 1.7 is a combination of two options. How can a range forward contract be constructed so that it has zero value?
Show that an ICON such as the one described in Section 1.7 is a combination of a regular bond and two options.
Describe the profit from the following portfolio: a long forward contract on an asset and a long European put option on the asset with the same maturity as the forward contract and a strike price
The Chicago Board of Trade offers a futures contract on long-term Treasury bonds. Characterize the traders likely to use this contract.
A trader writes a December put option with a strike price of S30. The price of the option is S4.Under what circumstances does the trader make a gain?
A trader writes a September call option with a strike price of $20. It is now May, the stock price is$18, and the option price is $2. Describe the trader's cash flows if the option is held until
Suppose that a June put option to sell a share for $60 costs $4 and is held until June. Under what circumstances will the seller of the option (i.e., the party with the short position) make a
Suppose that a March call option to buy a share for $50 costs $2.50 and is held until March.Under what circumstances will the holder of the option make a profit? Under what circumstances will the
Explain why a forward contract can be used for either speculation or hedging.
A trader sells a European call on a share for $4. The stock price is $47 and the strike price is $50.Under what circumstances does the trader make a profit? Under what circumstances will the option
A trader buys a European put on a share for $3. The stock price is $42 and the strike price is $40.Under what circumstances does the trader make a profit? Under what circumstances will the option be
Suppose that you own 5,000 shares worth $25 each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next four months?
You would like to speculate on a rise in the price of a certain stock. The current stock price is $29, and a three-month call with a strike of $30 costs $2.90. You have $5,800 to invest. Identify two
Suppose that you write a put contract on AOL Time Warner with a strike price of $40 and an expiration date in three months. The current stock price of AOL Time Warner is $41 and the contract is on
A trader enters into* a "snort cotton futures contract when the futures price is 50 cents per pound.The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the
A trader enters into a short forward contract on 100 million yen. The forward exchange rate is$0.0080 per yen. How much does the trader gain or lose if the exchange rate at the end of the contract is
Explain carefully the difference between writing a call option and buying a put option.
What is the difference between entering into a long forward contract when the forward price is $50 and taking a long position in a call option with a strike price of $50?
Prove the result in Section 25.5 that whenwith the dz, uncorrelated, f/g is a martingale for =gi-AppendixLO1 df [+]+ i= = [+]+ i=1 i=| g.igdzi i=1 and dg
Show that when and g provide income at rates q, and qg, respectively, equation (25.15) becomes(Hint: Form new securities f* and g* that provide no income by assuming that all the income from f is
At time zero the price of a non-dividend-paying stock is So. Suppose that the time interval between 0 and T is divided into two subintervals of length t and t. During the first subinterval, the
Show that the GARCH (1,1) model o = w+au-1 + Bo in equation (19.9) is equivalent to the stochastic volatility model dV = a(VL-V) dt +V dz, where time is measured in days, V is the square of the
Consider a variable that is not an interest rate: (a) In what world is the futures price of the variable a martingale? (b) In what world is the forward price of the variable a martingale? (c)
Suppose that the price of a zero-coupon bond maturing at time 7 follows the process dP(t,T) = HpP(t, T) dt + pP(t,T) dz and the price of a derivative dependent on the bond follows the process
A security's price is positively dependent on two variables: the price of copper and the yen/dollar exchange rate. Suppose that the market price of risk for these variables is 0.5 and 0.1,
Show that when w=h/g and h and g are each dependent on n Wiener processes, the ith component of the volatility of w is the ith component of the volatility of h minus the ith component of the
Prove equation (25.33) in Section 25.7.AppendixLO1
Explain the difference between the way a forward interest rate is defined and the way the forward values of other variables such as stock prices, commodity prices, and exchange rates are
The variable S is an investment asset providing income at rate q measured in currency A. It follows the process dS=usSdt+oss dz in the real world. Defining new variables as necessary, give the
"The expected future value of an interest rate in a risk-neutral world is greater than it is in the real world." What does this statement imply about the market price of risk for (a) an interest rate
Prove that, when the security f provides income at rate q, equation (25.9) becomes +q-ro. (Hint: Form a new security f* that provides no income by assuming that all the income from f is reinvested in
Suppose that an interest rate x follows the process dx = a(xo-x) dt +cxdz wherea, xo, and c are positive constants. Suppose further that the market price of risk for x is . What is the process for x
Deduce the differential equation for a derivative dependent on the prices of two non- dividend-paying traded securities by forming a riskless portfolio consisting of the derivative and the two traded

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