when I speak of calls being more expensive than puts, or viceversa, I mean in terms of IV levels. IV is the deﬁnitive parameter for judging cheapness or dearness of options. Next to price, IV is the most important parameter to have in view when looking at the array of options on aparticular asset. IVs are usually fairly uniform across the array or, if thereis a skew, IVs usually vary in smooth, regular intervals. Any anomalyshould jump right out—it would be a mispriced option.In terms of absolute price levels, it is natural for a perfectly at-themoney (ATM) call to be more expensive than the corresponding put whenthe underlying is a stock or index. This is because stocks, costing hardcash and the opportunity to earn interest on it, are discounted to the present. That means stock prices (and stock indexes as well) are on a long,gradual upward slope at the rate of general interest rates. This might seemdifﬁcult to believe, because such movement is masked by the noise ofdaily price ﬂuctuations, but it’s true. It has to be so in order to compensatefor the lost opportunity to earn interest.On the other hand, a perfectly ATM call should be the same price as itscorresponding put when the underlying is a futures contract. This is because the futures contract does not cost cash. Yes, you have to put up col-
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lateral, but that collateral can be cash in a money market fund or someother security. For this reason the Black model—the correct options pricing model to use for options on futures—is simpler than the Black-Scholesmodel, yet essentially the same in other respects.
THE GREEKS REVISITEDYour automobile has one gauge that tells you its velocity. An airplane hasseveral gauges—one for ground speed and others to show how the airplane is moving in space. As we saw in Chapter 1, in options, there are fourgauges. They have Greek names, so we call them the greeks. Paul Forchione, in his book Trading Options Visually, discusses the greeks sowell, I couldn’t top him. So this section is reprinted with his permission:Understanding the relative impact of the greeks on positions youhold is indispensable. Here are a few general observations.The delta of an at-the-money option is about 50. Out-of-themoney options have smaller deltas and they decrease the farther outof-the-money you go. In-the-money options have greater deltas andthey increase the farther in-the-money you go. Call deltas are positive and put deltas are negative.When you sell options, theta is positive and gamma is negative.This means you make money through time decay, but price movement is undesirable. So proﬁts you’re trying to earn through optiontime decay when you sell puts and calls may never be realized if thecommodity moves quickly in price. Also, rallies in price of the underlying asset will cause your overall position to become increasingly delta short and to lose money. Conversely, declines inunderlying asset price will cause your position to become increasingly delta long and to lose money.When you buy options, theta is negative and gamma is positive.This means you lose money through time decay but price movementis desirable. So proﬁts you’re attempting to earn through volatilemoves of the underlying asset may never be realized if time decaycauses losses. Also, rallies in price result in your position becomingincreasingly delta long and declines result in your position becoming increasingly delta short.Theta and gamma increase as you get close to expiration (theyespecially accelerate 30 days prior to expiration) and they’re greatest for at-the-money options. This means the stakes grow if you’reshort at-the-money or close-to-the-money options near expiration be-
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cause either the put or call can easily become in-the-money andmove point for point with the underlying. You can’t adjust quicklyenough to accommodate for such a situation.When you sell options, vega is negative. This means if impliedvolatility increases, your position will lose money, and if it decreases your position will make money. When you buy options, vegais positive, so increases in implied volatility are proﬁtable and decreases are unproﬁtable.Vega is greatest for options far from expiration. Vega becomesless of a factor while theta and gamma become more signiﬁcant asoptions approach expiration.For me, trading is the ongoing pursuit of proﬁts while mathematically managing risk. I think of trading in terms of sets of numbers that continually evolve.At any point in time, every options position can be reduced to aset of four numbers: delta, gamma, theta, and vega. These numbersare referred to as “the greeks” of a position. An options pricing program will calculate these greeks regardless of how many long andshort strike prices are involved in the position. Together, as a set ofnumbers, these greek parameters become a “snapshot-in-time”which shows the expected impact upon the overall position of various changes that may occur.For example, delta tells you how long or short your position is.Gamma tells you how quickly your delta will change as the underlying moves. Theta is the dollar gain of your position in one day fromtime decay (negative if you are losing money). And vega is theamount your position will proﬁt or lose if implied volatility changes.I look at these four numbers as a unique, comprehensive description of my position at that moment in time. These numbers aredynamically interrelated. They will change as time goes by and asmarket circumstances change (the underlying rallies or declinesand/or option implied volatility increases or decreases).For that reason, throughout the day I review my delta, gamma,theta and vega exposure and continually make decisions about reallocating my risk among the four greeks. My decisions are basedon an assessment of how I see the current market environment unfolding as well as on my personal risk proﬁle. I stand ready tomodify my positions if and when I judge they’re vulnerable to mymarket assessment.There are times I want to be “delta neutral” because I don’t wantto run the risk of losing money if I’m wrong about market direction.There are also times I want to intentionally bias my delta one wayor the other.
