an ICON was for the Long Term Credit Bank of Japan. The ICON specified thatif the yen-USD exchange rate, S;, is greater than 169 yen per dollar at maturity (in 1995), the holderof the bond receives $1,000. If it is less than 169 yen per dollar, the amount received by the holder ofthe bond is
1,000 — max, 10004 = ‘)|When the exchange rate is below 84.5, nothing is received by the holder at maturity.
Example 1.3: Range Forward Contract Range forward contracts (also known as flexible for-wards) are popular in foreign exchange markets. Suppose that on August 16, 2001, a U.S. companyfinds that it will require sterling in three months and faces the exchange rates given in Table 1.1. It
5 See Problems 1.24, 1.25, and 1.30 at the end of this chapter for how the decomposition is accomplished.Introduction 15
could enter into a three-month forward contract to buy at 1.4407. A range forward contract is analternative. Under this contract an exchange rate band straddling 1.4407 is set. Suppose that thechosen band runs from 1.4200 to 1.4600. The range forward contract is then designed to ensure thatif the spot rate in three months is less than 1.4200, the company pays 1.4200; if it is between 1.4200and 1.4600, the company pays the spot rate; if it is greater than !.4600, the company pays 1.4600.
Other, More Complex Examples
As mentioned earlier, there is virtually no limit to the innovations that are possible in thederivatives area. Some of the options traded in the over-the-counter market have payoffs dependenton maximum value attained by a variable during a period of time; some have payoffs dependent onthe average value of a variable during a period of time; some have exercise prices that are functionsof time; some have features where exercising one option automatically gives the holder anotheroption; some have payoffs dependent on the square of a future interest rate; and so on.Traditionally, the variables underlying options and other derivatives have been stock prices, stockindices, interest rates, exchange rates, and commodity prices. However, other underlying variablesare becoming increasingly common. For example, the payoffs from credit derivatives, which are
discussed in Chanter 27, depend on the creditworthiness of one or more companies
: weatherscussed in Chapter deper the creditworthiness of one more companies; weathe?derivatives have payoffs dependent on the average temperature at particular locations; insurancederivatives have payoffs dependent on the dollar amount of insurance claims of a specified type madeduring a specified period; electricity derivatives have payoffs dependent on the spot price of
electricity; and so on. Chapter 29 discusses weather, insurance, and energy derivatives.
SUMMARY
 
 
One of the exciting developments in finance over the last 25 years has been the growth ofderivatives markets. In many situations, both hedgers and speculators find it more attractive totrade a derivative on an asset than to trade the asset itself. Some derivatives are traded onexchanges. Others are traded by financial institutions, fund managers, and corporations in theover-the-counter market, or added to new issues of debt and equity securities. Much of this book isconcemmed with the valuation of derivatives. The aim is to present a unifying framework withinwhich all derivatives—not just options or futures—can be valued.
In this chapter we have taken a first look at forward, futures, and options contracts. A forwardor futures contract involves an obligation to buy or sell an asset at a certain time in the future for acertain price. There are two types of options: calls and puts. A call option gives the holder the right °to buy an asset by a certain date for a certain price. A put option gives the holder the right to sellan asset by a certain date for a certain price. Forwards, futures, and options trade on a wide rangeof different underlying assets.
Derivatives have been very successful innovations in capital markets. Three main types of traderscan be identified: hedgers, speculators, and arbitrageurs. Hedgers are in the position where theyface risk associated with the price of an asset. They use derivatives to reduce or eliminate this risk.Speculators wish to bet on future movements in the price of an asset. They use derivatives to getextra leverage. Arbitrageurs are in business to take advantage of a discrepancy between prices intwo different markets. If, for example, they see the futures price of an asset getting out of line withthe cash price, they will take offsetting positions in the two markets to lock in a profit.16
CHAPTER 1
QUESTIONS AND PROBLEMS(ANSWERS IN SOLUTIONS MANUAL)
 
