In Chapter 22, we discussed the primary difference between forward and futures contracts:
Futures are standardized and trade on exchanges while forward contracts have negotiable terms and therefore must be arranged in the OTC market. With the development of organized option exchanges during the past three decades, option contracts offer investors similar trading alterna- tives. The most important features of how these contracts are traded and quoted in the financial press are highlighted in the following sections.
Option contracts have been traded for centuries in the form of separate agreements or embedded in other securities. Malkiel, for example, tells the story of how call options were used to specu- late on flower prices during the tulip bulb frenzy in 17th-century Holland.1Then, and for most of the time until now, options were arranged and executed in private transactions. Collectively, these private transactions represent the OTC market for options. Like forward contracts, OTC option agreements can be structured around any terms or underlying asset to which two parties can agree. This has been a particularly useful mechanism when the underlying asset is too illiq- uid to support a widely traded contract. Also, credit risk is a paramount concern in this market because OTC agreements typically are not collateralized. This credit risk is one-sided with an option agreement because the buyer worries about the seller’s ability to honor his obligations, but the seller has received everything he will get up front and is not concerned about the buyer’s creditworthiness.
As in all security markets, OTC options ultimately are created in response to the needs and desires of the corporations and individual investors who use these products. Financial Option Market
Conventions
1See Burton G. Malkiel, A Random Walk Down Wall Street, 7th ed. (New York: Norton, 2000).
institutions, such as money-center banks and investment banks, serve as market makers by facilitating the arrangement and execution of these deals. Over the years, various trade asso- ciations of broker-dealers in OTC options have emerged (and, in some cases, faded), includ- ing the Put and Call Brokers and Dealers Association, which helped arrange private stock option transactions, and the International Swap and Derivatives Association, which monitors the activities of market makers for interest rate and foreign exchange derivatives. These trade groups create a common set of standards and language to govern industry transactions.
In April 1973, the Chicago Board of Trade changed the dynamics of option trading when it opened the Chicago Board Options Exchange (CBOE). Specializing in stock and stock index options, the CBOE has introduced two important aspects of market uniformity. Foremost, con- tracts offered by the CBOE are standardized in terms of the underlying common stock, the num- ber of shares covered, the delivery dates, and the range of available exercise prices. This stan- dardization, which increases the possibility of basis risk, was meant to help develop a secondary market for the contracts. The rapid increase in trading volume on the CBOE and other options exchanges suggests that this feature is desirable compared to OTC contracts that must often be held to maturity due to a lack of liquidity.
The centralization of the trading function also necessitated the creation of the Options Clear- ing Corporation (OCC), which acts as the guarantor of each CBOE-traded contract. Therefore, end users in option transactions ultimately bear the credit risk of the OCC. For this reason, even though the OCC is independent of the exchange, it demands the option seller to post margin to guarantee future performance. Again, the option buyer will not have a margin account because a future obligation to the seller is nonexistent. Finally, this central market structure makes moni- toring, regulation, and price reporting much easier than in the decentralized OTC markets.
Equity Options Options on the common stock of individual companies have traded on the CBOE since 1973. Several other markets, including the American (AMEX), Philadelphia (PHLX), and Pacific (PSE) Stock Exchanges, began trading their own contracts shortly after- ward. The CBOE remains the largest exchange in terms of option market volume with a market share of just under 40 percent, with the AMEX second at around 25 percent. Options on each of these exchanges are traded similarly, with a typical contract for 100 shares of stock. Because exchange-traded contracts are not issued by the company whose common stock is the underly- ing asset, they require secondary transactions in the equity if exercised.2
Panel A of Exhibit 23.1 displays price quotations for a sample of equity options as well as a summary of exchange-trading volume on February 14, 2002. To interpret this exhibit, suppose that an investor wanted to buy an option on Dell Computer common stock, a quote that is high- lighted on the chart. The first column indicates that Dell shares closed that day at a price of
$26.40, while the next two columns list the exercise prices and expiration months for the avail- able contracts. By convention, stock options expire on the Saturday following the third Friday of the designated month. The next two columns show the volume (number of contracts traded) and closing price, respectively, for Dell calls; the final two columns provide similar information for Dell puts.