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Viewing the proﬁt/loss curve of my options positions and adjusting my positions so the curve reﬂects my expectation of futurevolatility and price movement is what trading is all about. Theslope, or curvature, of my proﬁt/loss curve tells me the degree of riskI’m taking with respect to movement in the underlying asset, andwhat differentiates one volatility trader from another is the degreeof curvature each is comfortable with.Even if you and I share the same market opinion, trading decisions you make frequently will be different than mine because yourtolerance for risk is different. You may be more willing to be signiﬁcantly delta long or short. Or you may be less inclined to take vegarisk or more willing to accept unfavorable, negative theta. There areseveral ways for our decisions to diverge. It’s not that one approachis right and another is wrong. It’s a matter of understanding whereyou’re taking risk at that exact moment and consciously deciding ifyou want to make any changes in your exposure. You may decide tomake no changes now, but you must be open to modifying your position later that day or tomorrow if there are changes in the market orin your comfort level.I’m often asked “What’s the best bullish (or bearish) trade in aparticular commodity?” My response is always the same: There isno “best” directional trade because what’s best for you is probablydifferent than what’s best for me, even if we’re both bullish.Why? Your risk proﬁle is different than mine. You may be willing to lose money through negative time decay if you’re setting yoursights on large potential proﬁts. I, on the other hand, may have moremodest proﬁt expectations and don’t want to incur signiﬁcant negative time decay. As a result, the bullish trade I do (e.g., credit putspread) will be different than the one you do (e.g., bull call spread orlong call).3
TRUE DELTA AND GAMMAStandard pricing models produce delta and the other greeks as a byproduct. All too often, these models compute delta and gamma assuming a constant volatility. However, we know that volatilitychanges with changes in the price of the underlying. Even when pro-
3
Paul Forchione, Trading Options Visually (Smithtown, NY: Trade Wins, 1998),pp. 123–124, 128–129.
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jecting a very small change in the price of the underlying, volatilitymay change a small but important amount. When delta and gamma arecomputed by taking this into account, projecting a small change involatility (based on the skew model and CEV) to accompany a projected small change in the price of the underlying, the result is truedelta and gamma—more accurately representing the true behavior ofthe option.The difference this makes is sometimes very signiﬁcant. Take farOTM put options on the Standard & Poor’s (S&P 500) futures, for example. One put, at the time of this writing, has a delta of 9.32 using the standard model but a delta of 6.63 using the true delta model. While this maynot seem like much of difference in absolute terms, the trader who takesa large position in these puts will see a very wrong net delta using thestandard model and, perhaps without being aware of it, construct an imbalanced hedge.