 
Ll
1.4.1.5.
1.12.
1.13.1.14,1.15.
1.16.
. What is the difference between a long forward position and a short forward position?1.2.N13,
Explain carefully the difference between hedging, speculation, and arbitrage.
What is the difference between entering into a long forward contract when the forward price is $50and taking a long position in a call option with a strike price of $50?
Explain carefully the difference between writing a cal! option and buying a put option.
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 thecontract is (a) $0.0074 per yen; (b) $0. -009 1 per yen?
. A trader enters int 4% short 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 thecotton price at the end of the contract is (a) 48. 20 cents per pound; (b) SI. 30 cents per pound?
. 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 thecontract is on !00 shares. What have you committed yourself to? How much could you gain or lose?
. 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 twoalternative strategies, one involving an investment in the stock and the other involving investmentin the option. What are the potential gains and losses from each?
. 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?
. 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
opiion be exercised? VTaw a diagran showing ihe varialion of ihe trader "s profit wiih the stockprice at the maturity of the option.
. 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 theoption be exercised? Draw a diagram showing the variation of the trader’s profit with the stockprice at the maturity of the option.
A trader buys a call option with a strike price of $45 and a put option with a strike price of $40.Both options have the same maturity. The cal! costs $3 and the put costs $4. Draw a diagramshowing the variation of the trader’s profit with the asset price.
When first issued, a stock provides funds for a company. Is the same truc of a stock option? Discuss.Explain why a forward contract can be used for either speculation or hedging.
Suppose that a March cal! 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 circumstanceswill the option be exercised? Draw a diagram illustrating how the profit from a long position inthe option depends on the stock price at maturity of the option.
Suppose that a June put option to sell a share for $60 costs $4 and is held until June. Under whatcircumstances will the seller of the option (i.e., the party with the short position) make a profit? -Under what circumstances will the option be exercised? Draw a diagram illustrating how theprofit from a short position in the option depends on the stock price at maturity of the option.Introduction 17
 
1.17.
1.18.
1.19,
1.20.
121.
1.22.
1.23.
1.24.
1.25.
1.27.
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!September and the stock price is $25 at that time.
A trader writes a December put option with a strike price of $30. The price of the option is $4.Under what circumstances does the trader make a gain?
A company knows that it is due to receive a certain amount of a foreign currency in four months.What type of option contract is appropriate for hedging?
A United States company expects to have to pay 1 million Canadian dollars in six months.Explain how the exchange rate risk can be hedged using (a) a forward contract; (b) an option.The Chicago Board of ‘lrade offers a futures contract on long-term Treasury bonds. Characterizethe traders likely to use this contract.
“Options and futures are zero-sum games.” What do you think is meant by this statement?
Describe the profit from the following portfolio: a long forward contract on an asset and a longEuropean put option on the asset with the same maturity as the forward contract and a strikeprice that is equal! to the forward price of the asset at the time the portfolio is set up.
Show that an ICON such as the one described in Section 1.7 is a combination of a regular bondand two options.
Show that a range forward contract such as the one described in Section 1.7 is a combination oftwo options. How can a range forward contract be constructed so that it has zero value?
. 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 millionJapanese yen on January 1, 2003. Describe the payoff from this strategy.
Suppose that sterling-USD spot and forward exchange rates are as follows:Spot 1.608090-day forward 1.6056180-day forward 1.6018
What opportunities are open to an arbitrageur in the following situations?a. A 180-day European cal! option to buy £1 for $1.57 costs 2 cents.b. A 90-day European put option to sell £1 for $1.64 costs 2 cents.
ASSIGNMENT QUESTIONS
 
 
1.29,
1.30.
. 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? Assumethat the cost of storing gold is zero and that gold provides no income.
The current price of a stock is $94, and three-month call options with a strike price of $95currently sell for $4.70. An investor who feels that the price of the stock will increase is trying todecide between buying 100 shares and buying 2,000 call options (= 20 contracts). Both strategiesinvolve an investment of $9,400. What advice would you give? How high does the stock price haveto rise for the option strategy to be more profitable?
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 oi! with a strike price of $25, and a short position in call optionson oil with a strike price of $40.18
CHAPTER 1
 
