ine in the value of one contract will always be offset by an increase in the value of the othercontract. However, there is a chance that one party will get into financial difficulties and default.The financial institution then still has to honor the contract it has with the other party.
Suppose that some time after the initiation of the contracts in Figure 6.4, the contract withMicrosoft has a positive value to the financial institution, whereas the contract with Intel has anegative value. If Microsoft defaults, the financial institution is liable to lose the whole of thepositive value it has in this contract. To maintain a hedged position, it would have to find a thirdparty willing to take Microsoft’s position. To induce the third party to take the position, thefinancial institution would have to pay the third party an amount roughly equal to the value of itscontract with Microsoft prior to the default.
A financial institution has credit-risk exposure from a swap only when the value of the swap tothe financial institution is positive. What happens when this value is negative and the counterpartygets into financial difficulties? In theory, the financial institution could realize a windfall gain,because a default would lead to it getting rid of a liability. In practice, it is likely that thecounterparty would choose to sell the contract to a third party or rearrange its affairs in someway so that its positive value in the contract is not lost. The most realistic assumption for thefinancial institution is therefore as follows. If the counterparty goes bankrupt, there will be a loss ifthe value of the swap to the financial institution is positive, and there will be no effect on thefinancial institution’s position if the value of the swap to the financial institution is negative. Thissituation is summarized in Figure 6.13.
Potential losses from defaults on a swap are much less than the potential losses from defaults ona loan with the same principal. This is because the value of the swap is usually only a small fractionof the value of the loan. Potential losses from defaults on a currency swap are greater than on aninterest rate swap. The reason is that, because principal amounts in two different currencies areexchanged at the end of the life of a currency swap, a currency swap can have a greater value thanan interest rate swap.
Sometimes a financial institution can predict which of two offsetting contracts is more likely tohave a positive value. Consider the currency swap in Figure 6.10. AUD interest rates are higherthan USD interest rates. This means that, as time passes, the financial institution is likely to findthat its swap with General Motors has a negative value whereas its swap with Qantas has a positivevalue. The creditworthiness of Qantas is therefore more important than the creditworthiness ofGeneral Motors.
It is important to distinguish between the credit risk and market risk to a financial institutionin any contract. As discussed earlier, the credit risk arises from the possibility of a default by thecounterparty when the value of the contract to the financial institution is positive. The markettisk arises from the possibility that market variables such as interest rates and exchange rates willmove in such a way that the value of a contract to the financial institution becomes negative.146 CHAPTER 6
4 Exposure
Swap value
 
Figure 6.13 The credit exposure in a swap
Market risks can be hedged by entering into offsetting contracts; credit risks are less easy tohedge.
 
 
The two most common types of swaps are interest rate swaps and currency swaps. In an interestrate swap, one party agrees to pay the other party interest at a fixed rate on a notional principalfor a number of years. In return, it receives interest at a floating rate on the same notionalprincipal for the same period of time. In a currency swap, one party agrees to pay interest on aprincipal amount in one currency. In return, it receives interest on a principal amount in anothercurrency,
Principal amounts are not usually exchanged in an interest rate swap. In a currency swap,principal amounts are usually exchanged at both the beginning and the end of the life of the swap.For a party paying interest in the foreign currency, the foreign principal is received, and thedomestic principal is paid at the beginning of the life of the swap. At the end of the life of theswap, the foreign principal is paid and the domestic principal is received.
An interest rate swap can be used to transform a floating-rate loan into a fixed-rate loan, or viceversa. It can also be used to transform a floating-rate investment to a fixed-rate investment, or viceversa. A currency swap can be used to transform a loan in one currency into a loan in anothercurrency. It can also be used to transform an investment denominated in one currency into aninvestment denominated in another currency.
There are two ways of valuing interest rate swaps and currency swaps. In the first, the swap isdecomposed into a long position in oe bond and a short position in another bond. In the second,it is regarded as a portfolio of forward contracts.
When a financial institution enters into a pair of offsetting swaps with different counterparties, itis exposed to credit risk. If one of the counterparties defaults when the financial institution hasSwaps 147
positive value in its swap with that counterparty, the financial institution loses money, because itstill has to honor its swap agreement with the other counterparty.The swap market is discussed further in Chapter 25.
SUGGESTIONS FOR FURTHER READING
 
