option holder exercises his option, the clearing corporation assigns any party holding a short position on a random, arbitrary basis. Anoption buyer never ﬁnds out, nor does he care, who sold the option to him.An option seller never ﬁnds out, nor does he care, who bought the optionfrom him.Listed options have many attractive features. For one thing, severalstrike prices are usually available at regular price intervals. Also, severaldifferent durations (expiration dates) are usually available, following a setpattern. In stocks, for example, one set of options expires in 30 days orless, another set of options expires in approximately 31 to 60 days, anotherset expires in approximately 3 to 6 months, and so on, going out as far as 2years or more.Each listed option is standardized for the same quantity of the underlying asset. In the United States, for example, one stock option is based on100 shares of an underlying stock, and one futures option is based on onefutures contract. By standardizing options contracts, the exchanges makethem appealing to large groups of investors, which results in heavy tradingand a liquid market.As the markets are constantly moving, options prices are continuouslyquoted and changing. Market makers at the options exchanges are alwayspublicly posting prices at which they are willing to buy and sell each option. They stand ready to take the other side of your trade, and thus makea market in the options they are responsible for. This allows an optionholder to sell his option(s) at any time, and an option writer may buy toclose his position at any time.In the real estate example discussed previously, it is very possible,even likely, that the option holder will exercise his option prior to expiration. In contrast, the vast majority of listed option buyers never exercisethem; they simply sell them back on the open market. Many of these people are speculators who only expect to hold their option for a short time.Once the underlying makes a move in the expected direction (or perhaps amove in the wrong direction) they sell. In a sense, options are like hotpotatoes being tossed around among speculators. This accounts for quite abit of the options trading volume.Another big source of trading volume is institutional trading. Institutions may use options to hedge large positions, or simply trade large positions for speculation.
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THE LANGUAGE OF OPTIONS
So far we have only talked about options to buy. Options to buy something at a stated price for a limited time are call options. There is anothertype of option: an option to sell something. While these options can be abit more difﬁcult to conceptualize, options to sell something at a statedprice for a limited time are put options.
NOMENCLATUREAn option is identiﬁed by stating its underlying asset, the expirationmonth, the strike price, and the type (call or put), usually in that order.For example,Motorola April 20 callswould deﬁne an option expiring in April of this year. If the option expiresmore than a year from now, one might need to include a year indication ofsome kind, as in the following example.Motorola April04 20 callsIn this example, “04” means the year 2004.Also important is the way options prices translate into dollaramounts. Most stock options have a multiplier of 100, based on the factthat one option is for 100 shares of stock. So if you were to buy one option at a price of 2.20, for example, you would pay $220. Most index options also have a multiplier of 100. Multipliers for futures-based optionsvary from 50 to 500 or so.
LONGS AND SHORTSMost investors are familiar with being long, whether they realize it or not.When you own something, you are said to have a long position in it. Whenyou are long in the market, it means you hope to make a proﬁt from a rising market.Going short means to sell something, without ﬁrst owning it, to proﬁtfrom a falling market. The concept of going short can be confusing at ﬁrst.How can you sell something you don’t own? In securities, going short involves borrowing the securities (usually from your broker) to sell. Later, toclose the position, you buy, giving the shares back to your broker. With instruments such as futures and options, it’s much easier. You’re entering
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A Bit More Terminology
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into an agreement to buy or sell—that’s all. It is a contract with rights andobligations like any other contract. The only difference is that with futuresand options, you may get out of the contract at any time by placing an order that cancels your position before the obligations come due.However, the concepts of long and short are a bit more involved whenworking with options. When you buy an option, you are long the option.With a call option, you stand to beneﬁt from the underlying going up, soyou can be considered to be, in a general sense, long the underlying aswell. However, when you buy a put option, you stand to beneﬁt from theunderlying going down, so you can be considered to be, in a general sense,short the underlying. Table 1.2 summarizes the four possible scenarios.