UNDERSTANDING THE LIMITATIONS OF YOUR MODELDirty Harry once said, “A man’s got to understand his limitations.” WhileHarry was probably referring to the greedy, unrestrained mind of a criminal, I’m going to say that options traders have got to understand the limitations of the models they are using.We once heard from a customer who lost money on a trade that hissoftware had “picked” for him. Options trading software is just amodel. All models, while valuable, have their limitations. Traders whohave gained a mastery over their software understand not only howvaluable the models are, but also where the sources of risk, or uncertainty, lie.Here is what options analysis software can do with precision: With aprice projection for the underlying and a projection for volatility levels (orat least an assumption that current levels will continue), the program canaccurately project the future fair values of options involved in your position. The marketplace follows these models very well. In other words,the options marketplace is not going to abandon conventional pricingmodels any time soon and run amok. If you enter what turns out to be anaccurate prediction of the price of the underlying, as well as an accuratevolatility projection, then the option price(s) the program says will bethere at the future date will be extremely close. That much options analysis software can do.There are three things an options analysis program cannot predict,which the user must provide.
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1. Price movement of underlying. Options analysis software makes no
attempt to predict the future price direction of an underlying asset.That is why a graphic analysis has price as the horizontal axis—so youcan see what happens to your position across a broad range of underlying asset prices.2. Volatility changes—overall, intermonth, and interstrike (skew)
changes. In times of greater volatility, options are more expensive.When it’s quiet, options are cheap. A change in volatility can have a bigimpact on your options position. Yet, to my knowledge, there is nomodel that can predict the timing or magnitude of the next volatilitychange. And when a change comes, it may affect the options of a certain month more than another, or affect options unevenly acrossstrikes (a change in skew).Software can be programmed to track recent volatility and, unlessyou override these numbers, it typically applies them to the future. Inother words, it assumes that the current volatility situation will continue. If you have reason to believe otherwise, you can usually indicatean expected change in volatility in the program’s model. Currentvolatility skews, intermonth volatility differences, and CEV can alsobe tracked by a sufﬁciently advanced program and assumed to continue into the future.Isn’t there some predictability to volatility? Haven’t we read repeatedly how you can proﬁt by selling options when volatility is highand buying options when volatility is low? Yes, it is true that whenvolatility goes to an extreme, it is bound to return to normal levels.However, when and how fast it returns to normal is anybody’s guess.When an option expires, its ﬁnal value is determined only by theprice of the underlying. However, from the time an option is born untilthe ﬁnal minute of its life, volatility is an unpredictable wind thatblows more or less premium into it.3. Intermonth spread changes in agricultural futures contracts.
When modeling futures options prices, an options analysis programmust ﬁrst predict how each future’s price will behave relative to theone futures contract selected to be the independent variable. Then option fair values are computed based on those modeled futures prices.In agricultural futures, each contract can, and often does, trade asan independent commodity. That is because in agriculturals, timing ofdelivery is everything. Corn for March delivery is not the same as cornfor July delivery. Each contract trades on its own supply/demandcurve. Two contracts can even represent two completely differentcrops. For instance, “August Soybeans” and “November Soybeans”represent two different crops.
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In options analysis software, agricultural futures are often modeled using a constant basis model. The constant basis model simplysays that current intercontract price differentials will continue. In thiscontext, if you project that one of the contracts will go up a dollar, thesoftware assumes the other contracts will go up one dollar as well. Amore sophisticated model presumes that the contracts will move proportionately as they have in the past. But even that is not going to bevery accurate in a lot of scenarios.The intermonth spread changes in agriculturals are difﬁcult tomodel accurately and will always be a source of unpredictability andrisk for the options trader who takes a position in two or more different contract months.In conclusion, just as with many of the machines and instruments weuse, our knowledge of their limitations is the key to maximum and reliablebeneﬁt (and not getting hurt!). Every time you drive a car, you know thatyou could get hurt. And every time you use options software to trade anoption you could lose money. Just the same, options trading softwarehelps in so many ways—visualizing strategies, ﬁnding opportunities,avoiding mistakes, recording trades—that to trade options without software would be like ﬂying an airliner without instruments.