Bicksler, J., and A. H. Chen, “An Economic Analysis of Interest Rate Swaps,”” Journal of Finance, 41,no. 3 (1986), 645-55.
Dattatreya, R. E., and K. Hotta, Advanced Interest Rate and Currency Swaps: State-of-the Art ProductsStrategies and Risk Management Applications, Irwin, Chicago, 1993.
Hull, J., “Assessing Credit Risk in a Financial [nstitution’s Off-Balance Sheet Commitments,” Journalof Financial and Quantitative Analysis, 24 (December 1989), 489-502.
Hull, J., and A. White, “The Impact of Default Risk on the Prices of Options and Other DerivativeSecurities,” Journal of Banking and Finance, 19 (1985), 299-322.
Hull, J., and A. White, “The Price of Default,” RISK, September 1992, pp. 101-3.Litzenberger, R. H., “Swaps: Plain and Fanciful,” Journal of Finance, 47, no. 3 (1992), 831-50,Marshall, J. F., and K. R. Kapner, Understanding Swaps, Wiley, New York, 1993.
Smith, C. W., C. W. Smithson, and L. M. Wakeman, “The Evolving Market for Swaps,” MidlandCorporate Finance Journal, 3 (Winter 1986), 20-32.
Turnbull, S. M., “Swaps: A Zero Sum Game,” Financial Management, 16, no. | (Spring 1987), 15-21.
Wall, L. D., and J. J. Pringle, “Alternative Explanations of Interest Rate Swaps: A Theoretical andEmpirical Analysis,” Financial Management, 18, no. 2, (Summer 1989), 59-73.
QUESTIONS AND PROBLEMS(ANSWERS IN SOLUTIONS MANUAL)
 
 
6.1. Companies A and B have been offered the following rates per annum on a $20 million five-year
 
loan:Fixed rate Floating rateCompany A 12.0% LIBOR + 0.1%Company B 13.4% LIBOR + 0.6%
Company A requires a floating-rate loan; company B requires a fixed-rate loan. Design a swapthat will net a bank, acting as intermediary, 0.1% per annum and that will appear equallyattractive to both companies.
6.2. A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap,six-month LIBOR is exchanged for 12% per annum (compounded semiannually). The average ofthe bid—offer rate being exchanged for six-month LIBOR in swaps of all maturities is currently10% per annum with continuous compounding. The six-month LIBOR rate was 9.6% per annumtwo months ago. What is the current value of the swap to the party paying floating? What is itsvalue to the party paying fixed?148
6.3,
6.4.6.5.
6.6.6.7.6.8.
6.9.
CHAPTER 6
Company X wishes to borrow U.S. dollars at a fixed rate of interest. Company Y wishes toborrow Japanese yen at a fixed rate of interest. The amounts required by the two companies areroughly the same at the current exchange rate. The companies have been quoted the followinginterest rates, which have been adjusted for the impact of taxes:
 
Yen DollarsCompany X 5.0% 9.6%Company Y 6.5% 10.0%
Design a swap that will net a bank, acting as intermediary, 50 basis points per annum. Make theswap equally attractive to the two companies and ensure that all foreign exchange risk is assumedby the bank.
Explain what a swap rate is. What is the relationship between swap rates and par yields?
A currency swap has a remaining life of 15 months. It involves exchanging interest at 14% on£20 million for interest at 10% on $30 million once a year. The term structure of interest rates inboth the United Kingdom and the United States is currently flat, and if the swap were negotiatedtoday the interest rates exchanged would be 8% in dollars and 11% in sterling. All interest ratesare quoted with annual compounding. The current exchange rate (dollars per pound sterling) is1.6500. What is the value of the swap to the party paying sterling? What is the value of the swapto the party paying dollars?
Explain the difference between the credit risk and the market risk in a financial contract.Explain why a bank is subject to credit risk when it enters into two offsetting swap contracts.
Companies X and Y have been offered the following rates per annum on a $5 million 10-yearinvestment:
 
