You may recall from our discussion of bonds a basic distinction between bonds and stocks. While stocks have no built-in maturity date, almost all bonds do. What about options? In one way, they resemble bonds, having a predefined ending point. The nature of that ending point, however, is very different. That difference can be summed up as follows: Bonds mature; options expire.

The ending value of an option is not fixed in advance. It is linked to the value of an underlying asset. For example, a call option on IJK Corporation common stock is linked to the value of the stock as follows: Suppose that on January 2, 2010, you purchase a call option giving you the right to purchase 100 shares of IJK at $50 per share on any trading day until March 16, 2010, the expiration day. What is the option worth to you on March 16? If IJK stock is trading at more than $50 per share, the option has value. Let’s say the current market price is $55. Theoretically, you could exercise your option (i.e., buy the 100 shares of IJK at $50 per share). You would have paid $5,000 for $5,500 worth of stock. (We are ignoring, for the moment, the cost of these transactions.) Thus the theoretical value of this option is $500.

underlying asset

The asset an option holder has the right to buy (call) or sell (put).

On the other hand, if IJK is trading at less than $50 at the end of the March 16 trading day, it has no value. Exercising such an option would be pointless; it would be cheaper to buy the shares directly.

Similar considerations apply to the other basic kind of option, a put. The difference between calls and puts is simply this: Whereas a call gives you the right to buy something, a put gives you the right to sell something. In contrast to a call, the value of a put increases as the price of the underlying asset falls. For example, if you had purchased a put on IJK with an exercise price of $50, it would have a positive intrinsic value when the stock declined below $50 per share. Otherwise, its intrinsic value would be zero. Beyond this fundamental difference, calls and puts are quite similar: Each has a well-defined linkage to an underlying asset, an exercise price, and an expiration date.

After the expiration day, an option is worthless. Unlike a bond, which can be redeemed for its face value long after its maturity date, options that are neither sold nor exercised lose all value after expiration. (Of course, a bond should be redeemed as soon as possible so that it can be reinvested and continue to earn interest.) Other things being equal, options lose value as the expiration date approaches. For this reason, it is often said that options are a “wasting asset.”

But what is the value of an option before the last trading day? Let’s imagine that it is March 2, 2010; we have two weeks to go before a call option expires, and IJK stock is at $50 per share. There is no point in exercising this option now; it confers no advantage compared with just selling it in the open market. However, it appears that there is a reasonable chance that IJK will go above $50 per share sometime in the next two weeks. The option has value because sometime within the next two weeks, IJK’s stock price may go above $50 per share. Remember, we are ignoring transaction costs, and we haven’t yet considered how much you paid for the option.

The Ins and Outs of Options

When an option can be exercised for a profit, it is in-the-money; otherwise, it is out-of-the-money. A call option whose underlying asset price is higher than the exercise price of the call is in-the-money. Similarly, a put option whose underlying asset price is lower than the exercise price of the put is in-the-money. In either case, a holder of the option can make money by simultaneously exercising the option and either selling the underlying asset (if the option is a call) or buying the underlying asset (if the option is a put).

Usually, when options are characterized in this way, transaction costs are not taken into account. If transaction costs are included, some in-the-money options cost more to exercise than they are worth. Even if that weren’t so, it is seldom necessary to exercise an exchange-traded option. It is easier, and almost always more profitable, just to sell it. Even out-of-the-money options can be sold before expiration, because they have time value even though they have no intrinsic value.

Exchange-Traded Options

Calls and puts usually exist in tandem for underlying assets, striking prices, and expiration dates. However, market participants tend to favor calls in some circumstances and puts in other circumstances. Frequently, for example, after a long bull market in a stock, index, or commodity, you may see the volume of puts being traded on that underlying asset begin to increase. The total number of options contracts created between buyers and sellers, known as the open interest, may also increase. Nervous investors buy puts as a form of insurance against a sudden market panic. Speculators also buy puts, albeit for a different reason: They use puts to bet on a market downturn.

Other investors, or market makers, who do not expect an imminent change in the market, sell these puts and pocket the premium. What is true for stocks and bonds is also true for options—for every buyer there is also a seller. In the options world, the seller is frequently described as a writer, and the price he or she receives by selling you a call or a put is described as a premium. The insurance language is not accidental. Many investors buy options as a form of financial insurance.