1.31.
1.32.
1.33,
1.34.
Use the DerivaGem software to calculate the value of the range forward contract considered inSection 1.7 on the assumption that the exchange rate volatility is 15% per annum. Adjust theupper end of the band so that the contract has zero value initially. Assume that the dollar andsterling risk-free rates are 5.0% and 6.4% per annum, respectively.
A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $250per ounce and sell gold for $249 per ounce. The trader can borrow funds at 6% per year andinvest funds at 5.5% per year. (Both interest rates are expressed with annual compounding.) Forwhat range of one-year forward prices of gold does the trader have no arbitrage opportunities?Assume there is no bid—offer spread for forward prices.
Describe how foreign currency options can be used for hedging in the situation considered inSection 1.6 so that (a) ImportCo is guaranteed that its exchange rate will be less than 1.4600, and(b) ExportCo is guaranteed that its exchange rate will be at least 1.4200. Use DerivaGem tocalculate the cost of setting up the hedge in each case assuming that the exchange rate volatility is12%, interest rates in the United States are 3% and interest rates in Britain are 4.4%, Assume thatthe current exchange rate is the average of the bid and offer in Table 1.1.
A trader buys a European call option and sells a European put option. The options have the sameunderlying asset, strike price and maturity. Describe the trader’s position. Under whatcircumstances does the price of the call equal the price of the put? 
CHAPTER 2
MECHANICS OF FUTURESMARKETS
In Chapter 1 we explained that both futures and forward contracts are agreements to buy or sel! anasset at a future time for a certain price. Futures contracts are traded on an organized exchange,and the contract terms are standardized by that exchange. By contrast, forward contracts areprivate agreements between two financial institutions or between a financial institution and one ofits corporate clients.
This chapter covers the details of how futures markets work. We examine issues such as thespecification of contracts, the operation of margin accounts, the organization of exchanges, theregulation of markets, the way in which quotes are made, and the treatment of futures transactionsfor accounting and tax purposes. We also examine forward contracts and explain the difference
between the pattern of payoffs realized from futures and forward contracts.
2.1 TRADING FUTURES CONTRACTS
As mentioned in Chapter 1, futures contracts are now traded very actively al! over the world. Thetwo largest futures exchanges in the United States are the Chicago Board of Trade (CBOT,www.cbol.com) and the Chicago Mercantile Exchange (CME, www.cme.com). The two largestexchanges in Europe are the London International Financial Futures and Options Exchange
(www.liffeccom) and Eurex (www.eurexchange.com). Other large exchanges include Bolsa deMercadorias y Futuros (www.bmf.com.br) in Sao Paulo, the Tokyo International Financial Futures
Exchange (www.tiffe.or.jp), the Singapore International Monetary Exchange (www.simex.com.sg),and the Sydney Futures Exchange (www.sfe.com.au). For a more complete list, see the table at theend of this book.
We examine how a futures contract comes into existence by considering the corn futurescontract traded on the Chicago Board of Trade (CBOT). On March 5, an investor in New Yorkmight call a broker with instructions to buy 5,000 bushels of corn for delivery in July of the sameyear. The broker would immediately pass these instructions on to a trader on the floor of theCBOT. The broker would request a long position in one contract because each corn contract onthe CBOT is for the delivery of exactly 5,000 bushels. At about the same time, another investorin Kansas might instruct a broker to sell 5,000 bushels of corn for July delivery. This brokerwould then pass instructions to short one contract to a trader on the floor of the CBOT. The two
1920 CHAPTER 2
 
