week. This, as noted in earlier chapters, is basis risk. It must be noted that betas and other statistical calculations are based on historical data, and futures seldom reflect past history exactly.Before leaving this example, it would be reasonable to ask why a managerof a large portfolio would take a short futures position rather than simply sell thestock.One of the reasons may be liquidity. A highly liquid futures contract canabsorb a hedge without significantly affecting the futures market price, while salesin the stock market of the same magnitude could pull down the price of those individual stocks to a much greater extent. Further, many portfolio managers do notfind liquidation a feasible alternative because they are restricted to stocks of a particular kind. The cash generated from the sale of those stocks may not be immediately reinvested in other alternative areas. The futures market gives a managerthe opportunity and the flexibility to make potential adjustments in his portfoliowithout going through complete liquidation.
The Long HedgeStock index futures also can be used by the portfolio manager as a means of pricing futures acquisitions of stock for his portfolio. Most managers receive periodic inflows of capital resulting from contributions to pension funds, dividendsreceived, etc. If in the portfolio manager’s estimation the market is cheaper nowthan it will be at the expected time of the inflow, then he may wish to use the indexfutures to price the cost of his purchases now. Later, when he actually receives thefunds and makes the purchase of the securities, he will offset his futures. In doingso, the manager protects himself from a rise in the market before he receives hisfunds for investment. Of course, should the market fall during that time period, hewill have losses on his futures, which will offset the opportunity gains he had frompurchasing stock at a lower level. As with all properly constructed hedges, he givesup the opportunity to make windfall profits, while at the same time protecting himself against substantial losses.
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STOCK INDEX OPTIONSOptions on the stock index futures have become a very popular trading vehicle.Stock index futures, options on the futures, portfolios of individual stocks, andoptions on the individual stocks provide a very rich intellectual environment forportfolio managers to develop hedging, arbitrage, and investment strategies for avast array of time horizons. These derivative instruments when combined with aportfolio of stocks or bonds allow the portfolio manager and private investor (if heis big enough) to custom-design investments with risk/reward profits that matchthe investor’s needs and desires.Chapters 26 and 27 cover the options markets. The strategies discussed thereapply equally to stock index options, though they really only scratch the surfacein terms of sophistication and potential applications.
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Chapter 26
Commodity Options
The history of commodity trading in the U.S. is replete with stories of intrigue andconflict, of great fortunes gained and lost. None of the stories are more engrossing than those involving commodity options trading.Commodity options trading has been conducted in this country on an intermittent basis since the early 1860s. At that time the Chicago Board of Trade passeda rule prohibiting its members from trading options. A few years later with a newBoard of Governors, the rules were changed again, this time permitting membersto trade options. Throughout the rest of the 19th century, trading options on theCBOT was a sometime thing as battles raged between pro-options traders and antioptions forces. They fought through the legislature, in the courts, in the boardrooms, and with other exchanges.In 1936, it was charged that options played a role in a particularly blatant andsuccessful attempt to manipulate the grain markets on the CBOT. Congress heldhearings on the matter and subsequently passed the Commodity Exchange Act,which barred all trading in options on commodities under the regulation of theCommodity Exchange Authority.
263Copyright 2001 The McGraw-Hill Companies. Click Here for Terms of Use.
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In 1974, during hearings to revise the Commodity Exchange Act, Congressonce again addressed the question and at first seemed to lean toward extending theban to all commodities. Ultimately, however, after a good deal of testimony extollingthe economic virtues of commodity options, Congress decided to review the banon options for all previously regulated agricultural commodities while leaving adecision on other commodities up to the discretion of the Commodity FuturesTrading Commission. In 1982, the CFTC authorized a pilot program and has sinceallowed options trading on virtually all approved futures contracts.