Options create a link between a buyer and a seller that persists for the life of the option. For this reason, an option transaction is sometimes described as a zero-sum game with two players. This means that one player’s winnings are exactly offset by the other player’s losses. This contrasts with stock investments, in which there is no finite time span in which the players’ wins and losses cancel out. (Someone selling you a stock might have made a profit or a loss, depending only on its current price and the price at which he or she bought it. Your subsequent profit or loss bears no direct connection to the previous owner’s investment performance.)

Looked at in another way, however, options provide value to both buyer and seller, even though one of them has lost money. The value comes from reduction of risk, or more generally, improved correlation between assets and liabilities. This type of transaction, in which both parties may benefit, is the major justification for a whole range of derivatives known as swaps. We will discuss swaps in Chapter Eighteen.

swap

A two-party transaction involving securities, currencies, commodities, or other assets in conformance to a precise set of rules called a swap agreement.

If a call writer owns the underlying asset, then he has written a covered call. Though he may have to deliver the underlying asset, his risk is limited because he already owns that asset. The underlying asset is said to have been called away from him.

In contrast, a call that is written by someone who does not own the underlying asset is referred to as a naked call. Brokers are required to restrict this type of options trading strategy to investors who are able to engage in riskier investments. If the price of the underlying asset increases, a naked call writer has potentially unlimited losses. He can lose his shirt—maybe that’s why the call is “naked.”

Listed versus OTC Options

How options are regulated depends on the underlying asset:

• Exchange-traded options on stocks and stock indexes are regulated by the SEC.

• Options on exchange-traded futures are regulated by the Commodities Futures Trading Commission (CFTC).

• Over-the-counter options, offered primarily by major banks (and potentially very complex instruments), may come under the regulatory purview of either of those agencies, but may also be scrutinized by the Federal Reserve, the Office of the Comptroller of the Currency, and a trade association set up by the banks themselves, the International Swaps and Derivatives Association (ISDA).

Depending on the terms of the options contract, a call writer may be responsible for delivering the actual underlying asset, unless the terms call for cash settlement, in which case the buyer receives the net value of his or her option, equal to the difference between the market value and the striking price of the underlying asset, less brokerage commissions. For example, index options are settled in cash because it would be too burdensome to deliver each of the stocks underlying the index.

Combination Strategies

The following five combination strategies involve options and underlying assets.

Buy Stock and Buy Put

This strategy is typically used to protect an existing position in the underlying asset against a decline in value while retaining all of its upside potential. Investors who are nervous about a short-term decline that can erode the value of an asset can use a put to provide protection.

Let’s look at an example. Say that you own 1,000 shares of IJK Corporation, which is trading at $144, and you are nervous that the price is going to drop in the short term. But you don’t want to sell the stock outright—you just want short-term protection. What can you do? You can buy 10 “IJK 140” puts. Each of these puts gives you the right to sell 100 shares of IJK at $140 per share (up until expiration), protecting you against a sharp decline in the price of IJK.

Notice that the “insurance” doesn’t actually kick in until IJK goes below 140. This is somewhat like having a deductible on your insurance policy. There is an important difference to keep in mind. Insurance coverage is governed by the contract between you and the insurance company. The “insurance” obtained through purchase and sale of exchange-traded options is subject to market forces and may offer more or less protection than the theoretical value of the option. On the other hand, the fact that you can exercise an option that is in the money does provide you with a hedge that goes beyond the market’s forces of supply and demand.

Buy Stock and Sell Call

This is called a buy-write investment strategy. A different investor may not feel the need to insure the underlying asset, but wants to extract additional income from that asset. This can be done by writing a call against the asset you own. Remember that when you write a call, you are selling someone the right to buy something from you and receiving an amount of money known as the option’s premium. Since you own the underlying asset, it is a covered call, and as explained previously, your risk is limited to having the underlying asset “called away” from you, in which case you receive the striking price for your asset. The further “out of the money” the call when it is written, the less likely it is to be called away from you over the life of the option. On the other hand, if the underlying asset is very volatile or is subjected to an unexpected event, the option may be exercised. But this is what the writer receives a premium for—if there were no chance of exercise, the option would have no potential value to any (rational) buyer.