DEALING WITH ANOMALIES AND PRICING DIFFICULTIESNew options traders get excited when they ﬁnd a badly mispriced option.Unfortunately, 99 times out of 100 it is nothing but a bad quote. Fortunately, bad quotes are rare these days in stock and index options. However, bad quotes are common in futures options. For some reason, futuresoptions quotes are not disseminated very well intraday. Depending on themarket, bid and asked prices can be worthless or nonexistent. A last tradeprice can be way off sometimes. Volumes are the previous day’s volumes,not today’s cumulative volumes as they are in stock and index options. Inshort, you’re trading from a partial black hole. Even if you’re receivingreal-time streaming quotes from a reputable vendor, the option price yousee on your screen may not reﬂect the actual price on the trading ﬂoor.However, users of options trading software have a signiﬁcant advantage because they can deal with these holes in futures options prices. Youmay be able to ﬁgure out where prices really are—not with absolute certainty, but with a certain degree of conﬁdence—and thereby be able toplace good orders.The starting point for checking the saneness of an individual option
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price is to check its IV in comparison with the IVs of options around it. Ifan individual option’s IV deviates from the pattern of other option IVs, youprobably have a bad price.Consider the set of prices for May Coffee call options which existed atone time in the past. Can you spot the anomaly in Table 6.1?Right, the 160 calls cannot possibly be trading at 1.70. They might havetraded at that price once (perhaps earlier that day), but I guarantee youwill not be able to go in and sell any of them at 1.70. How do I know that?For one thing, their price is out of line. The 160s ought to be priced somewhere between the 150s (1.40) and the 170s (0.50). More importantly, theirIV is out of line. If you extrapolate the apparent curvature (skew) of theother option IVs, you will see that the 160s ought to be trading at approximately 49.5 percent.Let’s say you need to trade these 160 calls. How can you ﬁgure outwhere they’re actually trading, so you can place a reasonable order?Using an options analysis program, you can step the option price until you ﬁnd the IV that should be right for this option (in this case, 49.5percent). In this example, you would have found that an option price of0.85 is correct.Therefore, 0.85 is the probable mid-price for the bid and asked thatactually exists on the ﬂoor. You can take it from there, adding (if buying) or subtracting (if selling) an appropriate amount of slippage, depending on your urgency to make the trade and your experience withthis market’s liquidity.When an individual option stands out like this, it’s easy to deal with.Now let’s take a look at a more difﬁcult example.One February day, the orange juice market opened with a gap to theupside on news of a cold wave crossing the United States. Option volatilities, which had been sleeping at around 24 percent, were bound to jump. Ihad been holding a straddle for several days. I was ready to place an orderto sell my straddle, but at what price? (I wanted to place a limit order, nota market order.)
TABLE 6.1 May Coffee Call OptionsStrike
Option Price
IV
170160150140130120
0.501.701.402.504.909.00
N.A.59.5%46.5%43.6%42.7%41.9%
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During the ﬁrst hour of trading, options prices trickled into my systemat the rate of about one every ﬁve minutes. (The options which had not yetupdated still showed yesterday’s settlement prices.)I could see from the options prices that were coming in that the market was generally valuing these options at a new volatility level of about 38percent. The options I needed to trade had not updated yet. However,based on the 38 percent ﬁgure, I was able to use the above procedure andobtain likely prices for my options. I placed my order and was ﬁlled.Later in the day, after all the options prices had updated, I could seethat my trades occurred at decent prices. In other words, I had correctlyassessed the prices of my options.In conclusion, you can deal with missing prices and pricing anomaliesin the futures options arena. The key is IV. By paying attention to generalIV levels and skew curvatures, you can assess the appropriateness of anyindividual option’s price. When a price is obviously wrong, you can use thetrick of stepping price until IV is in line to ﬁgure out what the actual priceprobably is.