A BIT MORE TERMINOLOGYNow just a bit more terminology, and then we can look at why options aresuch an interesting trading vehicle.It is very important that the options trader be familiar with the termsand concepts. In this section, the examples refer to stock options. However, the same terms and concepts apply to all asset types.The value of an option is comprised of two components: intrinsicvalue and time value. You’ll never see these two components quoted separately. You’ll just see the total price of the option. Nevertheless, it is important to realize that the value of an option comes from these two elements.To draw an analogy, the value of a company can be said to consist of(a) book value plus (b) all the rest. Book value, meaning what the company is worth if one were to break it up and sell all its assets, is like an option’s intrinsic value. All the rest, including good will and the potential forfuture earnings, is like an option’s time value.An option’s intrinsic value is what you could gain by exercising the option and immediately closing your new position in the underlying. For example, say the price of IBM is 100 and you have a 95 call. If you were to exerciseyour option, you’d pay 95 for the stock. Then you could immediately sell the
TABLE 1.2 Four Possible ScenariosPosition
Exposure
Long callsShort callsLong putsShort puts
Long the underlyingShort the underlyingShort the underlyingLong the underlying
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THE LANGUAGE OF OPTIONS
stock on the market for 100, realizing a proﬁt of 5. Thus, the intrinsic value ofthe option is 5.An option is said to be in the money when it possesses some intrinsicvalue. Call options are in the money when their strike price is below thecurrent price of the underlying (as in the preceding example). It’s the reverse for put options. Puts are in the money when their strike price isabove the current price of the underlying.When an option’s strike price is equal to (in practice, very close to) theprice of the underlying, it is said to be at the money.Call options are said to be out of the money when their strike is abovethe current price of the underlying. Puts are out of the money when theirstrike is below the current price of the underlying. (See Figure 1.1.)Time value, the other component of an option’s value, represents thepossibility of the underlying moving in the option’s favor (up for calls,down for puts) during the remaining life of the option. “Isn’t it just as possible for the stock to move the wrong way?” one might ask. Yes it is. However, if the stock moves the wrong way, an option’s value can drop, atmost, to zero. On the other hand, if the stock moves the right way, the option’s value can, theoretically, go up without limit. That is why options almost always have some time value. Time value represents the summationof all the possible intrinsic values the option might have, at all the differentunderlying prices possible on or before expiration, factoring in the probabilities of the stock reaching each of those prices.
FIGURE 1.1 Strike Price
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A Bit More Terminology
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Time value can be a challenge to estimate. For that reason, optionstraders refer to mathematical models, implemented in computer programs, to compute the fair value of an option.In the previous IBM example, we showed how an in-the-money optioncould be exercised to get into a stock position at below market price.Would it ever make sense to exercise an out-of-the-money option?The answer is no. To exercise an out-of-the-money call would be topay more than the current market price for a stock. To exercise anout-of-the-money put would be to sell a stock for less than the currentmarket price of the stock. It never makes sense to exercise an out-ofthe-money option.In fact, it seldom makes sense to exercise an in-the-money option either. Why? Because you’d be throwing away its time value. Let’s illustratethis by extending the IBM example. You have a 95 call and the stock is currently at 100. Your call, if it has more than a few days of life left, is probably worth something more than 5; let’s say 6.5. (This would be an intrinsicvalue of 5 plus a time value of 1.5.)If you exercise the option and then sell the stock, as before, you gain$500 on the stock transaction. However, you no longer have an optionworth $650. Thus, you lost $150—the option’s time value. It would be better to sell your option on one of the options exchanges. Not only do you recover the full value of your option this way, but it is also simpler to do justone option transaction, versus two transactions the other way.Here is a little pop quiz to see if you have grasped the concepts wehave been discussing.1. A stock is at 60. A 65 call on this stock has a price of 1.75. Is this option
in-the-money, at-the-money, or out-of-the-money? What is this option’sintrinsic value? What is this option’s time value?Answers: The option is out-of-the-money and has an intrinsic value ofzero and a time value of 1.75.2. A stock is at 70. A 60 call on this stock has a price of 11.40. Is this op-
tion in-the-money, at-the-money, or out-of-the-money? What is this option’s intrinsic value? What is this option’s time value?Answers: The option is in-the-money, has an intrinsic value of 10 and atime value of 1.40.3. A stock is at 50. A 55 put on this stock has a price of 6.60. Is this option
in-the-money, at-the-money, or out-of-the-money? What is this option’sintrinsic value? What is this option’s time value?Answers: The option is in-the-money, has an intrinsic value of 5 and atime value of 1.60.