Buy Stock, Buy Put, and Sell Call

One can combine the two previous strategies, in effect paying for put “insurance” with the premium earned from writing the call. It may appear from the payout diagram in Figure 16-1 that the asset is becoming more and more like cash, and indeed, careful analysis of costs is warranted to make sure that someone besides the broker can make money from this strategy. This strategy is the basis for a relationship between the price of puts and calls known as put-call parity. This relationship, based on arbitrage, allows you to derive the price of a put if you know the price of a call with the same strike price and expiration date. Likewise, you can derive the price of a call from the corresponding price of a put. Put-call parity is a useful means for comparing relative value of calls and puts, and it can also be used as a gauge of market sentiment.

put-call parity

Relationship between prices of puts and calls allowing you to derive a fair price for one if you know a fair price for the other—as long as they have the same strike price and expiration date.

Straddles and Strangles

Straddles and strangles are two related options strategies for benefiting from an increase in the volatility of the underlying asset. Each involves the simultaneous purchase of a put and a call on the same underlying asset. A straddle consists of a combination of put and call options with the same strike price, usually close to the current market value. The options should also share the same time to expiration. A strangle, in contrast, consists of a call and a put option with different strike prices, each option being out of the money.

Straddles are more expensive positions to initiate, but may show a profit for a smaller move in the underlying asset than would be required by a strangle. Part of the reason for this has to do with the so-called delta of the option (see Options and the “Greeks”).

Figure 16-1. Payout diagram for buy stock, buy put, and sell call.

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Calendar Spreads

Calendar spreads are options positions spread out over time, usually to bet on a shift in the relationship between near-term options and those with longer to run, based on changes in the value of the underlying asset. For example, a trader may feel that the near-term price of an option is “rich” relative to an option with a later expiration date. The trader could sell the near-term option and buy the option with the longer expiration date, making a profit if the price of the near-term option declines relative to the price of the long-dated option. On the other hand, this can be a risky trade, especially if the trader does not own the underlying asset (i.e., if he or she is writing a naked call).

Determining the Value of an Option

Intuitively, it seems that if the clock hasn’t run out, the option still has some value. That value comes from the chance that the underlying asset’s value will increase enough to make the option worth exercising before the expiration date. This situation is described by saying that the option has a time value, but no intrinsic value, because it is not currently worth exercising.

What if IJK Corporation stock were to increase to $52 per share, with one week left to expiration? The option would then have an intrinsic value of $2 per share, and it would also have some time value (i.e., another week remaining in which it could increase in price).

But the underlying price may also decrease. How can you figure out what this option is really worth? This was an unsolved problem until 1973, when Fischer Black and Myron Scholes introduced their famous Black-Scholes option pricing model containing a formula, based on several restrictive assumptions, for determining the fair value of an option. One of those assumptions was that the option could be exercised only on the day of expiration (European style) rather than at any time up to expiration (i.e., American style). Later that year, Robert Merton extended the theory. In 1997, Merton and Scholes shared a Nobel Prize in Economics for their pioneering work in options pricing theory. (Unfortunately, Fischer Black had already passed away and so could not share in the award.)

Trading options with the help of their formula in the 1970s was like shooting fish in a barrel. Only a few savvy investors understood how to price options. They could spot big mispricings and make lots of money. Eventually, the rest of the street caught on. Now a version of the Black-Scholes options program comes built into many software packages—and can even be found on good calculators. To get a feel for what goes into the formula, recall from our previous example that we needed to know the following:

• The current price of the underlying asset

• The exercise price of the option

• How much time remains until expiration

In addition to these three numbers, Black and Scholes identified two other important factors:

• The volatility of the underlying asset—how much its price tends to fluctuate

• The risk-free rate—how much your money can earn when put into the safest possible investment, a Treasury bill

Armed with these five factors and the program, you can determine the theoretical fair value of a stock option—in other words, what it should cost. With that number in hand, it seems, you will always know whether a stock option is fairly valued, a bargain, or expensive. Almost, but not quite. There is a little problem with one of the numbers you need to provide for the program to do its work. That number is the volatility, the jumpiness or tendency for the stock’s price to fluctuate. What the formula wants you to tell it is how volatile the stock’s price is right now—its instantaneous volatility. But you can only estimate that number. At best, you can guess what the stock’s volatility was at different times in the past—its historical volatility—and assume that there is some predictability to its future volatility. What you wind up doing is estimating the future volatility from your guess of its historical volatility.