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Tips forBeginners
M
any people ask how they should prepare themselves to trade.That’s a good sign. It’s right to prepare yourself before jumping in.Here are some of the steps I consider important, not only for beginners, but also for experienced traders at all levels.Read. Read another book about options. Read a good book abouttrading. For a list of some of the best, see the bibliography at the end ofthis section. When you read about the experiences of seasoned traders,you beneﬁt from their mistakes without having to pay for it by losing yourown money! Bypassing years in the school of hard knocks, you can arriveat successful trading years earlier. By the way, even after you’re an experienced trader, you should still read a trading book once in a while!Attend a seminar. You can learn valuable information from instructors who have traded successfully for years. Just as importantly, you canmeet other people who have workable methods and swap valuable ideaswith them.Do some paper trading. Decide on a period of time in which youwill restrict yourself to mock trades (no real money involved). After youdecide on a period of time, double it. There is no reason to be in a hurry.There will always be trading opportunities. Odds are you will be glad youweren’t using real money during this training time!Some doubt the value of paper trading. However, if handled properly, it can be good practice and an excellent representation of how youmight actually perform. Obviously, you have to be honest with yourself.A speciﬁc decision to trade must be accompanied by an immediate entryin a log. Once a trade is entered, you’re stuck with it. No fair using the149
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delete key! Enter the current date and time with every trade. As for price,to be conservative you should enter the “asked” on purchases, the “bid”on sales.One of the problems people have with paper trading is maintainingtheir motivation. Here’s an idea: You might tell yourself that unless youachieve a certain proﬁt objective during the trial period, you’re not goingto allow yourself to get started with real money. Instead, you’re going tohave to go around again and do another trial period. This creates an incentive to do well in the trial period.Select and use good trading tools from the start. Get into thegroove with good software and favorite Internet sites, so that you buildconﬁdence to make sound trading decisions based on discipline. This willenable you to have a system and be in the game for the long run.Using an options pricing model will help you intelligently select thebest option or option strategy to trade. Using graphic analyses will helpyou visualize the way positions should perform. Referring to historicalvolatility charts will give you a perspective on the current volatility environment. In short, having these “instruments” in front of you will help youtrade more intelligently. Trade without them and you’ll be stumbling inthe dark.A good portfolio manager, speciﬁcally designed for options, willmake it easy to keep track of your paper trading and get you into thehabit of good recordkeeping. A good portfolio manager should also provide you with the ability to create another good habit—setting an objective and a stop for every position you enter. The program should be ableto alert you when any of your positions hits its objective or stop, so youcan take action.When you start trading, start small. Trade in lots of just two to ﬁvecontracts at ﬁrst. Again, there is no reason to be in a hurry. We hear horrorstories of beginners who get greedy and place large initial orders. Aftertwo or three mistakes, they’re out of trading capital and out of the game!If you place just a small part of your capital at risk at any one time, inany one position, you’ll give yourself the space to make a few mistakes andstill have capital to continue trading and apply what you’ve learned. You’llalso be able to survive a streak of just plain bad luck. The markets arefairly random, and your decision-making system, whatever it may be, cansometimes fail several times in a row. You have to be able to survive astring of losses.When should you exit a trade? That’s simple. You exit a trade whenthe prospects don’t look good anymore. Whether you’re showing a gain orloss at the time is irrelevant. What matters is whether the position is likelyto make money going forward.A key question that always seems to clear the mind is to ask yourself if
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you would enter the trade anew at this point. In other words, if you had noposition, would you place a trade to open the position now? If so, hold onto the trade, assured that it’s a good one. If not, you might want to considerclosing the trade very soon.Some traders, myself included, have difﬁculty closing a successfultrade at a good time. We hold on past the peak. Let’s say it’s a simple longstock position. The stock has shot up, ﬁlling you with glee. You brag aboutit to friends. Now it’s time for a reality check. Would you buy the stocknow? No? Likely, not many other fools would buy at the new, high price either! When you sense that happiness welling up and you feel like bragging,it’s time to seriously consider selling. Almost every time I’ve bragged abouta stock, or an option position, that was the peak.Select the right kind of broker. For trading options, I deﬁnitely