How to Trade Options: Interest Rates, Dividends, Calls Versus Puts

Volatility

Volatility is a measure of how much a security has previously moved in a given amount of time either up or down, and by implication, a measure of the future potential movement. It is important in determining an option’s theoretical value, and it is essentially the factor in the formula that accounts for the probability that the underlying stock can move to or beyond the strike price before the expiration date. If a high-beta (highly volatile) semiconductor stock and a conservative bank stock are both trading at $30 a share, you would not expect both to have the same probability of reaching $35 by a certain date. Their option prices would reflect this difference as a consequence of their different volatilities.

Historical volatility is calculated using the statistical formula for the standard deviation of a previous set of prices over a defined time period—typically 20, 50, or 100 days. One problem with that, however, is that each of these time periods can yield a slightly different volatility value and different data sources use different sets of historical values for their calculation. The greater issue is that none of the historical probability periods may produce an accurate prediction of the stock’s future volatility. The market may therefore price an option quite differently from its theoretical price. It is important to know all this so that you can keep a realistic perspective on the theoretical prices you see for options on quote screens or other services.

As discussed in the Introduction, it is really the implied volatility of an option (that which is determined in the marketplace) rather than the historical volatility (calculated from historical data) that is key, since what you pay for an option is determined by the implied volatility. But it is the historical volatility that is used to create the theoretical value that we at least use as a rough benchmark to determine whether an option is undervalued, fairly valued, or overvalued.

Volatility is discussed in greater detail in Chapter 9.

Interest Rates

Interest rates play a role in determining option prices as they affect the cost an arbitrageur would have to pay to carry a riskless stock-and-option position. Although a very minor one from day to day, the effect can be noticeable when comparing option prices during periods of very low interest rates with those of very high interest rates. For the short duration of most option trades, the impact of interest rates will be imperceptible unless they are changing somewhat dramatically in a short period of time—say, weeks. Option writers can expect to get slightly higher option premiums when interest rates are higher, all other things being equal.

Dividends

Option prices are affected by dividends, although some models omit them for convenience. Since dividends are cash distributions to shareholders from the earnings of the company, once paid, they are no longer part of the company’s net worth. To reflect this fact, the stock price is reduced on the appropriate date by the amount of the dividend (and the stock is therefore said to trade ex-dividend on that date). No adjustments are made to the price or terms of options on stocks that pay dividends. Therefore, one would expect call options to be priced somewhat lower for stocks paying dividends and put prices somewhat higher, since the option buyer gets no benefit from the payout. Furthermore, the dividend represents value that is removed from the company’s net worth each quarter rather than being reinvested inside the company and thus reduces the growth prospects of the stock. Indeed, the value of a call option does tend to be lower on a dividend stock and put options slightly higher because buyers know the stock price will be lowered on the ex-dividend date. As the dividend approaches, options tend to anticipate the expected drop in value caused by the dividend.

The change is very slight and occurs gradually, and because the stock price is continually changing, there is no arbitrage that can take advantage of this option price change on a riskless basis. There is, however, a common arbitrage on dividend paying stocks whereby arbs will buy the stock, sell ITM call options that expire after the dividend will be paid, and purchase puts at the same strike price and month. The position is placed at a net price equal to the strike price (give or take a few cents) such that if arbs are assigned on the stock prior to the dividend, they make no money. But they don’t lose any either, and if they are not assigned, they pocket the dividend and then exercise their put to sell the stock, earning a dividend payment that was acquired with virtually no risk. Dividend arbitrage on certain stocks can occur on millions of shares. As such, investors implementing option strategies on high dividend-paying stocks should be aware of this arb activity.

Calls versus Puts

Our discussion thus far about option pricing has made no real distinction between the pricing of puts and the pricing of calls. There are, however, differences, and, while small, they are worthy of note.