floor traders would meet, agree on a price to be paid for the corn in July, and the deal would bedone.
The investor in New York who agreed to buy has a Jong futures position in one contract; theinvestor in Kansas who agreed to sell has a short futures position in one contract. The priceagreed to on the floor of the exchange is the current futures price for July corn. We will supposethe price is 170 cents per bushel. This price, like any other price, is determined by the laws ofsupply and demand. If at a particular time more traders wish to sell July corn than buy Julycorn, the price will go down. New buyers then enter the market so that a balance between buyersand sellers is maintained. If more traders wish to buy July corn than to sell July corn, the pricegoes up. New sellers then enter the market and a balance between buyers and sellers ismaintained.
Closing Out Positions
The vast majority of futures contracts do not lead to delivery. The reason is that most traderschoose to close out their positions prior to the delivery period specified in the contract. Closing outa position means entering into the opposite type of trade from the original one. For example theNew York investor who bought a July corn futures contract on March 5 can close out the positionby selling (i.e., shorting) one July corn futures contract on Apri! 20. The Kansas investor who sold(.e., shorted) a July contract on March 5 can close out the position on by buying one July contracton April 20. In each case, the investor’s total gain or loss is determined by the change in the futuresprice between March 5 and April 20.
It is important to realize that there is no particular significance to the party on the other side of atrade in a futures transaction. Consider trader A who initiates a long futures position by tradingone contract. Suppose that trader B is on the other side of the transaction. At a later stage trader Amight close out the position by entering into a short contract. The trader on the other side of thissecond transaction does not have to be, and usually is not, trader B.
2.2 THE SPECIFICATION OF THE FUTURES CONTRACT
 
 
 