THE LANGUAGEAlthough options may be written on actual commodities or on futures contracts,this section will focus on options on futures contracts. Trading strategies and concepts are basically the same, however.Options trading has its own terminology, which is considerably differentfrom that of futures trading. For example, a “call option” is an obligation of thegrantor (seller) to provide a long futures position to the grantee (buyer) at a predetermined price on or before the exercise date of the option contract, if and whenthe buyer chooses to exercise his right. Thus, a call option is a right to buy. It establishes a buying price for the buyer of the call.A “put” option is an obligation of the grantor (seller) to provide a short futuresposition to the grantee (buyer) at a predetermined price on or before the exercisedate of the option contract, if and when the grantee chooses to exercise his right.Thus, a put option is a right to sell. It establishes a selling price for the buyer ofthe put.A “double” option allows the purchaser the right to acquire either (not both)a long or short futures position at a specified price on or before a specified date ifand when he chooses to exercise his right.The “strike price” is the predetermined price at which the futures position istransferred from the seller to the buyer if the option is exercised.The term “exercise” refers to the buyer’s decision to require the seller to fulfill the terms of the contract. If a call option is exercised, the option seller must provide to the buyer an underlying futures position at the strike price specified. Whena put option on a futures contract is exercised, the seller of the option must provide a short futures position at the strike price specified.The “premium” is the amount of money paid by the buyer of an option to theseller for the right to exercise the option at the strike price. The seller receives thepremium regardless of whether the option is actually exercised. That is a one-timepayment to the seller. Irrespective of what happens to price, there are no further payments by the buyer unless he exercises.
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The “expiration date” is the last day of the option’s life. The buyer of anoption must decide whether to exercise or to abandon his right to exercise theoption either on this date or before. Options that allow exercise only at expirationare called European options. Options that permit exercise during the life of theoption are called American options.An option is said to be “at-the-money” if its strike price is equal (or approximately equal) to the current market price of the underlying futures contract.A call is said to be “in-the-money” if its strike price is below the currentprice of the underlying futures contract (i.e., if the option has intrinsic value). Aput is “in-the-money” if its strike price is above the current price of the underlying futures contract (i.e., if the option has intrinsic value).An “out-of-the-money” option is a put or call option that currently has nointrinsic value. That is, a call whose strike price is above the current futures priceor a put whose strike price is below the current futures price.The “intrinsic value” of an option is the dollar amount that could be realized if the option were to be currently exercised (see “in-the-money”).An option “margin” is the sum of money that must be deposited and maintained in order to provide protection to both parties to a trade. The exchange establishes minimum margin amounts. Brokerage firms often require margin depositsthat exceed exchange minimums. In turn, they post and maintain customer margins with the clearing corporation. Buyers of options do not have to post marginsbecause their risk is limited to the option premium.“Margin calls” are additional funds that a person with a futures position orthe writer of an option may be called upon to deposit if there is an adverse pricechange or if margin requirements are increased. Buyers of options are not subjectto margin calls.“Naked writing” of an option refers to writing a call or a put on a futures contract in which the writer has no opposite cash or futures market position. This isalso known as uncovered writing.An option “series” refers to all options of the same class having the same strikeprice and expiration date.An option “spread” refers to a position consisting of both long and shortoptions of the same class, such as having a long position in a call with one strikeprice and expiration and a short position in another call with a different strike priceand/or expiration.An option “straddle” is a combination in which the put and the call have thesame strike price and the same expiration.The “time value” of an option is the amount by which an option premiumexceeds the option’s intrinsic value. If an option has no intrinsic value, its premium is entirely time value.The “writing” of an option refers to the sale of an option in an opening transaction.265
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THE GREEK LANGUAGE AND OPTIONSThere are a number of Greek words used to describe changes in options value.These include:
1. DeltaDelta is the change in the market price:Delta =
Option Price ChangeMarket Price Change
For example, if the market price changes by 1 and the option price changesby .3, the delta is .3 or 30 percent. This 30 percent actually reflects the expected(market-generated) probability that the option will expire in-the-money.This also tells us something useful about hedging. As noted elsewhere inthis book, hedging is essentially the establishment of a counter balancing position. So, if one knows that an option moves .3 for each one point of change in themarket price, then the appropriate hedge ratio one should use is the reciprocal, or1=3.3This means that three options are needed to get a complete 100 percent counter balance hedge position.Delta neutral means your option position is hedged. The long deltas (the sumof the deltas associated with the calls you own) equal the short deltas (the sum ofthe deltas associated with the puts you own). The delta tells one how much pricechange can be expected with a move in market price or how long or short your position is. Positive deltas mean you have a bullish position and will profit if prices goup. Negative deltas mean you will profit if prices go down.