Fixed rate Floating rateCompany X 8.0% LIBORCompany Y 8.8% LIBOR
Company X requires a fixed-rate investment; company Y requires a floating-rate investment.Design a swap that will net a bank, acting as intermediary, 0.2% per annum and will appearequally attractive to X and Y.
A financial institution has entered into an interest rate swap with company X. Under the terms ofthe swap, it receives 10% per annum and pays six-month LIBOR on a principal of $10 million forfive years. Payments are made every six months. Suppose that company X defaults on the sixthpayment date (end of year 3) when the interest rate (with semiannual compounding) is 8% perannum for all maturities. What is the loss to the financial institution? Assume that six-monthLIBOR was 9% per annum halfway through year 3.
. A financial institution has entered into a 10-year currency swap with company Y. Under the
terms of the swap, it receives interest at 3% per annum in Swiss francs and pays interest at8% per annum in U.S. dollars. Interest payments are exchanged once a year. The principalamounts are 7 million dollars and 10 million francs. Suppose that company Y declaresbankruptcy at the end of year 6, when the exchange rate is $0.80 per franc. What is the costto the financial institution? Assume that, at the end of year 6, the interest rate is 3% per annumin Swiss francs and 8% per annum in U.S. dollars for all maturities. All interest rates are quotedwith annual compounding.Swaps 149
6.11.
6.12.
6.13.
6.14,
6.15.
6.16,
6.17.
Companies A and B face the following interest rates (adjusted for the differential impact of taxes):
 
A BUS. dollars (floating rate) LIBOR + 0.5% LIBOR + 1.0%Canadian dollars (fixed rate) 5.0% 6.5%
Assume that A wants to borrow U.S. dollars at a floating rate of interest and B wants to borrowCanadian dollars at a fixed rate of interest. A financial institution is planning to arrange a swapand requires a 50-basis-point spread. If the swap is equally attractive to A and B, what rates ofinterest will A and B end up paying?
After it hedges its foreign exchange risk using forward contracts, is the financial institution’saverage spread in Figure 6.10 likely to be greater than or less than 20 basis points? Explain youranswer.
“Companies with high credit risks are the ones that cannot access fixed-rate markets directly.They are the companies that are most likely to be paying fixed and receiving floating in an interestrate swap.” Assume that this statement is true. Do you think it increases or decreases the risk of afinancial institution’s swap portfolio? Assume that companies are most likely to default wheninterest rates are high.
Why is the expected loss from a default on a swap less than the expected loss from the default on aloan with the same principal?
A bank finds that its assets are not matched with its liabilities. It is taking floating-rate depositsand making fixed-rate loans. How can swaps be used to offset the risk?
Explain how you would value a swap that is the exchange of a floating rate in one currency for afixed rate in another currency
The LIBOR zero curve is flat at 5% (continuously compounded) out to 1.5 years. Swap rates for2- and 3-year semiannual pay swaps are 5.4% and 5.6%, respectively. Estimate the LIBOR zerorates for maturities of 2.0, 2.5, and 3.0 years. (Assume that the 2.5-year swap rate is the average ofthe 2- and 3-year swap rates.)
ASSIGNMENT QUESTIONS
 
6.18.
6.19.
 
The one-year LIBOR rate is 10%. A bank trades swaps where a fixed rate of interest is exchangedfor 12-month LIBOR with payments being exchanged annually. Two- and three-year swap rates(expressed with annual compounding) are 11% and 12% per annum. Estimate the two- and three-year LIBOR zero rates.
Company X is based in the United Kingdom and would like to borrow $50 million at a fixed rateof interest for five years in U.S. funds. Because the company is not well known in the UnitedStates, this has proved to be impossible. However, the company has been quoted 12% per annumon fixed-rate five-year sterling funds. Company Y is based in the United States and would like toborrow the equivalent of $50 million in sterling funds for five years at a fixed rate of interest. Ithas been unable to get a quote but has been offered U.S. dollar funds at 10.5% per annum. Five-year government bonds currently yield 9.5% per annum in the United States and 10.5% in theUnited Kingdom. Suggest an appropriate currency swap that will net the financial intermediary0.5% per annum.150
6.20.
CHAPTER 6
Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annumand to receive three-month LIBOR in return on a notional principal of $100 million withpayments being exchanged every three months. The swap has a remaining life of 14 months. Theaverage of the bid and offer fixed rates currently being swapped for three-month LIBOR is12% per annum for all maturities. The three-month LIBOR rate one month ago was 11.8% perannum. All rates are compounded quarterly. What is the value of the swap?
. Suppose that the term structure of interest rates is flat in the United States and Australia. The
USD interest rate is 7% per annum and the AUD rate is 9% per annum. The current value of theAUD is 0.62 USD. Under the terms of a swap agreement, a financial institution pays 8% perannum in AUD and receives 4% per annum in USD. The principals in the two currencies are$12 million USD and 20 million AUD. Payments are exchanged every year, with one exchangehaving just taken place. The swap will last two more years. What is the value of the swap to thefinancial institution? Assume all! interest rates are continuously compounded.
. Company A, a British manufacturer, wishes to borrow U.S. dollars at a fixed rate of interest.
Company B, a U.S. multinational, wishes to borrow sterling at a fixed rate of interest. They havebeen quoted the following rates per annum (adjusted for differential tax effects):
 