When developing a new contract, the exchange must specify in some detail the exact nature of theagreement between the two parties. In particular, it must specify the asset, the contract size (exactlyhow much of the asset will be delivered under one contract), where delivery will be made, and whendelivery will be made.
Sometimes alternatives are specified for the grade of the asset that will be delivered or for thedelivery locations. As a general rule, it is the party with the short position (the party that hasagreed to sell the asset) that chooses what will happen when alternatives are specified by theexchange. When the party with the short position is ready to deliver, it files a notice of intention todeliver with the exchange. This notice indicates selections it has made with respect to the grade ofasset that will be delivered and the delivery location.
The Asset
When the asset is a commodity, there may be quite a variation in the quality of what is available inthe marketplace. When the asset is specified, it is therefore important thal the exchange stipulateMechanics of Futures Markets 21
the grade or grades of the commodity that are acceptable. The New York Cotton Exchange hasspecified the asset in its orange juice futures contract as
U.S. Grade A, with Brix value of not less than 57 degrees, having a Brix value to acid ratio of not lessthan 13 to | nor more than 19 to 1, with factors of color and flavor each scoring 37 points or higherand 19 for defects, with a minimum score 94.
The Chicago Mercantile Exchange in its random-length lumber futures contract has specified that
Each delivery unit shall consist of nominal 2x4s of random lengths from 8 feet to 20 feet, grade-stamped Construction and Standard, Standard and Better, or #1 and #2; however, in no case maythe quantity of Standard grade or #2 exceed 50%. Each delivery unit shall be manufactured inCalifornia, Idaho, Montana, Nevada, Oregon, Washington, Wyoming, or Alberta or BritishColumbia, Canada, and contain lumber produced from grade-stamped Alpine fir, Englemannspruce, hem-fir, lodgepole pine, and/or spruce pine fir.
For some commodities a range of grades can be delivered, but the price received depends the gradechosen. For example, in the Chicago Board of Trade corn futures contract, the standard grade is“No. 2 Yellow’, but substitutions are allowed with the price being adjusted in a way established bythe exchange.
The financial assets in futures contracts are generally well defined and unambiguous. Forexample, there is no need to specify the grade of a Japanese yen. However, there are someinteresting features of the Treasury bond and Treasury note futures contracts traded on theChicago Board of Trade. The underlying asset in the Treasury bond contract is any long-termU.S. Treasury bond that has a maturity of greater than 15 years and is not callable within 15 years.In the Treasury note futures contract, the underlying asset is any long-term Treasury note with amaturity of no less than 6.5 years and no more than 10 years from the date of delivery. Incases, the exchange has a formula for adjusting the price received according to the coupon andmaturity date of the bond delivered. This is discussed in Chapter 5.
bothocotn
The Contract Size
The contract size specifies the amount of the asset that has to be delivered under one contract. Thisis an important decision for the exchange. If the contract size is too large, many investors who wishto hedge relatively small exposures or who wish to take relatively small speculative positions will beunable to use the exchange. On the other hand, if the contract size is too small, trading may beexpensive as there is a cost associated with each contract traded.
The correct size for a contract clearly depends on the likely user. Whereas the value of whatis delivered under a futures contract on an agricultural product might be $10,000 to $20,000,it is much higher for some financial futures. For example, under the Treasury bond futurescontract traded on the Chicago Board of Trade, instruments with a face value of $100,000 aredelivered.
In some cases exchanges have introduced “mini” contracts to attract smaller investors. Forexample, the CME’s Mini Nasdaq 100 contract is on 20 times the Nasdaq 100 index whereas theregular contract is on 100 times the index.
Delivery Arrangements
The place where delivery will be made must be specified by the exchange. This is particularlyimportant for commodities that involve significant transportation costs. In the case of the Chicago22 CHAPTER 2
Mercantile Exchange’s random-length lumber contract, the delivery location is specified as
On track and shall either be unitized in double-door boxcars or, at no additional cost to the buyer,each unit shall be individually paper-wrapped and loaded on flatcars. Par delivery of hem-fir inCalifornia, Idaho, Montana, Nevada, Oregon, and Washington, and in the province of BritishColumbia.
When alternative delivery locations are specified, the price received by the party with the shortposition is sometimes adjusted according to the location chosen by that party. For example, in thecase of the corn futures contract traded by the Chicago Board of Trade, delivery can be made atChicago, Burns Harbor, Toledo, or St. Louis. However, deliveries at Toledo and St. Louis aremade at a discount of 4 cents per bushel from the Chicago contract price.
Delivery Months
A futures contract is referred to by its delivery month. The exchange must specify the preciseperiod during the month when delivery can be made. For many futures contracts, the deliveryperiod is the whole month.
The delivery months vary from contract to contract and are chosen by the exchange to meet theneeds of market participants. For example, the main delivery months for currency futures on theChicago Mercantile Exchange are March, June, September, and December; corn futures traded onthe Chicago Board of Trade have delivery months of January, March, May, July, September,November, and December. At any given time, contracts trade for the closest delivery month and anumber of subsequent delivery months. The exchange specifies when trading in a particularmonth’s contract will begin. The exchange also specifies the last day on which trading can takeplace for a given contract. Trading generally ceases a few days before the last day on which deliverycan be made.
Petes DesotosPrice Wuotes
The futures price is quoted in a way that is convenient and easy to understand. For example, crudeoil futures prices on the New York Mercantile Exchange are quoted in dollars per barrel to twodecimal places (i.e., to the nearest cent). Treasury bond and Treasury note futures prices on theChicago Board of Trade are quoted in dollars and thirty-seconds of a dollar. The minimum pricemovement that can occur in trading is consistent with the way in which the price is quoted. Thus, itis $0.0! per barrel for the oil futures and one thirty-second of a dollar for the Treasury bond andTreasury note futures.
Daily Price Movement Limits
For most contracts, daily price movement limits are specified by the exchange. If the price movesdown by an amount equal to the daily price limit, the contract is said to be /imit down, If it movesup by the limit, it is said to be /imit up. A limit move is a move in either direction equal to the dailyprice limit. Normally, trading ceases for the day once the contract is limit up or limit down.However, in some instances the exchange has the authority to step in and change the limits.
The purpose of daily price limits is to prevent large price movements from occurring because ofspeculative excesses. However, limits can become an artificial barrier to trading when the price ofthe underlying commodity is increasing or decreasing rapidly. Whether price limits are, on balance,good for futures markets is controversial.Mechanics of Futures Markets 23
Position Limits
Position limits are the maximum number of contracts that a speculator may hold. In the ChicagoMercantile Exchange’s random-length lumber contract, for example, the position limit at the timeof writing is 1,000 contracts with no more than 300 in any one delivery month. Bona fide hedgersare not affected by position limits. The purpose of the limits is to prevent speculators fromexercising undue influence on the market.
2.3. CONVERGENCE OF FUTURES PRICE TO SPOT PRICE
 