Assume this investor wanted to buy a March 2002 Dell call with an exercise price of $25. This contract would cost a total of $260, calculated as the stated “per share” price of $2.60 multiplied by 100 shares. In exchange for that payment, the holder of this American-style call would then be able to exercise the option in mid-March—or any time before then—by paying $2,500 (=$25
× 100) and receiving 100 Dell shares from the option seller, who is obligated to make that Price Quotations
for Exchange- Traded Options
956 CHAPTER 23 OPTIONCONTRACTS
2Call options issued directly by the firm whose common stock is the underlying asset are called warrants. We discuss the use and valuation of these contracts in Chapter 24.
3Recall from Chapter 21 that a call option’s value can be divided into two components: the intrinsic value, which is the greater of either zero or the stock price minus the exercise price, and the time premium. In this example, the Dell call is said to be in the money because it has positive intrinsic value, whereas an option with no intrinsic value is out of the money.
exchange at the buyer’s request. That request will only be rational if the mid-March price of Dell is greater than $25. If that price closes below $25, the investor will simply let the call expire without acting on the option; that is her right as the derivative buyer. Finally, notice that with the February share price being $26.40, the investor could immediately recover $1.40 of the $2.60 she paid for the contract. Thus, her time premium of $1.20 (=$2.60 – $1.40) preserves her right to buy Dell stock at a price of $25 for the next month even if the market value of those shares moves higher.3
Consider another investor who sells the “March 25” Dell put. In return for an up-front receipt of $75 (=$0.75 ×100), he now must stand ready to buy 100 shares of stock in mid-March for
$2,500 if the option holder chooses to exercise his option to sell. The stock price will, of course, have to fall from its current level before this would occur. The investor in this case has sold an out-of-the-money contract and hopes that it will stay out of the money through expiration, let- ting the passing of time “decay” the time premium to zero. As we saw earlier, the front-end pre- mium is all that sellers of put or call options ever receive, and they hope to retain as much of it as possible. Like the long position in the call, the short put position benefits from an increase in Dell share prices.
Finally, notice that all the options listed in Panel A of Exhibit 23.1 expire within a few months of the quotation date. In fact, the expiration dates available for these exchange-traded contracts are the two nearest-term months (February and March for Dell) and up to two additional months from a quarterly cycle beginning in either January, February, or March. In the case of Dell options, May 2002 (which is part of the quarterly cycle beginning in February) is the additional month listed.
Panel B of the figure lists quotations for long-term equity anticipation securities (LEAPS), which are simply call and put options with longer expiration dates. Like the contracts just described, LEAPS are also traded on the CBOE and have comparable terms. For instance, a Dell call with the same $25 exercise price expiring in January 2003 would cost the investor $590 (=$5.90 ×100).
Thus, by extending the expiration date by ten months (i.e., from March 2002 to January 2003), the option’s price increases from $2.60 to $5.90. Of course, since these two contracts had the same exercise price, this difference is purely because of additional time premium. The effect that time to expiration has on the value of an option will be examined in greater detail shortly.
Stock Index Options As we saw in Chapter 21, options on stock indexes, such as Standard and Poor’s 100 or 500, are patterned closely after equity options; however, they differ in one important way: Index options can only be settled in cash. This is because of the underlying index, which is a hypothetical portfolio that would be quite costly to duplicate in practice. First traded on the CBOE in 1983, index options are popular with investors for the same reason as stock index futures: They provide a relatively inexpensive and convenient way to take an investment or hedging position in a broad-based indicator of market performance. Index puts are particu- larly useful in portfolio insurance applications, such as the protective put strategy described ear- lier and again at the end of this chapter.
Prices for four of the more widely traded contracts are listed in Exhibit 23.2. They are inter- preted in the same way as equity option prices, with each contract demanding the transfer of 100 “shares” of the underlying index. For example, the March S&P 500 index call and put con- tracts with an exercise price of 1,100 could be purchased for $3,810 (=$38.10 ×100) and $1,600 (=$16 ×100), respectively. On the expiration date, which will be the third Friday of the month, the
958 CHAPTER 23 OPTIONCONTRACTS
EXHIBIT 23.1STOCK OPTION QUOTATIONS A. Regular Expiration Dates
Source:The Wall Street Journal,15 February 2002. Printed with permission from The Wall Street Journal,Dow Jones & Co. Inc.
EXHIBIT 23.1STOCK OPTION QUOTATIONS (CONTINUED) B. Long-Term Equity Anticipation Securities (LEAPS)
960
EXHIBIT 23.2 STOCK INDEX OPTION QUOTATIONS
Source: The Wall Street Journal, 8 February 2002. Printed with permission from The Wall Street Journal, Dow Jones & Co. Inc.
holder of the call would exercise the contract to “buy” $110,000 worth of the index if the prevail- ing S&P 500 level is greater than 1,100, with the put being exercised at index levels less than 1,100.