Sterling US. DollarsCompany A 11.0% 7.0%Company B 10.6% 6.2%
Design a swap that will net a bank, acting as intermediary, 10 basis points per annum and thatwill produce a gain of 15 basis points pcr annum for cach of the two companics. 
CHAPTER 7
MECHANICS OF OPTIONS MARKETS
We introduced options in Chapter |. A call option is the right to buy an asset for a certain price; aput option is the right to sell an asset for a certain price. A European option can be exercised onlyat the end of its life; an American option can be exercised at any time during its life. The are fourtypes of option positions: a long position in a call, a long position in a put, a short position in acall, and a short position in a put. In this chapter we explain the way that exchange-traded options
markets are organized. the terminology used. how contracts are traded. how margin requirementsmarxsets are organized, the terminoiogy used, now contracts are tracec, now margin requirements
are set, and so on. Later chapters will discuss trading strategies involving options, the pricing ofoptions, and ways in which portfolios of options can be hedged.
Options are fundamentally different from the forward, futures, and swap contracts discussed inthe last few chapters. An option gives the holder of the option the right to do something. Theholder does not have to exercise this right. By contrast, in a forward, futures, or swap contract, thetwo parties have committed themselves to some action. It costs a trader nothing (except for the
margin requirements) to enter into a forward or futures contract, whereas the purchase of an
mar equi utures contract,
option requires an up-front payment.
7.1_UNDERLYING ASSETS
 
Exchange-traded options are currently actively traded on stocks, stock indices, foreign currencies,and futures contracts.
Stock Options
The exchanges trading stock options in the United States are the Chicago Board Options Exchange(www.cboe.com), the Philadelphia Stock Exchange (www.phlx.com), the American Stock Exchange
(www.amex.com), and the Pacific Exchange (www.pacifex.com). Options trade on more than500 different stocks. One contract gives the holder the right to buy or sell 100 shares at the specified
strike price. This contract size is convenient as the shares themselves are usually traded in lots of 100.
Foreign Currency Options
The major exchange for trading foreign currency options is the Philadelphia Stock Exchange. Itoffers both European and American contracts on a variety of different currencies. The size of onecontract depends on the currency. For example, in the case of the British pound, one contract givesthe holder the right to buy or sell £31,250; in the case of the Japanese yen, one contract gives the
151152 CHAPTER 7
holder the right to buy or sell 6.25 million yen. Foreign currency options contracts are discussedfurther in Chapter 13.
Index Options
Many different index options currently trade throughout the world. The most popular contracts inthe United States are those on the S&P 500 Index (SPX), the S&P 100 Index (OEX), the Nasdaq 100Index (NDX), and the Dow Jones Industrial Index (DJX). All of these trade on the Chicago BoardOptions Exchange. Some index options are European and some are American. For example, thecontract on the S&P 500 is European, whereas that on the S&P 100 is American. One contract is tobuy or sell 100 times the index at the specified strike price. Settlement is always in cash, rather thanby delivering the portfolio underlying the index. Consider, for example, one call contract on theS&P 100 with a strike price of 980. If it is exercised when the value of the index is 992, the writer ofthe contract pays the holder (992 — 980) x 100 = $1,200. This cash payment is based on the indexvalue at the end of the day on which exercise instructions are issued. Not surprisingly, investorsusually wait until the end of a day before issuing these instructions. Index options are discussedfurther in Chapter 13.
Futures Options
In a futures option (or options on futures), the underlying asset is a futures contract. The futurescontract normally matures shortly after the expiration of the option. Futures options are nowavailable for most of the assets on which futures contracts are traded and normally trade on thesame exchange as the futures contract. When a call option is exercised, the holder acquires trom thewriter a long position in the underlying futures contract plus a cash amount equal to the excess ofthe futures price over the strike price. When a put option is exercised, the holder acquires a shortposition in the underlying futures contract plus a cash amount equal to the excess of the strikeprice over the futures price. Futures options contracts are discussed further in Chapter 13.
7.2. SPECIFICATION OF STOCK OPTIONS
 