2. GammaGamma is the name given to the rate of change in the delta. So it really reflects therate of change of the rate of change. If an option has a delta of .55 and a gammaof .05, then the option would have a delta of .6 if the underlying futures goes upone full point.
3. VegaVega is a measure of volatility. It is the change in option price associated with a 1percent change in volatility. Historical volatility is usually measured by the standard266
Commodity Options
deviation (log normal). Implied volatility is the volatility that is imbedded in a givenoption price. You can calculate the implied volatility in any option premium byholding all elements of the price model constant and solving the equations forvolatility, i.e., run the option model backward.When volatility is very low, and you expect that it will explode upward soon,a logical strategy would be to buy out-of-the-money calls and sell further out-ofthe-money calls. This is a very short-term trade with limited risk of loss equal tothe difference in the value of the calls bought and the value of the calls sold, andlimited gain equal to the difference in the strike prices less the difference in the premiums. With high volatility, the deltas of out-of-the-money options often movecloser to .5, thus causing the premiums between strike prices to narrow.
4. ThetaTheta is the change in the option premium associated with the passage of time. Itis referred to as the rate of time decay associated with an options premium and isbasically a function of the square root of time remaining on the option’s life. It isusually expressed in option premium points to indicate how much the premiumwould lose in one day if all other factors remained the same and the futures pricewas constant. Thus a theta of .02 on an option would suggest that it would lose twoticks in value for each one day of time remaining.
OPTIONS VERSUS FUTURESThere are some important differences between an options contract and a futures contract. A futures contract is a bilateral contract requiring action by both parties andobligating both the buyer and the seller to fulfill the conditions by delivery and payment. An option contract, on the other hand, is a unilateral contract. Unlike afutures contract, the buyer and the seller of the option do not have an equivalentobligation to perform. The purchaser of an option has the right but not the obligation to require the seller to perform under the contract, and the seller is obligatedto do so only if the buyer exercises his right. The converse, however, is not true.The seller of an option cannot require the purchaser to exercise. Only the buyer hasthe right to require fulfillment of the contract termsPerhaps the most distinguishing feature of an option contract is the limitedliability of the purchaser. The potential loss to an option purchaser is limited to the“premium” he pays the seller at the time of the purchase of the option. His potential for gain, theoretically, is limited only by the extent of the price movement ofthe underlying contract. In contrast, on the futures contract the holder of a position(either long or short futures position) remains liable to margin calls as long as hisposition remains open.267
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In short, therefore, the purchaser of an option contract can lose, at a maximum,only the amount he pays for the option. This is so because, if the price does notmove in his favor, he fails to “exercise” his option. Instead, he simply abandons it.An analogy can be drawn with an insurance contract. The writer of the insurancepolicy receives the premium for undertaking the risk but has to stand ready in thefuture to make any payments due the person who bought the insurance if that person submits a valid claim. If he does not submit the claim, the insurance companystill keeps the premium.One major advantage of options over futures markets for the business is that,when prices are extremely volatile, options can reduce the demands on cash flow.For example, if you have purchased a futures contract and it declines, you willhave to pay in more margin, which, of course, must be paid in cash. If, on the otherhand, you have purchased a call option, you will have a one-time payment; nomatter how far the price falls, you will not be asked to post more money. The converse of this is, of course, also true. If prices go up, the futures position will yieldcash to you while no such thing will happen with the option. Options thus providemore certainty in planning cash flow exposure.Options permit a range of investment and resource management strategies notavailable from futures. Options used in conjunction with futures and actual inventories of a product afford a wide range of strategies for a merchandiser, producer,or processor in managing inventories. They can provide greater control with lowercapital requirements than do futures alone.To a large extent options are substitutes for stop orders on futures. You canattempt to limit your risk on a futures position by placing a stop loss order at whatever level you choose. Then, if the market touches that level, your broker wouldautomatically offset the futures contract at the price stipulated or at the next bestpossible price.In essence, the purchase of an option serves the same purpose as the stoploss order serves in the futures contract. They are both there to limit losses. Thedifferences between the two, however, are:1. A stop loss order may not always be exercised at the price stipulated sothe loss cannot be absolutely fixed in advance. The size of the option premium, however, is fixed in advance, and the loss cannot exceed the sizeof the premium.2. A poorly disciplined trader may decide not to use stop loss orders and tomeet margin calls when he should not, thus sticking with a losing positionin the hope that the market will reverse. This can lead to very large losses. An option, on the other hand, does not give that discretion to the holder. Once he buys the option, the marketplace decides whether it will be prof-
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itable to exercise it. The holder has no more decisions to make if the market moves against him, or fails to rise to the exercise price.3. One can get whipsawed in a market using stop loss orders. The market canset off a stop order, causing the offset of the futures contract, and then themarket could turn around and go the opposite direction. Due to the offset,you would be without a position in the market and unable to take advantage of the rise.In sum, the option is a more certain way of limiting losses. The value of thiscertainly has to be weighed against the size of the premium paid. It may be a veryhigh price to pay for the luxury of not having to exercise the self-discipline requiredin using stop loss orders or for limiting the potential that you will get whipsawed.Other differences between options and futures will become apparent as youread some of the strategies for trading options discussed in the next chapter.