Foreign Currency Options Foreign currency options are structurally parallel to the cur- rency futures contracts discussed in Chapter 22. That is, each contract allows for the sale or pur- chase of a set amount of foreign (i.e., non-U.S. dollar) currency at a fixed exchange (FX) rate. A currency call option is like the long position in the currency futures since it permits the contract holder to buy the currency at a later date. (Of course, unlike futures, options do not require that this exchange be made.) A currency put is therefore the option analog to being short in the futures market. These contracts exist for several major currencies, including the Euro, Australian dollars, Japanese yen, Canadian dollars, British pounds, and Swiss francs. The majority of cur- rency options trading, which began in 1982, occurs on the PHLX. Exhibit 23.3 shows quotes from a sample of the available CAD contracts, along with the spot foreign exchange rates for the same trading day.
Like the FX futures market, all the prices are quoted from the perspective of U.S.-based investors. Consider, for example, an investor who lives in New York and holds Canadian-dollar- denominated provincial government bonds in her portfolio. It is February, and when the bonds come due in one month, she will need to convert the proceeds back into U.S. dollars, which exposes her to a possible weakening in the Canadian currency. Accordingly, she buys the March put on the Canadian dollar with an exercise price of USD 0.63/CAD for a total price of USD 345.00 (=50,000 ×0.0069). This option would allow the holder to sell CAD 50,000 in March for a total price of USD 31,500 (=50,000 ×0.63). Obviously, our investor will only exercise the contract if the spot USD/CAD price prevailing in March is less than 0.63 (i.e., if the Canadian dollar weakened relative to the U.S. currency). Finally, because the spot rate is USD 0.62865/CAD, this option is in the money—that is, the contract price of 0.0069 consists of 0.00135 (=0.63 – 0.62865) of intrinsic value and 0.00555 of time premium.
Options on Futures Contracts Although they have existed for decades in the OTC mar- kets, options on futures contracts have only been exchange-traded since 1982. Also known as futures options, they give the holder the right, but not the obligation, to enter into a futures con- tract on an underlying security or commodity at a later date and at a predetermined price. Pur- chasing a call on a futures allows for the acquisition of a long position in the futures market, while exercising a put would create a short futures position. On the other hand, the seller of the call would be obligated to enter into the short side of the futures contract if the option holder decided to exercise the contract, while the seller of the put might be forced into a long futures position. Exhibit 23.4 lists quotations for options based on a wide variety of underlying assets, including agricultural, metal, and energy commodities; Treasury bonds and notes; foreign cur- rencies; and stock indexes. Consistent with the trading patterns for the futures contracts we examined earlier, futures options on financial assets represent the largest part of the market.
To understand how these contracts work, consider a commodity futures option. The April call option on copper with an exercise price of $0.76 per pound would cost the buyer $0.0180 per pound of copper covered by the futures position. As each copper futures contract on the Com- modity Exchange (CMX) requires the transfer of 25,000 pounds of the metal, the total purchase price for this futures call is $450 (=25,000 ×0.018). Also, because the April copper futures price on this day was $0.7475, this contract was out of the money so that its per-ounce price of 1.80 cents was purely a time premium.
As with any call position, the holder will only exercise at the expiration date if the prevailing price of the underlying asset exceeds the exercise price; she will let it expire worthless otherwise.
This payoff structure might fit the need of an electronic appliance manufacturer exposed to higher copper prices as a factor of production or a speculator bullish on copper prices. In this
962 CHAPTER 23 OPTIONCONTRACTS
EXHIBIT 23.3 FOREIGN CURRENCY OPTION QUOTATIONS
© 2002 Bloomberg L.P. All rights reserved. Reprinted with permission.
Source: The Wall Street Journal, 15 February 2002. Printed with permission from The Wall Street Journal, 963
Dow Jones & Co. Inc.
964 CHAPTER 23 OPTIONCONTRACTS
example, suppose that on the expiration date of the option, the contract price of the April copper futures has risen to $0.79. At this point, the holder will exercise her option and assume a long position in an April futures with a contract price of $0.76 per pound, which will require posting a margin account. Her new position will immediately be marked to mar- ket, however, and $750 (= [0.79 – 0.76] × 25,000) will be added to her margin account.
Alternatively, she may decide to unwind her “below market” futures contract immediately and take the $750 in cash.