 
In most of the rest of this chapter, we will focus on exchange-traded stock options. As alreadymentioned, an exchange-traded stock option in the United States is an American-style optioncontract to buy or sell 100 shares of the stock. Details of the contract—the expiration date, the strikeprice, what happens when dividends are declared, how large a position investors can hold, and soon—are specified by the exchange.
Expiration Dates
One of the items used to describe a stock option is the month in which the expiration dateoccurs. Thus, a January call trading on IBM is a call option on IBM with an expiration date inJanuary. The precise expiration date is 10:59 p.m. Central Time on the Saturday immediatelyfollowing the third Friday of the expiration month. The last day on which options trade is thethird Friday of the expiration month. An investor with a long position in an option normally hasuntil 4:30 p.m. Central Time on that Friday to instruct a broker to exercise the option. Thebroker then has until 10:59 p.m. the next day to complete the paperwork notifying the exchangethat exercise is to take place.Mechanics of Options Markets 153
Stock options are on a January, February, or March cycle. The January cycle consists of themonths of January, April, July, and October. The February cycle consists of the months ofFebruary, May, August, and November. The March cycle consists of the months of March, June,September, and December. If the expiration date for the current month has not yet been reached,options trade with expiration dates in the current month, the following month, and the next twomonths in the cycle. If the expiration date of the current month has passed, options trade withexpiration dates in the next month, the next-but-one month, and the next two months of theexpiration cycle. For example, IBM is on a January cycle. At the beginning of January, options aretraded with expiration dates in January, February, April, and July; at the end of January, they aretraded with expiration dates in February, March, April, and July; at the beginning of May, they aretraded with expiration dates in May, June, July, and October; and so on. When one option reachesexpiration, trading in another is started. Longer-term options, known as LEAPS (long-term equityanticipation sccuritics), also trade on some stocks. These have expiration dates up to three ycarsinto the future. The expiration dates for LEAPS on stocks are always in January.
Strike Prices
The Chicago Board Options Exchange normally chooses the strike prices at which options can bewritten so that they are spaced $2.50, $5, or $10 apart. When the price of a stock is $12, we mightsee options trading with strike prices of $10, $12.50, and $15; when the stock price is $100, wemight see strike prices of $90, $95, $100, $105, and $110. As will be explained shortly, stock splitsand stock dividends can lead to nonstandard strike prices.
When a new expiration date is introduced, the two or three strike prices closest to the currentstock price are usually selected by the exchange. If the stock price moves outside the range definedby the highest and lowest strike price, trading is usually introduced in an option with a new strikeprice. To illustrate these rules, suppose that the stock price is $84 when trading begins in theOctober options. Call and put options would probably first be offered with strike prices of $80,$85, and $90. If the stock price rose above $90, it is likely that a strike price of $95 would beoffered; if it fell below $80, it is likely that a strike price of $75 would be offered; and so on.
Terminology
For any given asset at any given time, many different option contracts may be trading. Consider astock that has four expiration dates and five strike prices. If call and put options trade with everyexpiration date and every strike price, there are a total of 40 different contracts, All options of thesame type (calls or puts) are referred to as an option class. For example, IBM calls are one class,whereas IBM puts are another class. An option series consists of all the options of a given classwith the same expiration date and strike price. In other words, an option series refers to aparticular contract that is traded. The IBM 50 October calls are an option series.
Options are referred to as in the money, at the money, or out of the money. An in-the-money optionwould give the holder a positive cash flow if it were exercised immediately. Similarly, an at-the-money option would lead to zero cash flow if it were exercised immediately, and an out-of-the-moneyoption would lead to a negative cash flow if it were exercised immediately. If Sis the stock price andK is the strike price, a call option is in the money when S > K, at the money when S = K, and out ofthe money when S < K. A put option is in the moncy when S < K, at the moncy when S = K, andout of the money when S > K. Clearly, an option will be exercised only when it is in the money. Inthe absence of transactions costs, an in-the-money option will always be exercised on the expirationdate if it has not been exercised previously.154 CHAPTER 7