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THE LANGUAGE OF OPTIONS
4. A stock is at 50. A 50 call on this stock has a price of 3.20. Is this option
in-the-money, at-the-money, or out-of-the-money? What is this option’sintrinsic value? What is this option’s time value?Answers: The option is at-the-money, has an intrinsic value of zero anda time value of 3.20.One ﬁnal question: In question 2 above, do you think this option couldtrade below 10 (its intrinsic value)?Answer: Yes it could. Anything could happen in an open market.However, practically speaking, it would not trade for much less than 10.That is because traders are constantly watching the options markets forbargains, and snap them up in an instant. So if you were to offer this option for sale at, say, 9.8, someone would quickly buy it from you, becausethey know they can immediately exercise it and sell the stock, realizing a0.20 point proﬁt.Even if an option’s time value has dropped to zero, it is always worthits intrinsic value, and you should be able to sell it for intrinsic value, orperhaps just a bit less. Thus intrinsic value serves practically as a “ﬂoorlevel” for the price of an option. When an option is trading at intrinsicvalue, it is said to be trading at parity.Previously, I pointed out that a great many options are never exercised. It does not make sense to exercise an option that has any appreciable time value; you’d be throwing away money. However, it is whenan option’s time value is zero or nearly zero that option holders arelikely to exercise. Conversely, if you sell (short) an option with zero ornearly zero time value, you are apt to be assigned—and it can happenthat very day.Early assignment may or may not be a signiﬁcant danger to you. It depends on the nature of the position you would be left holding. (More willbe said on this in Chapter 4.)
OFFSETTING OPTION TRADESThe only way to close an option position before expiration is to do the opposite transaction in the marketplace. This applies to both puts and calls,whether long or short. When you have bought a call, the only way to ridyourself of the position is to sell the same call. Buying a put will not do it.Selling some other call on the same underlying does not do it. Such tradesmight reduce your risk, but they would only build (and complicate) youroriginal position.
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American versus European
11
EXPIRATION, EXERCISE, AND ASSIGNMENTThe alternatives to closing a position with an opposite transaction are tolet the option expire or to exercise it. If the option is out-of-the-money atexpiration, it has no value and therefore should be allowed to expireworthless. However, if the option is in-the-money at expiration, it hasvalue and should be exercised.When you exercise a stock option, you pay for and receive shares ofstock. This is an important point to remember. Let’s say you have a longcall position that gives you the right to buy 100 shares of a stock at $50. Ifyou intend to exercise it, make sure you have enough in your account tocover the $5,000 payment you need to make! Futures and index optionswork differently. When you exercise futures options, you are immediately in a futures position and no cash changes hands. When you exercise index options, you simply receive the intrinsic value as a cashsettlement. For example, if you have an index option that is 4.00 in-themoney at expiration, you receive $400 posted to your account. There isno delivery of anything (besides cash), and it does not create a new position in another security.It is not always required that the option holder submit an exercise notice. Exercise is automatic for some instruments if the option is a certainamount in-the-money. It is important to understand what will happen ifyou do nothing with an in-the-money option at expiration. Speak with yourbroker if you are unsure. It never hurts to submit an exercise notice, asyou would not want to let a valuable option just disappear!