Why do you need to guess about a historical number? The problem is choosing an appropriate time frame for calculating the historical volatility. Should we look back a year? Six months? Three months? What if the stock was very volatile last week, but fairly inactive for months previously? Which are the relevant numbers? There’s no way to know for sure. In any event, investors tend to use rules of thumb to choose what they believe to be a relevant period of historical volatility. Six months seems to work here, nine months there.

Options and the “Greeks”

Options pricing theory helps us to understand how the value of an option should change when one of the factors determining an option’s price changes. If you spend much time with options, you will soon run across references to the Greeks. This is shorthand for a set of Greek letters used in formulas to calculate the sensitivity of an option’s value to small changes in one of those factors (e.g., time to expiration, price of underlying asset, interest rates). The five “Greeks” are as follows:

• Delta (δ) is the sensitivity of an option’s price to a change in the value of the underlying asset, all other things remaining constant.

• Gamma (γ) is the sensitivity of an option’s price to a change in the option’s delta, all other things remaining constant.

• Rho (ρ) is the sensitivity of an option’s price to a change in the risk-free interest rate, all other things remaining constant.

• Theta (θ) is the sensitivity of an option’s price to a change in the time to expiration, all other things remaining constant.

• Vega (a mnemonic for volatility, not a Greek letter) is the sensitivity of an option’s price to a change in volatility, all other things being equal.

sensitivity

Measure of the degree of responsiveness of some financial variable to a small change in some market condition. In mathematical terms, a partial derivative or partial difference.

There’s another approach to the problem, which sort of comes at it backward. Instead of solving for the theoretical fair value price, you simply set it equal to the market price of the option. Then you plug in all the other numbers and solve for the volatility. Now you can solve the Black-Scholes formula for volatility, the only remaining unknown. The answer you get is called the implied volatility. It is the volatility implied by the price the market has put on the option.

Implied volatility can be used in many different ways. Like prices and volumes, it can be charted to show its month-by-month, day-by-day, or even moment-by-moment changes. These changes can be graphed for technical analysis or subjected to a variety of statistical tests.

One basic way of using implied volatility is to compare the value of different options on the same underlying asset. For example, a stock such as IBM has over 100 different exchange-traded options at any given time. How can one stock generate so many options? Consider that exchange-traded options may have, say, a dozen different strike prices and five expiration dates. For each of these combinations, there can be both a call and a put being traded. Thus,

12 strike prices X 5 expiration dates X 2 call/put = 120 different options

Each of these options has a market price, but how much are they really worth? You can use the Black-Scholes formula to calculate the theoretical value of these options, but as we explained previously, this requires estimating the volatility of the underlying asset. On the other hand, you can get a feel for the relative value of these options by calculating their implied volatility. This can be a useful way of pricing options that trade infrequently. First, you get the implied volatility, using a liquid option on the stock or other underlying asset. Then you use that volatility to come up with a “quasi-market price,” which you can think of as the price the option might have if it were more actively traded.

Remember, this method doesn’t tell you what any of the options are worth in absolute terms, but only how the market is pricing them against each other. For example, you might find that the put options have a lower implied volatility than the calls, or that certain out-of-the-money options have a significantly higher implied volatility than their in-the-money brethren.

Another approach taken by traders compares implied volatility with historical volatility numbers. For example, if the 180-day historical volatility of a stock is 15 percent, and its implied volatility (as calculated from its most liquid option) is only 10 percent, these traders might reason that “volatility is cheap,” because the stock’s implied volatility is lower than at least one estimate of its current volatility. Theoretically, volatility and price should rise and fall together. Therefore, either the future volatility of the stock should diminish, bringing it into line with the option’s price, or else the price of the option should increase, reflecting the market’s current volatility. Traders can put on positions to exploit either or both of these possibilities.

Finally, implied volatility can be used as a benchmark to identify the market’s idea of the relevant historical volatility (e.g., 90-day versus 180-day). Some go one step further, interpreting implied volatility as the market’s forecast of the future volatility of the stock.

All of this information can be incorporated into options trading strategies. We’d like to remind you, however, that successful options trading requires a combination of skill, access to good information, and ability to execute trades at a reasonable cost. A little luck doesn’t hurt, either.