The intrinsic value of an option is defined as the maximum of zero and the value the optionwould have if it were exercised immediately. For a call option, the intrinsic value is thereforemax(S — K, 0). For a put option, it is max(K — S, 0). An in-the-money American option must beworth at least as much as its intrinsic value because the holder can realize a positive intrinsic valueby exercising immediately. Often it is optimal for the holder of an in-the-money American optionto wait rather than exercise immediately. The option is then said to have time value.
The time value of an option is the part of the option’s value that derives the possibility of futurefavorable movements in the stock price. Suppose that the price of a call option with two months tomaturity is $3 when the stock price is $30 and the strike price is $28. The intrinsic value of theoption is 30 — 28 = $2 and the time value is 3 — 2 = $1. In general, the value of an option equalsthe intrinsic value of the option plus the time value of the option. The time value of the option iszero when (a) the option has reached maturity or (b) it is optimal to exercise the optionimmediately.
Flex Options
The Chicago Board Options Exchange offers flex options on equities and equity indices. These areoptions where the traders on the floor of the exchange agree to nonstandard terms, Thesenonstandard terms can involve a strike price or an expiration date that is different from what isusually offered by the exchange. It can also involve the option being European rather thanAmerican. Flex options are an attempt by option exchanges to regain business from the over-the-counter markets. The exchange specifies a minimum size for flex option trades.
Dividends and Stock Splits
The early over-the-counter options were dividend protected. If a company declared a cash dividend,the strike price for options on the company’s stock was reduced on the ex-dividend day by theamount of the dividend. Fxchange-traded options are not generally adjusted for cash dividends. Inother words, when a cash dividend occurs, there are no adjustments to the terms of the optioncontract. As we will see in Chapter 12, this has significant implications for the way in which optionsare valued.
Exchange-traded options are adjusted for stock splits. A stock split occurs when the existingshares arc “split” into more shares. For cxample, in a 3-for-1 stock split, three new shares areissued to replace each existing share. Because a stock split does not change the assets or the earningability of a company, we should not expect it to have any effect on the wealth of the company’sshareholders. All else being equal, the 3-for-1 stock split should cause the stock price to go downto one-third of its previous value. In general, an n-for-m stock split should cause the stock price togo down to m/n of its previous value. The terms of option contracts are adjusted to reflect expectedchanges in a stock price arising from a stock split. After an n-for-m stock split, the strike price isreduced to m/n of its previous value, and the number of shares covered by one contract is increasedto n/m of its previous value. If the stock price declines in the way expected, the positions of boththe writer and the purchaser of a contract remain unchanged.
Example 71 Consider a cali option to buy 100 shares of a company for $30 per share. Supposethat the company makes a 2-for-1 stock split. The terms of the option contract are then changed sothat it gives the holder the right to purchase 200 shares for $15 per share.
Stock options are adjusted for stock dividends. A stock dividend involves a company issuing moreMechanics of Options Markets 155
 
shares to its existing shareholders. For example, a 20% stock dividend means that investors receiveone new share for each five already owned. A stock dividend, like a stock split, has no effect oneither the assets or the earning power of a company. The stock price can be expected to go down asaresult of a stock dividend. The 20% stock dividend referred to is essentially the same as a 6-for-5stock split. All else being equal, it should cause the stock price to decline to 5/6 of its previousvalue. The terms of an option are adjusted to reflect the expected price decline arising from a stockdividend in the same way as they are for that arising from a stock split.
Example 7.2 Consider a put option to sell 100 shares of acompany for $15 per share. Suppose thatthe company declares a 25% stock dividend. This is equivalent to a 5-for-4 stock split. The terms ofthe option contract are changed so that it gives the holder the right to sel! 125 shares for $12.
Adjustments are also made for rights issues. The basic procedure is to calculate the theoreticalprice of the rights and then to reduce the strike price by this amount.
Position Limits and Exercise Limits
The Chicago Board Options Exchange often specifies a position limit for option contracts. Thisdefines the maximum number of option contracts that an investor can hold on one side of themarket. For this purpose, long calls and short puts are considered to be on the same side of themarket. Also, short calls and long puts are considered to be on the same side of the market. Theexercise