AMERICAN VERSUS EUROPEANOptions can also be classiﬁed in terms of style, which relates to the twoways in which they can be exercised. If an option can be exercised anytime up until expiration, it is said to be American style. However, manyoptions can be exercised only on expiration day. These are said to be European style. Note: This is not a reference to which continent the optionstrade on. Both American and European style options trade in America, Europe, and on other continents.In the United States, all stock options and more than half of the indexoptions are American style; the remaining index options are Europeanstyle. Some futures-based options are American style and others are European style.An option buyer intending to exercise needs to know which style options he is getting. An option seller might prefer European style options,
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THE LANGUAGE OF OPTIONS
because he’d rather not be concerned about being assigned before expiration. For the options buyer who has no intention of exercising, the onlydifference is that American style options are a bit more valuable—and aquality options pricing model will bear this out.
QUOTATIONSFigure 1.2 illustrates how options are quoted in two popular businessnewspapers. Both identify the underlying stock in boldface type and listseveral options per stock. For each option, they print the option’s expiration month, strike, last trade price, and day’s volume. Note that many moreoptions exist than what is shown. One newspaper lists only actively tradedoptions and the other apparently lists only the nearby options (the onesexpiring the soonest).More complete listings can be seen in trading software, as in the example in Figure 1.3. This matrix of IBM options shows the stock price, today’s price change, and volume (number of shares traded), as well as theprice, change, and volume for 42 of IBM’s options. Even more options areavailable at strikes above and below those shown (and could be seen by
FIGURE 1.2 Option Quotes
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Quotations
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FIGURE 1.3 IBM as Seen on Trading Software
scrolling vertically), as well as farther out expiration dates (which couldbe seen by scrolling to the right).This illustrates the rather large array of options available on manystocks and other types of ﬁnancial instruments. The strike prices areshown vertically at ﬁve-dollar (“nickel”) intervals. The options are separated into two sections: calls in the upper section and puts in the lowersection. In each section, the row where the strike is marked with a “>” represents the closest-to-the-money strike. In the top section (calls), rowsabove that mark represent progressively farther out-of-the-money strikes,while rows beneath it represent progressively farther in-the-money strikes.In the bottom section (puts), the reverse is true, since strikes are listed inthe same numerical order.You might want to take a few moments to study how option pricesvary by strike and by expiration. Can you see the smooth progression fromexpensive to cheaper options as you go from in-the-money toward out-ofthe-money? Also, options expiring the soonest (called the nearbys) are inthe left column, while farther out options ﬂow to the right. Do you see thatthe farther out options (with more time remaining) are more valuable thanthe nearby options?
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THE LANGUAGE OF OPTIONS
As this was a signiﬁcant down day for IBM, with the stock dropping 5points, you can see the relative amounts by which the call options droppedand the put options gained in value. Higher-priced options changed themost. However, lower-priced options probably changed by greater percentage amounts. Also note that trading volume is especially concentratedin the nearby expiration months and in those options closest to the money.Many of these options traded thousands of contracts on this day.
THE SPECIAL PROPERTIES OF OPTIONSOptions have some unique properties that make them very special as atrading vehicle. For starters, unlike stocks and futures, their performanceis nonlinear. Every point a stock or futures contract moves results in thesame amount gained or lost. Their performance graph is a straight line(see Figure 1.4).In contrast, an option’s performance graph curves upward, meaningthat as the underlying moves in favor of the option, the option makesmoney faster. Yet, as the underlying moves against the option, the optionloses money slower. (In Figure 1.5, focus on the dotted line, which represents today’s performance of the option.)The fact that the performance line curves upward like this, and that ultimately an option’s value can go up without limit but can drop only tozero, is a very attractive feature for option buyers.