The primary attraction of this derivative is the leverage that it provides to an investor. In this example, the call buyer has been able to control 25,000 pounds of copper for two months for an investment of $450. Had she purchased the copper, it would have cost her $18,687.50 (=25,000 ×0.7475), assuming that the spot and futures prices were the same on this date. Fur- ther, even if it only required a 5 percent margin, a long position in the copper futures contract would necessitate a cash outlay of $934.38. Since leverage is the driving force behind this mar- ket, in most cases the option is set up to expire at virtually the same time as the underlying futures contract. This indicates that actually acquiring a futures position is not a primary con- cern of the option users.
THE FUNDAMENTALS OF OPTION VALUATION
Although we know that options can be used by investors to anticipate future levels of security prices, the key to understanding how they are valued comes from recognizing that they also are risk reduction tools. Specifically, in this section we show that an option’s theoretical value depends on combining it with its underlying security to create a synthetic risk-free portfolio. That is, it always is theoretically possible to use the option as a perfect hedge against fluctuations in the value of the asset on which it is based.
Recall that this was essentially the same approach we used in Chapter 21 to establish the put- call parity relationships. The primary differences between put-call parity and what follows are twofold. First, the hedge portfolio implied by the put-call parity transaction did not require spe- cial calibration; it simply consisted of one stock long, one put long, and one call short—a mix- ture that required no adjustment prior to the expiration date. However, hedging an underlying asset position’s risk with a single option position—whether it is a put or a call—often involves using multiple contracts and frequent changes in the requisite number to maintain the riskless portfolio. Second, the put-call parity paradigm did not demand a forecast of the underlying asset’s future price level whereas the following analysis will. Indeed, we will see that forecast- ing the volatility of future asset prices is the most important input the investor must provide in determining option values.
While the mathematics associated with option valuation can be complex, the fundamental intu- ition behind the process is straightforward and can be illustrated quite simply. Suppose you have just purchased a share of stock in WYZ Corp. for $50. The stock is not expected to pay a divi- dend during the time you plan to hold it, and you have forecast that in one year the stock price will either rise to $65 or fall to $40. This can be summarized as follows:
The Basic Approach
TODAY ONEYEAR
65 50
40
Suppose further that you can either buy or sell a call option on WYZ stock with an exercise price of $52.50. If this is a European-style contract that expires in exactly one year, it will have the following possible expiration date values:
Although you do not know what the call option is worth today, you know what it is worth at expi- ration, given your forecast of future WYZ stock prices. The dilemma is establishing what the option should sell for today (i.e., C0).
This question can be answered in three steps. First, design a hedge portfolio consisting of one share of WYZ stock held long and some number of call options (i.e., h), so that the combined position will be riskless. The number of call options needed can be established by ensuring that the portfolio has the same value at expiration no matter which of the two forecasted stock val- ues occurs, or
65 +(h)(12.50) =40 +(h)(0) leaving
There are both direction and magnitude dimensions to this number. That is, the negative sign indicates that, in order to create the necessary negative correlation between two assets that are naturally positively correlated, call options must be sold to hedge a long stock position. Further, given that the range of possible expiration date option outcomes (i.e., 12.5 – 0) is only half as large as the range for WYZ stock (i.e., 65 – 40), twice as many options must be sold as there is stock in the hedge portfolio. The value h is known as the hedge ratio.4Thus, the risk-free hedge portfolio can be created by purchasing one share of stock and selling two call options.
The second step in the option valuation process assumes capital markets that are free from arbitrage. Specifically, suppose no arbitrage possibilities exist in these markets so that all risk- less investments are priced to earn the risk-free rate over the time until expiration. That is, the hedge portfolio costing $[50 – (2)(C0)] today would “grow” to the certain value of $40 by the following formula:
[50 – (2.00)(C0)](1 +RFR)T=40 where:
RFR=the annualized risk-free rate T=the time to expiration (i.e., one year)
h= −
− = −
( )
(65 40. ) .
0 12 5 2 00
TODAY ONEYEAR
max[0,65 – 52.5] =12.50 C0
max[0,40 – 52.5] =0
4In some valuation models (e.g.. Black-Scholes), the hedge ratio is expressed as the option’s potential volatility divided by that for the stock. In this example, that would be (0 – 12.5) ÷(65 – 40) =–0.5, meaning that the option is half as volatile in dollar terms as the share of stock. Of course, this alternative calculation is just the reciprocal of the value of h=–2.00.