When Options Near Expiration: A View of 3 Apple Options

Option theory may work great –  in theory, but sometimes it pays to take a look at how options actually behave in the open market.

Case in point, what really happens as an option nears its expiration date?

Our new ZeccoPulse contributor Adam Warner wrote a couple of articles (here and here) on how a stock might get “pinned” to a strike price on expiration. One reason?

You probably know that option values decay over time on an exponential basis. The closer to expiration, the faster the decay, culminating on expiration day itself when the option finally settles at its intrinsic value. With little to no time value, positions become “binary.” Options either have value or they don’t.

One way to view the value of an option is the probability of that it will have any intrinsic value at the end of expiration day. When there’s lots of time left, anything can happen. But when time is short, outcomes become more certain. When that happens, changes in the underlying stock or index get magnified in the price and characteristics of the options.

 

A view of 3 options on Apple

To see what I mean, let’s focus on three individual option contracts on Apple (AAPL) as they traded over the past couple of months – the Apple (AAPL) 350 calls for February, March, and July 2011.

I selected the 350 strike because the stock has traded around this level over the time period in question. This stock shows how these three options contracts traded – using the midpoint between the bid and the ask for each option as of the day’s close:

The purple line on the stock chart shows the 350 price level. All three call options rose and fell along with the stock, but at different rates. In percentage terms, those February options (which have now expired, of course) jumped around a lot more than the July options did – especially when the stock crossed through the 350 area.

One could say they had higher gamma, which is another way of saying that the delta of those options was subject to more rapid change.

 

Option greeks review: Delta, gamma, and theta

An option’s delta is simply a theoretical measurement of the rate at which an option gains or loses value when the underlying stock moves by $1. An option with a delta of 50 (actually 0.50, but I like to multiply it by 100 to represent one 100-share contract) should – in theory, of course – move by 50 cents per $1 move in the stock.

Here’s the delta for each of those three call options.

Why would the July 350 calls maintain a steadier delta than the others? Well, when time is short, options are more influenced by their actual intrinsic value – or potential intrinsic value to be more accurate.

Just a few days before expiration with Apple near 360, those February calls were far more influenced by the difference between the stock price and the strike price than other factors. Another way to look at it is that the time premium embedded in those options quickly vanished, providing a lot less of a cushion than those July options, which still have a few months to go until expiration.

The tendency for the delta of an option to change as the underlying stock changes is measured by the option’s gamma. That’s sort of the “delta of the delta.” While the delta shows how much the option might change in value based on a move in the stock, the gamma is a theoretical measurement of how much the delta itself will change.

Here’s a look at the theoretical gamma of these options:

Options that are deep in the money or way out of the money have lower gamma because the delta of these options doesn’t change very much if the stock moves by $1 even if their values change. The at-the-money options have the potential for more delta movement – especially near expiration.

In a way, gamma represents risk. If you’re long the option, it represents the risk that any unrealized gains you have will evaporate. If you’re short the option (although naked short call positions require level 5 options approval at Zecco Trading), it represents the risk that you’re going to suffer large losses quite quickly.

Of course the flip side to this is the option’s theta, a theoretical measurement of option time decay. Those who sell options near expiration get a lot of time decay on a per-day basis, which you can see on this chart of the theoretical theta of these options.

Theta is shown as a negative value because it represents time decay, which is good for those who sell options (not so good for those who are long). There’s not much theta in the July options (check back in June though), but plenty in, say, the March options that are expiring soon.

Notice the inverse relationship between gamma and theta? In a sense it represents the trade-off between risk and reward. If you’re long an option that has months to expiration, you don’t suffer a lot of time decay, but you don’t get a lot of gamma – and its potential reward in terms of increasing delta – either.

As expiration day looms, risk and reward become less theoretical and a lot more real. All the unknowns become finally known, the greeks become incalculable, and option values converge to a binary state – either in-the-money or out-of-the-money at 4:01 pm on expiration Friday.

 

Important Note
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Content, including research, tools and securities symbols, is for educational and informational purposes and should not be intended as a recommendation or solicitation to engage in any particular securities transaction or investment strategy. You alone are responsible for evaluating which securities and strategies better suit your financial situation and goals, risk profile, etc. The projections regarding the probability of investment outcomes are hypothetical and not guaranteed for accuracy or completeness. They do not reflect actual investment outcomes and are not guarantees of future results, and do not take into consideration commissions, margin interest and other costs that will impact investment outcomes. Content may be out of date or time-sensitive, and is subject to change or removal without notice. Supporting documentation for any claims made in this post will be supplied upon your email request to editor@zecco.com.

At the time of distribution of the material contained herein, neither Zecco Trading nor Zecco Forex was a market maker or acted as the contra-party for customer transactions through the firm’s principal accounts for the securities discussed.

Zecco Holdings, Zecco Trading, Zecco Forex, and their officers/partners/employees may hold a nominal financial interest in any of the securities discussed herein, with the nature of the interest consisting of, but not limited to, any option, right, warrant, future, long, or short position.

Neither Zecco Trading nor Zecco Forex has participated as a manager or co-manager in public offerings of the securities mentioned herein within the last twelve months.

While Delta represents the consensus of the marketplace as to the theoretical price movement of the option relative to the underlying security there is no guarantee that this forecast will be correct.

While Gamma represents the consensus of the marketplace as to the amount a theoretical option’s delta will change for a corresponding one-unit (point) change in the price of the underlying security there is no guarantee that this forecast will be correct.

While Theta represents the consensus of the marketplace as to the amount a theoretical option’s price will change for a corresponding one-unit (day) change in the days to expiration of the option contract there is no guarantee that this forecast will be correct.

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options.