Theoretically, the price of a call option considers the possibility of the underlying stock rising to infinity. The put, however, accounts only for the probability that the stock goes to zero. Stated another way, a $40 stock can only drop by a maximum of $40 or 100 percent, yet it could conceivably go up by $60 (150 percent) or more. The probabilities of the stock going to either of these extremes during the option’s life may be miniscule, but from a statistical perspective, they are meaningful. They require that options pricing formulae use an assumed distribution other than a normal (bell-shaped) distribution for prices of the underlying. The options pricing formula developed by Fischer Black and Myron Scholes accounts for this phenomenon by utilizing a lognormal distribution, which essentially holds that prices may range between zero and infinity, corresponding well with the reality of stock prices. The result is that call prices contain a small positive bias in price over the equivalent (same strike and month) put. That is to say, that for a stock at exactly $50 with a volatility of 20 percent, a 50-strike call with 60 days to go would theoretically be $1.64, while the 50-strike put would theoretically be $1.60.

Option Skews and Anomalies

As you will discover, some options may trade near their theoretical values while others may deviate significantly from the formula-derived price. You will also observe, however, that when an option trades above or below its theoretical value, most others in the same month will also, and by a similar amount. Both of these observations are very important to the development of option strategies.

When demand for a specific option on a given stock is particularly high, the price of that option will be expected to rise, perhaps well above the theoretical value. Let’s say that XYZ is trading at $25 and there is abnormally strong demand for the May 30 call option. As that occurs, it presents opportunities for riskless arbitrage between that option and its underlying stock, which tends to bring that option back into line with other options in the same month and with the stock itself. Such arbitrage is rather straightforward and widely practiced by professional traders, market makers, and brokerage firms.

Aiding in the maintenance of price relationships between options is the fact that market makers price them by computer, and when they want to change the prices on a particular stock’s options, they commonly do so by simply changing the implied volatility in their pricing model. That results in all of the options on a given stock (at least those in the same month) being ratcheted up or down, essentially in unison, by the press of a button.

But there are other pricing anomalies that commonly occur with option prices that cannot be rectified by an arbitrage trade. The most common deviation in option pricing is the tendency of a given class of options (those on the same underlying stock) to trade at prices that imply a higher or lower volatility than the historical volatility used in the Black-Scholes formula. This happens extremely often and is readily visible when viewing an option chain, as both actual and theoretical prices are typically available in most option chains. An example is illustrated in Table 2.4, using Apple Computer (AAPL).

TABLE 2.4 Market Price versus Theoretical Value

Data source: Power Options^® www.poweropt.com/.

Table 2.4 shows us that on this day in January 2011, the market prices of options on AAPL closed considerably higher than those calculated by Black- Scholes. This is supported by data from McMillan Analysis Corp., showing the actual historical volatilities for AAPL to be as follows:

Depending on which time period you use for your volatility calculation, the implied volatility is almost double and, accordingly, so are actual prices. This may be a relatively extreme example, but the phenomenon is quite common. You will also notice that the implied volatilities in different months are not even the same. They are very high for the current month option, then dip by 25 percent in the next month and begin rising each subsequent month. (The full option chain shows almost identical implied volatilities in all strikes of the same month.) These are the realities of option pricing.

The reasons for such a differential between actual and theoretical pricing may be varied. The market may simply be expecting higher volatility in future months than during the period on which historical volatility was calculated. Or the market may be injecting a bias to either the upside or downside on the stock, which manifests itself as a higher implied volatility for both put and call options.

It is important to note that, regardless of the direction of an inherent bias being priced in by the market, both puts and calls on the same underlying will rise or fall accordingly. This phenomenon can be very misleading to those trying to interpret a directional message from the price of an option alone. When bad news comes out or is anticipated on a particular stock, there may, for example, be an increased demand for puts on that stock, causing put prices to rise above theoretical value. What happens, due to market forces and arbitrage, is that both the puts and calls on that stock will rise above theoretical value, and they will do so by a similar amount (i.e., the implied volatility of the puts will be similar to that of the calls).

Such differences in option prices between actual and theoretical or between actuals in different months are called skews—anomalies between the prices of different options on the same instrument. They cannot be arbitraged away, but they can be used in the development of option strategies that may offer a statistical advantage over time. The overvaluation in AAPL call options is somewhat akin to finding a blackjack table that pays 3-1 for a blackjack instead of 2-1. Over a large number of hands, it represents a definite statistical advantage to the player, but you still may not get one in the short run.