PICKING AN OPTIONS BROKERAn earlier section discussed selecting a broker for futures transactions. Chances areyou will find that your futures broker also handles commodity options transactions and is well-prepared to provide the trading support you need. In a few instancesthe trader may also handle cash options.Picking an options broker should be done with care. There are many scamoperators who sell options on coins, precious metals, etc. They often are not registered and are selling in violation of state and federal laws. Shop around and find out:1. What kind of services the firm offers and what kind of commission itcharges for those services.2. How much experience the broker has had in trading options.3. Whether the broker is registered with the NFA/CFTC. Is he a member ofany professional options organization or an exchange? If so, you can contact them for further information about the firm; e.g., is the firm in goodstanding? Are there any public records of past disciplinary action?After you have picked your broker and before you decide to enter into anyparticular option transaction, check out the following:1. What kind of contract is it? Is it a U.S. or a foreign option, and is it anexchange-traded or a dealer option? The difference here can be substantial. A U.S. option is more easily monitored, and all parties to it are under
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the regulation and scrutiny of the Commodity Futures TradingCommission. An exchange option has a ready secondary market in contrast to most dealer options and, therefore, your option position can be easily offset. In addition, exchange-traded options are standardized contractswith information readily and easily available about the underlying commodity. The opposite is true of many other options.2. Who guarantees the transaction, and what is the financial solvency ofthat party? The guarantor of options on futures will be an exchangeclearinghouse. If it is a U.S. exchange, the federal government is monitoring the exchange’s, the broker’s, and the clearinghouse’s financial condition. That does not mean, of course, they couldn’t still go bankrupt. Ifit is a foreign exchange, find out how the guarantee works and exactly howyour account will be settled if there is a bankruptcy. An independentoption dealer who is selling non-exchange options is the guarantor.3. How much does the premium represent as a percentage of the value ofthe underlying commodity or futures contract? With some independentoptions dealers, these fees are unconscionably high.4. What is the break-even point for your option? That is, how much willthe price have to change before the option will become profitable?5. How will the option premium, if you are buying, be passed to the sellerand, if you are a seller, under what conditions will you receive the premium?6. How much is the premium being marked up over what it cost at the timeof origination? This is particularly important if you are not buying itdirectly on an exchange, such as would be the case with foreign optionsand dealer options.7. How much commission are you paying and what services are you gettingfor the commission?8. What are independent research people indicating the future prices of theunderlying commodity will be? Remember, the premium represents theexpected value of the expected volatility of prices. If most people expectvery little price change, premiums should be quite low.9. How do you exercise your option, and what do you get when you exercise? Study the terms and conditions of the contract.10. When and how will your broker notify you of the execution of your contract and the current status of your account?
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11. Where can you get regular information about the value of your option andthe price of the underlying commodity? If this is not available, beware.In short, know as much about your dealer as you do about your business partner and only deal with someone you know, trust, and are comfortable with. Thedealer is using your money. Pick a professional who knows the business.