recommend trading with a ﬁrm that specializes in options. At this time thereare only a handful of online brokerages specializing in options. Withoutnaming them here, you can recognize them by the fact that their advertising and literature clearly welcome options traders. Having your account atone of these brokerages gives you a better chance of having your ordersexecuted properly and your account records, including margin requirements, handled properly. Trading is challenging enough without having todeal with a broker who does not understand options.How do I open an account? Most online brokerages make it easy toopen an account. You just click the “Open an Account” link in their website, and begin ﬁlling in the required information and click-signing agreements. Then they usually require a signature or two on real paper, so therewill be instructions on how to print the necessary forms and where to sign.You will send these papers in with your check or other instructions onhow to fund your account.How much capital should I start off with? I recommend startingoff with at least $10,000, and closer to $50,000, if possible. At $10,000you’re going to be under pressure to make your ﬁrst few trades winners, sothat you start building your account. Try to keep your trades small atﬁrst—I mean really small (e.g., $1,000 in each trade)—and keep at leasthalf of the account in cash at all times. If your account does go south atﬁrst, resist the tendency to get careless and take more risks with the remainder. The market brings new opportunities every week, sometimes exceptional ones, and if you still have some cash, you’re there to participateand ﬁght back.What are the margin requirements like? When buying options, themargin requirements are zero; you just have to pay for the options in full.Requirements are very reasonable in equity and index options when shorting covered options (that is, when the options you’re selling are notnaked). Margin requirements for selling naked options on low-priced
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stocks or indexes are reasonable (although you won’t be able to do it withjust $10,000). Requirements for selling naked options on high-pricedstocks or indexes are quite high. Some brokerages charge even higher thanthe exchange minimum requirements for naked options (it’s their prerogative to do so). If you plan on selling naked options, you should ask the brokerage about their margin requirements up front.Should I use only limit orders? Market orders and limit orders bothhave their place, depending on your urgency to trade. I use both kinds.When the market is calm and I feel like there is time to fool around and tryto save a few bucks, I use a limit order and go in somewhere between thebid and the asked. More often I use a limit order at the asking price (if buying) or the bid price (if selling).However, there are times when it’s best to use a market order. For instance, when I decide its time to get out of a trade, I want out! I haverarely received a bad ﬁll using a market order in stock options and indexoptions. It’s the futures options markets that can be dicey, especially inNew York. I would not recommend using market orders in the New Yorkfutures markets.Feel comfortable with your trading. If you ﬁnd a strategy boring,do something more exciting. If you ﬁnd a strategy too anxiety producing,switch to something calmer. If you ﬁnd that you are trading positions thatare too large, start trading smaller positions. If you ﬁnd the risk of nakedwriting intolerable, don’t do it. You must discover your own risk tolerance level and an approach that is interesting to you. Sometimes thiscan take years.Expect to pay some dues at ﬁrst. To arrive at a trading approachthat is comfortable for you will take some trial and error. Don’t be surprised if your trading account goes downhill during this time. Again, papertrading prior to real trading is a good idea. Still, when you begin real trading, it is very common for some things to go wrong at ﬁrst.Act only on your own analysis. Once you have formulated yourown approach, it’s okay to listen to the opinions of others, but do yourown research and make decisions independently. Do not listen to thenews. If you do listen to the news, take everything with a grain of salt.Newscasters do not know whether the market will go up or down, andat the end of the day they do not know why it moved the way it did. Noone does.The market already knows what you know. Resist the temptationto believe that you have an edge because of some event that is coming orhas just happened. For example, “Interest rates are going to be reduced tomorrow, so the stock market should go up.” The fact is, everyone probablyalready knows this and the market has already discounted it. Or, “Company XYZ just announced better-than-expected earnings, and the stock
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should go up in the next few days as the word gets around.” If you thinkyou are among the ﬁrst to ﬁnd out about this company’s numbers and mostother people don’t know yet, you are just fooling yourself. Believe me, unless you are privy to inside information, you (and I) are probably amongthe last to receive the news.The markets quickly digest news. Only surprises move the markets, and even then only for brief periods. It takes a pretty big event, suchas the terrorist attacks on September 11, 2001, to move the markets forseveral days. Otherwise