As the delivery month of a futures contract is approached, the futures price converges to the spotprice of the underlying asset. When the delivery period is reached, the futures price equals—or isvery close to—the spot price.
To see why this is so, we first suppose that the futures price is above the spot price during thedelivery period. Traders then have a clear arbitrage opportunity:
1, Short a futures contract.2, Buy the asset.3. Make delivery.
These steps are certain to lead to a profit equal to the amount by which the futures price exceeds
the snot price. As traders exploit this arbitrage opportunity, the futures price will fall, Suppose nexttne spot price. As tracers sont this arbitrage opportunity, the futures price win tau, suppose next
that the futures price is below the spot price during the delivery period. Companies interested inacquiring the asset will find it attractive to enter into a long futures contract and then wait fordelivery to be made. As they do so, the futures price will tend to rise.
The result is that the futures price is very close to the spot price during the delivery period.Figure 2.{ iliustrates the convergence of the futures price to the spot price. in Figure Z.ia thefutures price is above the spot price prior to the delivery month, and in Figure 2.1b the futures
SpotFutures pricepriceFuturesprice
  
(a) (b)
Figure 2.1 Relationship between futures price and spot price as the delivery month is approached.(a) Futures price above spot price; (b) futures price below spot price24 CHAPTER 2
price is below the spot price prior to the delivery month. The circumstances under which these twopatterns are observed are discussed later in this chapter and in Chapter 3.
2.4 OPERATION OF MARGINS
 
 
If two investors get in touch with each other directly and agree to trade an asset in the future for acertain price, there are obvious risks. One of the investors may regret the deal and try to back out.Alternatively, the investor simply may not have the financial resources to honor the agreement.One of the key roles of the exchange is to organize trading so that contract defaults are avoided.This is where margins come in.
Marking to Market
To illustrate how margins work, we consider an investor who contacts his or her broker onThursday, June 5 to buy two December gold futures contracts on the New York CommodityExchange (COMEX). We suppose that the current futures price is $400 per ounce. Because thecontract size is 100 ounces, the investor has contracted to buy a total of 200 ounces at this price.The broker will require the investor to deposit funds in a margin account. The amount that must bedeposited at the time the contract is entered into is known as the initial margin. We suppose this is$2,000 per contract, or $4,000 in total. At the end of each trading day, the margin account isadjusted to reflect the investor’s gain or loss. This practice is referred to as marking to market theaccount.
Suppose, for example, that by the end of June 5 the futures price has dropped from $400 to$397. The investor has a loss of $600 (= 200 x $3), because the 200 ounces of December gold,which the investor contracted to buy at $400, can now be sold for only $397. The balance in themargin account would therefore be reduced by $600 to $3,400. Similarly, if the price of Decembergold rose to $403 by the end of the first day, the balance in the margin account would be increasedby $600 to $4,600. A trade is first marked to market at the close of the day on which it takes place.It is then marked to market at the close of trading on each subsequent day.
Note that marking to market is not merely an arrangement between broker and client. Whenthere is a decrease in the futures price so that the margin account of an investor with a longposition is reduced by $600, the investor’s broker has to pay the exchange $600 and the exchangepasses the money on to the broker of an investor with a short position. Similarly; when there is anincrease in the futures price, brokers for parties with short positions pay money to the exchangeand brokers for parties with long positions receive money from the exchange. Later we willexamine in more detail the mechanism by which this happens.
The investor is entitled to withdraw any balance in the margin account in excess of the initialmargin. To ensure that the balance in the margin account never becomes negative a maintenancemargin, which is somewhat lower than the initial margin, is set. If the balance in the marginaccount falls below the maintenance margin, the investor receives a margin call and is expected totop up the margin account to the initial margin level the next day. The extra funds deposited areknown as a variation margin. If the investor does not provide the variation margin, the brokercloses out