T2W Trading Community

I'll bet you probably never considered how international options trading can be! We know there are American options, which can be exercised at any time from when they are bought until their date of expiration (we call that "early exercise.") There are also European options, which cannot be exercised early, and can only be exercised on their expiration date. Well today we're going to learn about the "Greeks." This term should not be new to anybody who is already trading options. The reason is that they are so important, that unless you have a basic understanding of what they are, and how to use them, you are going to be trading with a serious disadvantage.

So what are these Greeks? Simply put, we can call them risk measurements, (sorry I had to throw in a little options humor there). Previously we learned that the theoretical value of an option can be determined by plugging some variables into the Black-Scholes formula. Well the Greeks tell an options trader the theoretical change in the options price given a change in one of the variables. They represent rates of change. For those of you familiar with the Calculus, you may recognize that the Greeks are really partial derivatives, but we won't dwell on that here. The variables that have Greeks associated with them are: stock price, time to expiration, projected volatility, and the risk free rate of return. The two other variables needed to price options using Black-Scholes, namely exercise price, and dividend rate, do not have associated Greeks.

This week we'll discuss some basic aspects of one of the most widely used of the Greeks. We'll follow up with more details and the rest of the Greeks later on.

Delta
The Delta of an option is a percentage that represents the change in the options price given a 1 point change in the price of the underlying stock. Notice that as the price of a stock increases, the price of a Call option will also increase (assuming all other things being equal.) On the other hand, the price of a Put option will decrease as the stock price increases. So Call option deltas will range from 0 to 100, while Put deltas range from -100 to 0 (the percentage sign is generally omitted.)

Calls that are very much out of the money (OTM) will have very small deltas. In other words, a small change in stock price will not have much of an affect, whereas a deep in the money (ITM) Call will move very close to the same amount as the change in the stock. At the money (ATM) Calls have deltas of about 50, meaning that for small changes in the stock price, the Call will change by about half of the stock price of change.

Put options are similar, but the signs are reversed. Okay, just to be sure, I'll spell it out. Puts that are very much OTM have deltas close to 0. Deep ITM Puts have deltas close to -1, and ATM Puts have deltas of about -50.

Here are some examples. The prices of the options with the stock equal to 100 are given. Notice how the option prices change with the stock price at 100.5 and at 99. It will help your understanding of this important topic if you can independently verify the numbers in the last 2 columns.

(click to enlarge)

Notice that the Call delta minus the Put delta for a given strike price equals 100. This is usually true although the difference may be slightly greater. It will never be less than 100.

Another important and useful way of looking at delta, is to consider it as an equivalent stock position (ESP.) Using this approach, we will be able to take a combination of stock and options and know that it will have the characteristics of a given number of shares of stock, hence, an ESP.

We just need a couple of rules to be able to do this. First, stock always has a delta of 100. So if we're long 300 shares we have 300 deltas, if we're short 800 shares we have -800 deltas. Since an option contract represents 100 shares of stock, to keep the accounting straight, we need to think of stock in lots of 100 shares. In the preceding example, we would think of it as 3 lots of 100 shares times 100 deltas to get 300.

Second, for each option position, we multiply the number of contracts by the delta. Keep in mind that the number of contracts will be positive if we're long the options and negative if we're short. So if we're long 10 of the Feb 85 Calls, we have +10 x +90 = +900 deltas. On the other hand, if we're short 5 of the Feb 120 Puts, then we have -5 x -86 = +430 deltas. Remember, a minus times a minus is a plus. Finally, to arrive at our ESP, we add up all the options and stock deltas in our position.

Believe me, it sounds a lot worse than it is. Most options trading platforms show you the value of the deltas, and some of the better ones, will calculate the ESP for you. There are also many commercially available software products that are quite reasonably priced.

Let's look at a hypothetical position:

The bottom line is that even though this position looks pretty complicated, it boils down to just being long the equivalent of about 180 shares of stock. That's a lot more manageable.