FIGURE 1.4 Straight Line
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Time
15
FIGURE 1.5 Curved Line
TIMEAnother property of options is a pesky little thing called “time decay.” Withthe passing of time, all other things being equal (i.e., the underlying pricehas not changed), an option’s value falls. In Figure 1.5, the dashed line represents the theoretical value of this call option 64 days from now (halfwayto expiration), while the solid line represents the theoretical value of theoption at expiration. As you can see, if the stock does not move above 25(the strike price of this option), the value of this option will fall graduallyand inexorably to zero.Many options traders are attracted to selling options (rather than buying them) in order to put this time decay property in their favor. While it iswonderful to have time working in your favor, this can convey a falsesense of security. Time is precisely what gives the underlying a chance tomove—potentially against the option seller’s position.So there is a trade-off. The option buyer has the nonlinear performance line of an option in his favor, but time works against him. The option seller has time in his favor, but the nonlinear performance line of theoption works against him.To limit the damage of time decay, the option buyer may determine tohold his position for only a short time. To limit the damage from an adverse price movement, the option seller may decide to use a stop order.
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THE LANGUAGE OF OPTIONS
Time DecayThe traditional time decay curve that is frequently given in options booksand literature is depicted in Figure 1.6.
OptionValue
TimeFIGURE 1.6 Traditional Time Decay Curve
It is important for the option trader to understand that this is onlycorrect for at-the-money options. In-the-money and out-of-the-money options have different time decay curves (see Figures 1.7 and 1.8).
OTMOptionValue
TimeFIGURE 1.7 In-the-Money
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Time
ITMOptionValueIntrinsic Value
TimeFIGURE 1.8 Out-of-the-Money
To visualize how time decay works for options at different “money”levels, consider this analogy. You have a funnel full of liquid that is slowlydraining out. The center of the funnel represents at-the-money options. Tothe left of center are the progressively in-the-money options and to theright are the progressively out-of-the-money options (see Figure 1.9).
FIGURE 1.9 Funnel Analogy(Continued)
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THE LANGUAGE OF OPTIONS
The depth of the liquid at various places represents how much timevalue remains in these options. For instance, the depth of the liquid in themiddle shows that the at-the-money options have the greatest time value.The deep in-the-money and far out-of-the-money options, where the liquidis shallowest, have the least time value.Now visualize the liquid slowing draining out. As the surface levelgradually drops, the deep in-the-money and far out-of-the-money optionswill be the ﬁrst to lose all of their time value. Over time, the liquid’s surface level will drop faster, because the drainage rate is constant and thereis less surface area. Eventually, the at-the-money options will be the onlyones with any time value, and that will be slipping away faster than everas very little liquid remains in the funnel. At the expiration date, all of theliquid has drained, and none of the options have any time value.In truth, at-the-money options have faster time decay (a higher theta)than in-the-money and out-of-the-money options, so this analogy is notentirely correct. To be more accurate, we would need to begin the analogywith the surface of the liquid somehow “heaped up” near the center, andpicture the surface of the liquid gradually ﬂattening out over time as theat-the-monies lose time value faster.
VOLATILITYThe other unique property of options is their sensitivity to volatility. Optionson more volatile assets, all else being equal, are more expensive. Options onless volatile assets are cheaper. This can make a big difference. Even options on the same underlying can be twice as expensive during a periodwhen the asset’s price is perceived to be volatile than during quieter periods.This gives options an extra dimension. Not only can options be tradedbased on expected price moves in the underlying (called directional trading), but they may also be traded based on expected swings in volatilitylevels. You would buy options when volatility is low and the options arecheap, and sell options when volatility is high and the options are expensive. This kind of trading is called volatility-based trading, and is discussedin detail in Chapter 3.
HOW OPTIONS RESPOND TO CHANGING CONDITIONSAs we have learned, options can be said to have (and move in) three dimensions: (1) price, because options respond to changes in the price of
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The Greeks
their underlying; (2) volatility, because options respond to changes in theperceived volatility of their underlying; and (3) time, because an option’svalue decays over time, all else being constant.The ﬁrst two dimensions are tradable, as these elements ﬂuctuate, giving traders the opportunity to speculate on their future direction. Time isdifferent. While a trader may put time on his side by selling options, time isnot quite the same as the dimensions of price and volatility. Time onlymarches forward, and the effect of time decay is very gradual, acceleratingsomewhat for an at-the-money option approaching expiration.One other factor that affects option prices is a change in interest rates.However, this effect is very small, and it will not be discussed in much detail in this book.It is important to understand how changes in all these factors affectthe value of options. Changes in the underlying price or interest ratescause the values of calls and puts to move in opposite directions. For instance, when the price of the underlying goes up, calls go up and puts godown. Volatility and time affect calls and puts in the same way. When theunderlying becomes more volatile, both the calls and the puts go up invalue. With the passing of time, both calls and puts decline in value.How changing conditions affect option values is summarized inTable 1.3.