WHAT’S AN OPTION WORTH? DETERMINING THEOPTION PREMIUMIt should be implicit in the foregoing that one needs to evaluate very carefully thefactors that affect the value of the option premium. These include:1. The current price level of the underlying commodity relative to the strikeprice of the option.2. The length of time the option has left before it expires. The longer the lifeof the option, the more time you are buying and the greater time there isfor the market to reach the strike price.3. The volatility of the price for the underlying commodity. The more volatilethe price, the greater chance that the market will reach the strike pricewithin a given time period.4. The expectations generally held that the commodity price will rise abovethe strike price. This is related to each of the three preceding elements.5. Interest rates—higher interest rates generally mean higher premiums.
Fair Market Value ConceptTo understand option value, you need to focus on the concept of fair market value.Fair market value is defined as the expected break-even price for both thebuyer and the seller. The word “expected” is important here because, by definition,we are dealing with the occurrence of an event that is some time in the future. Thismeans we have to focus on probabilities. As noted earlier, probability distributions reflect long-run estimates of the results you would expect to achieve over alarge number of transactions. In the short run with only a few transactions, you mayhave distortions and mispricings. These are opportunities for profit.The first step in calculating the fair market value for an option is to establishthe probability that a particular price will be achieved. Recall that, at expiration, anoption price must be either zero or positive. Hence, the effort here is to establish the
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probability that at expiration the difference between the strike price and the marketprice will be either zero or some positive number.The reasons for trying to figure out how to value an option are two-fold.First, it will demonstrate clearly how one determines advantageous option tradingopportunities. Second, it will demonstrate the need for a computerized methodology if you are going to be regularly involved in trading options.To illustrate the importance of getting the pricing right, and how importantgetting it even a little bit wrong can be, consider the following. Assume that theS&P futures are at 400, and a 410 call is at $20 fair market value. Assume also themarket rises to 450 and you exercise the call, giving you a $20 net profit (450 –410 – 20). You have a profit ratio of 2-to-1. If, however, the call had been mispricedand you bought it at less than fair market value, say $10, your net profit would be$30, a 3-to-1 ratio, or a 150 percent difference.The formula for determining the value of the call premium is as follows:Call Premium
=
The greater of zero or the difference between the market price at exercise minus the strike price multipliedtimes the probability(ies) of achieving a final marketprice greater than zero.
For example, assume that the market price for the S&P is at 400 and that thestrike price you are interested in is 400. Assume further that at expiration only twofinal prices are possible, P1 = 350 or P2 = 450; and that there is a 50/50 probability either could be achieved. The fair market value of this option is calculated asfollows:Call PremiumCall PremiumCall Premium
=+==
(Probability of P1) × the greater of (0, 350 – 400)(Probability of P2) × the greater of (0, 450 – 400).5(0) + (1 – .5)(50)$25
NOTE: The second probability is equal to 1 minus the first probability.In other words, over the long run, half the time both the buyer and the seller of this option should expect to make $25 and half the time they should expectto lose $25. The expected long-term return on this option is equal to zero and it ispriced at a fair market value. But if the option were actually priced to you at $20and you bought it, in the long run you should expect the probabilities to work inyour favor and you will have a net profit (over the long run) of $5.If in the above example, you had four potential prices—P1 = 350, P2 = 375,P3 = 425, and P4 = 450—all with an equal probability (P) of occurrence, then theproper calculation for the premium would be as follows:
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Call Premium
=+===
P(P1)max(0, 350 – 400) + P(P2)max(0, 375 – 400)P(P3)max(0, 425 – 400) + P(P4)max(0), 450 – 400)(.25)(0) + (.25)(0) + (.25)(25) + (.25)(50)0 + 0 + 6.25 + 12.5018.75
You can see that the greater the number of possible price scenarios there are,the more complex this calculation becomes. It also means that the more timeremaining on the life of an option, the more potential price scenarios there are andall the more reason why these sorts of computations can be accomplished onlywith a computer (see Figure 26.1).
