Learn When You Should Exercise an Option Early
While the math behind options pricing models may seem daunting, the underlying concepts are not. The variables used to come up with a “fair value” for a stock option are the price of the underlying stock, volatility, time, dividends, and interest rates.
The first three deservedly get most of the attention, because they have the largest effect on option prices. But it is also important to understand how dividends and interest rates affect the price of a stock option. It is also these two variables that are crucial to understanding when to exercise options early.
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The Black-Scholes model
The first option pricing model, the Black-Scholes model, was designed to evaluate European-style options, where early exercise is not permitted. So Black and Scholes never addressed the problem of when to exercise an option early and how much the right of early exercise is worth. Being able to exercise an option at any time should theoretically make an American-style option more valuable than a similar European-style option, although in practice there is little difference in how you trade them.
Because stock options are American-style, and carry with them the right of early exercise, different models were developed to accurately price them. Most of these are refined versions of the Black-Scholes model, adjusted to take into account dividends and the possibility of early exercise. To appreciate the difference this can make, you first need to understand when an option should be exercised early.
The role of interest rates in determining when to sell early
The short answer as to when you should exercise an option early is: only when its theoretical value is exactly at parity and its delta is exactly 100. That may seem obtuse, but as we go through the effect interest rates and dividends have on option prices, I will also bring in a specific example to show when this occurs. First let’s look at the effect interest rates have on option prices, and how they can determine if you should exercise a put option early.
An increase in interest rates will drive up call premiums, and cause put premiums to decrease. To understand why, you need to think about the effect of interest rates when comparing an option position to simply owning the stock. Since it is much cheaper to buy a call option than 100 shares of the stock, the call buyer is willing to pay more for the option when rates are relatively high, since he can invest the difference in the capital required between the two positions.
Interest rates have been steadily falling in the United States, to the point where the current Fed Funds target is down to 1.0%. With the short-term rates available to individuals of around 0.75 to 2.0%, interest rates have a minimal effect on option prices right now. This is likely to change in the future, and all the best option analysis models include interest rates in their calculations, using a “risk-free” interest rate such as US Treasury rates.
Interest rates are the critical factor in determining whether to exercise a put option early. A stock put option becomes an early exercise candidate anytime the interest that could be earned on the proceeds from the sale of the stock at the strike price is large enough. Determining exactly when this happens is difficult, since each individual has different opportunity costs, but it does mean that early exercise for a stock put option can be optimal at any time provided the interest earned becomes sufficiently great.
Another consideration: dividends
How dividends affect early exercise is easier to pinpoint. Cash dividends affect option prices through their effect on the underlying stock price. Because the stock price is expected to drop by the amount of the dividend on the ex-dividend date, high cash dividends imply lower call premiums and higher put premiums.
While the stock price itself usually undergoes a single adjustment by the amount of the dividend, option prices anticipate that dividends will be paid in the weeks and months before they are announced. The dividends paid should be taken into account when calculating the theoretical price of an option and projecting your probable gain and loss when graphing a position. This applies to stock indices as well. The dividends paid by all stocks in that index (adjusted for each stock’s weight in the index) should be taken into account when calculating the fair value of an index option.
Dividends are critical to determining when it is optimal to exercise a stock call option early, so both buyers and sellers of call options should consider the impact of dividends. Whoever owns the stock as of the ex-dividend date receives the cash dividend, so owners of call options may exercise in-the-money options early to capture the cash dividend. That means early exercise makes sense for a call option only if the stock is expected to pay a dividend prior to expiration date.
Traditionally, the option would be exercised optimally only on the day before the stock’s ex-dividend date. But recent changes in the tax laws regarding dividends now mean that it may be two days before now, if the person exercising the call plans on holding the stock for 60 days to take advantage of the lower tax for dividends.
Example
Say you own a call option with a strike price of 90 that expires in two weeks. The stock currently trading at $100, and is expected to pay a $2.00 dividend tomorrow. The call option is deep in-the-money, and should have a fair value of 10 and a delta of 100. So the option has essentially the same characteristics as the stock. There are three possible choices of what to do
1. Do nothing (hold the option).
2. Exercise the option early.
3. Sell the option and buy 100 shares of stock.
Which of these choices is best? If you hold the option, it will maintain your delta position. But tomorrow the stock will open ex-dividend at 98 after the $2.00 dividend is deducted from its price. Since the option is at parity, it will open at 8, the new parity price, and you will lose two points ($200) on the position.
If you exercise the option early and pay the strike price of 90 for the stock, you throw away the 10-point value of the option, and effectively purchase the stock at $100. When the stock goes ex-dividend, you lose $2 per share when it opens two points lower, but also receive the $2.00 dividend since you now own the stock.
Since the $2.00 loss from the stock price is offset by the $2.00 dividend received, you are better off exercising the option than holding it. That is not because of any additional profit, but because you avoid a two-point loss. You must exercise the option early just to ensure you break even.
What about the third choice, selling the option and buying stock? This seems very similar to early exercise, since in both cases you are replacing the option with the stock. The decision of which to do depends on the price of the option. In this example, we said the option is trading at parity (10) so there would be no difference between exercising the option early or selling the option and buying the stock.
But options rarely trade exactly at parity. Suppose your 90 call option is trading for more than parity, say $11.00? Now if you sell the option and purchase the stock you still receive the $2.00 dividend, and own a stock worth $98, but you end up with an additional $1.00 you would not have collected if you exercised the call.
Alternately, if the option is trading below parity, say $9.00, you want to exercise the option early, effectively getting the stock for $99.00 plus collecting the $2.00 dividend.
So the only time it makes sense to exercise a call option early is if the option is trading at, or below, parity, and the stock goes ex-dividend tomorrow.
Summary
While interest rates and dividends are not the primary factors affecting an options price, an option trader should be aware of their effects. In fact, the primary drawback I have seen to many of the option analysis tools available is that they use a simple Black Scholes model and ignore interest rates and dividends.
The impact of not adjusting for early exercise can be very large, since it can cause an option to seem undervalued by as much as 15%. When you are competing in the options market against other investors and professional market makers, it doesn’t make any sense to not use the most accurate tools available.
Jim Graham is OptionVue’s Product Manager and develops and enhances the company’s OptionVue 5 Options Analysis Software to meet the real-world needs of institutional and individual options traders. You can find more valuable options trading information at www.OptionVue.com.