THE GREEKSOptions traders use several parameters, named after Greek letters, thattell them how sensitive an option is to changing conditions.The ﬁrst of these is delta. Delta measures how much the price of anoption moves in response to a one-point increase in the price of the underlying. For example, if an option moves up 0.5 when its underlying moves
TABLE 1.3 How Changing Conditions Affect Option Values
Underlying price goes upUnderlying price goes downVolatility goes upVolatility goes downTime passesInterest rates increaseInterest rates decrease
Call Options
Put Options
Go upGo downGo upGo downGo downGo upGo down
Go downGo upGo upGo downGo downGo downGo up
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THE LANGUAGE OF OPTIONS
up 1.0, the option’s delta is said to be 50, because you would theoreticallygain $50 per option contract.Since the values of call and put options move in opposite directionswith a change in the underlying price, calls have positive deltas and putshave negative deltas. Call options have deltas ranging from 0 to 100, whileput options have deltas ranging from –100 to 0.Note that at-the-money calls typically have a delta close to 50, whileat-the-money puts typically have a delta close to –50. To illustrate this, let’scontrast buying 100 shares of stock versus buying one at-the-money call. Ifthe stock goes up one point, the stockholder gains $100. However, the option holder will theoretically gain $50. So why not just buy the stock then,since it makes more money? Because the option costs much less than thestock, and gains a greater percentage. Note that buying two of these options would obtain the same delta as buying 100 shares of the stock. Andtypically, two (or even 10 or more) of these options cost less than 100shares of stock.Another greek, vega, measures how much the price of an optionmoves in response to a one-point increase in volatility. For example, if anoption has a vega of 23, and volatility increases from 18% to 19%, the option’s price will increase by 0.23 and its value by $23. All options have positive vega.Theta measures how much the price of an option should drop today,due to the passage of time. For example, if an option has a theta of –5, itsprice should fall 0.05, and its value by $5, by the end of the day. All optionshave negative theta.Rho measures how much the price of an option should change (positive for calls and negative for puts) in response to a one-point increase ininterest rates. For example, if a call option should increase 0.02 when interest rates go up one point, the option’s rho is said to be 2.All the greeks are theoretical. That is, they measure how an optionshould respond to changing conditions. The same mathematical modelsused to calculate an option’s fair value also produce the greeks as byproducts. That’s important to understand. Just as an option’s fair valueconstantly changes in response to changing inputs, the greeks alsochange. In fact, there is another greek—gamma—that’s just for measuring how fast delta changes!Sophisticated options traders use the greeks to gauge their risk, asthe greeks reveal the exposures of their current position. In a way, thegreeks are more valuable the more complicated the position gets. For example, market makers often hold positions (long and short) in many different options on a particular asset. By viewing the net greeks of theirposition (computed by adding up the greeks of each option in which they
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The Role of the Market Maker
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have a position, times the number of contracts they have in each option),they can determine their net risk, and make adjustments if necessary.For example, if they see that their net delta is –617, they may buy 600shares of stock to change their net delta to –17, bringing it reasonablyclose to zero, or delta-neutral. Holding a delta-neutral position meansthe total position value should remain unchanged when the price of theunderlying changes.
THE ROLE OF THE MARKET MAKERIndividual investors seldom trade with each other. More often, thoughnever knowing it, they trade with market makers. Market makers mustpost two prices for every option: the price they are willing to buy it for (thebid price) and the price they are willing to sell it for (the asked price). Market makers are bound by agreement with the exchanges to post bid and