Option Investor
Educational Article

By Popular Request, A Greek Review

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When trading options, there are a lot more factors to pay attention to, when compared to just trading stocks. Several months ago, I wrote a series of articles on all these factors that we need to pay attention to. Lately, I've had a veritable flood of email requesting detailed information on how to pick the right option strike, gauge what to expect in terms of option appreciation from a given move in the underlying stock, along with a host of other questions that are best answered by a detailed treatment of the myriad factors that determine option pricing.

Rather than just send curious readers digging through the archives in search of the appropriate articles, I thought it would make sense to re-issue this introductory article tonight. This way, we can bring the new readers up to speed, starting at the beginning.

Due to the plethora of additional factors that influence option pricing, most notably "the Greeks", it is possible to enter an option trade that produces a loss, even when a corresponding trade in the underlying equity or index would have produced a profit. Understanding these factors and their influence on option pricing is essential to profitable option trading, especially in the volatile market we currently have at our disposal.

So what are the Greeks? In order to answer that question, we need to say a few words about how option prices are calculated. Option prices are determined by applying the standard Black-Scholes pricing model, which uses 5 inputs to create the theoretical price of the option. They are as follows:

1. Time to expiration
2. Strike price
3. Value of the underlying equity or index
4. Implied volatility of the underlying equity or index
5. The risk-free interest rate
Discussion of the inner workings of the Black-Scholes model is far beyond the scope of this article, and there have been numerous books written on the subject for the inquisitive student. Rather than delving into theory, I thought it would be far more productive to deal with the practical measures of option pricing and strike selection that can aid us in our pursuit of profits. These measures are commonly referred to as the Greeks and the four most important Greeks, in my opinion, are Delta, Gamma, Theta and Vega.

Delta measures the amount that a given option will move with respect to the underlying security and is stated in terms of percentage from 0 to 100. If a stock moves $1 and the option in question increases in value by $0.40, we know that the option had a Delta of 40. At-the-money (ATM) options typically have a delta of 50, while out-of-the-money (OTM) options have a Delta less than 50 and in-the-money (ITM) have a Delta greater than 50. As we move further out-of-the-money, Delta approaches zero, while it approaches 100 as we move deeper in-the-money. Neither of these extremes are met in practical application, but the basic relationship should give us a useful working understanding.

Gamma is used to describe the rate-of-change of an option's Delta, and those that understand the relationship can use their knowledge to give their trading profits an extra boost. Putting the relationship in physics terms, Delta is the equivalent of velocity, while Gamma can be equated to acceleration. If you recall your high school physics, you'll remember that acceleration can really boost velocity over time. The same is true of the Delta-Gamma relationship. I'll leave you to ponder that concept and we'll revisit it in exacting detail on our next visit.

The one constant in the universe (aside from taxes) is the passage of time, and Theta is the Greek that measures the impact of Father Time on option prices. Options are, by definition, a wasting asset, meaning that the portion of the option premium that is attributable to time, declines day after day. Adding insult to injury, the rate of decay of the time-related portion of an option's value increases as expiration Friday draws near. The majority of an option's time value disappears in the final 30 days of its life and most of that evaporates in the final 2 weeks. During expiration week, an equity must move in your favor substantially, just to offset the loss in value due to Theta-decay in an OTM or ATM option.

Volatility is perhaps the most apparent determinant of option pricing; at least it has seemed that way during recent months as we have watched the VIX race from 35 to 57 and then back down to the low 20's. While normal trending markets don't have nearly that kind of volatility movement, when it does occur, it can yield outsized returns for appropriately positioned traders, and exact staggering losses from those unaware of its potential effects. Last week, I highlighted the perils of trading in a high-volatility environment. Traders that sell options in such an environment can reap substantial rewards, but need to be cognizant of the inherent risks that come with the territory.

One interesting point about time-value in options is that on a percentage basis, ATM options are the most expensive in terms of time value. So when we buy ATM options, we need to understand that we are buying the most time-value possible for that expiration month, and every last shred of that time-value will melt away by expiration Friday. By expiration, either all the time value will have melted away leaving a worthless option (great for option sellers, but unpleasant for option buyers), or the stock will have appreciated so that the option is ITM, now possessing intrinsic value equivalent to how far in the money the option is.

As a simple example, let's take a $50 OCT Call on stock XYZ which is trading for $3.00 one month before expiration. If on expiration Friday, the price of the stock is $48 (even if that is above the price of the stock one month earlier), the option will expire worthless, with no time value and no intrinsic value. On the other hand, if XYZ appreciates to $54 by expiration Friday, the option will be worth $4.00 ($4 intrinsic value, and no time value). In both cases, the time value of the option fades away to nothing by expiration, but if the stock moves sufficiently so that our option is in the money, we have real, as opposed to anticipated value.

Delta and Vega are fairly easy to quantify, and there are a number of websites that provide this data for those interested in learning the inter-relationships and how they influence the potential success of option trading. One of my favorite sites is www.ivolatility.com, which provides detailed analysis of option Greeks, as well as historical volatility charts. While this site also provides an option calculator to determine Theta and Gamma for specific options, I think these two Greeks are more important to understand from a qualitative sense, so I tend to focus less on the actual numbers and more on their general influence on option prices.

One interesting trend I have noticed in recent months is that online brokers are doing a better job of catering to option traders. All 3 of the brokers that I currently use, have recently added options analysis tools to their trading sites. This provides me with the ability to research the various Greeks on a prospective option trade without ever leaving the trading screen. In addition to basic option calculators that provide the ability to check Delta, Gamma, Vega and Theta for any option, these sites now provide charts of both historical and implied volatility. Using this latter tool, I can see where a stock's volatility is in relation to its historical range, helping me to make sure I am buying low volatility and selling high volatility. We'll devote a future article to just talking about volatility and how to use it to our advantage.

When properly understood, the inter-relationship of the Greeks on option pricing can be very useful to option traders (both buyers and sellers) who understand how to capitalize on the opportunities provided. Now that we've covered the basics, we're ready to dig into all the details you can stand. Fortunately, I don't have to write the whole series of articles again, as they are archived in the Options 101 section on the website. If this article whetted your appetite for more details, then feel free to peruse the list of articles below.

The Greeks, Part 1 - Delta and Gamma
Application of Gamma and Delta to Strike Selection
Back to the Olympians of Old
Oh, That Vexing Volatility
Volatility - Part Deux
The Greeks - Putting It All Together
A Greek Encore
Varying Views on Volatility
A Primer on Online Volatility Tools - Part I

Happy Reading!


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