Figure 26.1 Option Pricing Probability Diagram
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Interest CostsAs noted above, interest costs are an important element in the pricing of options.The $25 option premium derived in the earlier examples says two things. First, inthe long run you expect to get zero returns. Second, because you didn’t include aninterest calculation for the use of your money during that time, the seller gets theuse of your money for free. Generally, people do not want to work for free and inthe process give up the opportunity to earn interest on their money. Therefore,option formulas should always include an interest adjustment. The formula forthat interest adjustment is as follows:Interest Adjustment =
1× The Premium1 + Rt
Where R = the interest ratet = number of yearsSo, if we assume a 10 percent interest rate per year, then the $25 option valuewe derived above is really adjusted as follows:11= .9091 =(1 + .10) 1.10$25 × .909= $22.73Fair Market Premium = $22.73.Hence, we need to revise the formula we derived above to:Fair Market Value =
N1t × ∑ Prob.(P) (Mkt. Price – Strike Price)(1 + R) i=k
VolatilityFuture volatility is an unknown, but it is also a major factor affecting optionsprices. As the price jumps around, the probability increases or decreases that a different price than the one you assumed a moment ago will actually emerge at expiration of the option.Volatility is normally measured by a statistic called the standard deviation.The standard deviation, you may remember from your basic statistics courses,assumes that the prices being considered are normally distributed around an average price. A normal distribution is depicted in Figure 26.2.Now, we know that futures prices are not normally distributed, so the bellshaped curve shown on the next page is not really a relevant or correct assump274
Commodity Options
Figure 26.2 Normal Distribution Curve
1 StandardDeviation
Average
2 StandardDeviation
tion. The reasons are three-fold. First, the bell-shaped curve shown above suggests that prices can actually go below zero. We know that is not true. Second, itsuggests that normally free prices can go below and stay below cost of productionin the long run. We know that is not true. Third, we know also that there are natural impediments such as price supports, political actions, subsidies, etc. that causeprices not to follow a normal distribution.To get around these problems and others, mathematicians use logarithmsand create what are called log normal distributions. They calculate the standard deviation using what are called log normal distribution assumptions. This is far toocomplex to get into here, so suffice it to say that the formula shown earlier actually gets changed and is expressed in logarithmic relationships.
TimeThe last factor to consider in pricing options is time. In brief, the more time remaining, the more value there is to an option. The reason for this is that the longer thetime period, the more price possibilities that could occur. Hence, sellers of optionsextract an insurance premium associated with the possibility that their price rangeassumptions will be wrong. This calculation really gets into complex higher mathematics. So we will skip it.To summarize, we end with an option formula stated as follows:Option Value =
N1t × ∑ Prob.(P) (Mkt. Price – Strike Price)(1 + R) i=k
+ adjustment for expected volatility + adjustment for time275
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FUTURES VERSUS PHYSICALS VERSUS FINANCIALSAre the factors that go into pricing options different if you are pricing an optionon financials? On physicals? On futures?The answer is yes. Table 26.1 lists the adjustments one would make to thebasic option formula shown on the previous page for each of the three categories:futures, physicals, and financials.Note that options formulae for physicals and financials also require adjustment for the cost of storing or holding a commodity over time and, in the case offinancials, for dividends or coupons earned.Why does an option on actuals differ from an option on futures? There areseveral reasons. First, the liquidity (ability to get in and out of the market withoutunduly affecting price) is often much different in cash markets than in futures markets. Second, the deliverable supply in futures markets and the potential for manipulation in either cash or futures markets may be different. Third, the cost of exercise of an option is different. In the case of an option on a futures you are expectedto post margin. In the case of an option on a physical commodity, you pay for itin full. Fourth, tax issues and tax treatment of gains and losses in futures may bequite different than the tax treatment associated with gains or losses on physicaltransactions. Fifth, the dates of expiration may be much different in physical transactions than in futures. Sixth, the attraction of using options on futures as part ofa portfolio management strategy is oftentimes much greater than using options onphysicals as a part of a portfolio management strategy. Seventh, options done onphysicals often are tailored to particular commercial needs and, therefore, havevery little resale value.
Table 26.1 Adjustments for Futures, Physicals, and FinancialsFuturesPriceStrikeVolatilityInterest RateTime
PhysicalsPriceStrikeVolatilityInterest RateTimeHolding Cost
FinancialsPriceStrikeInterest RateTimeTimeYield
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ARE OPTIONS FOR YOU?This chapter should have impressed two things upon you. First, options are, orcan be, a very useful trading tool especially for limiting potential losses. You canuse them instead of stop orders to get in or out of the market at a known cost.Second, the pricing of options is very complex, is not for amateurs, and can’treally be done conveniently without a computer or sophisticated calculator