By Guy Bower of www.guybower.com*
If you have been trading options or warrants for even just a little while, you’ve come across the concept of the delta. It is a relatively simple concept that acts as a measure of the rate of change in an option’s price versus a change in the underlying market.
If you find a simple book on options or look at some of the brochures and information from various exchanges, you’ll see the concept of the delta receives some attention, but not much. This is also true for many of the warrant seminars and marketing materials you see.
In this first of a four-part series, we will look at the basic definition of a call option delta. We will keep things relatively simple here, so apologies to those who already know this stuff. In the next three parts of the series, we will be able to roll up our sleeves and see how to use the delta in real-time trading. This week, we lay the foundation.
What is the delta?
Essentially, a delta is there to help you understand how an option behaves.
Suppose we have a 1% rally in our share price. Think, for a moment, about how the price of a deep in-the-money call option will change in relation to the price of a far out-of-the-money call option.
One would think the price of the in-the-money option is more likely to move a greater amount than the price of the out-of-the-money call option. In fact, picture a call option way, way, way out-of-the-money. The price may not even move at all!
The way to measure the degree that an option price will move in relation to a movement in the underlying asset price is called the delta and is available in most options software packages.
Measurement and Interpretation of the Call Delta
The delta can be expressed in two ways:
- As a percentage -- For example, the delta of an October $35.00 strike call option in NAB is currently +61%. This means that, for every 10c rise in NAB, the fair value for the $35.00 call will increase by approximately 6c.
- As a decimal -- In the example I just gave you, you would say the delta for the $35.00 call is +0.61. This is the more common method, but the interpretation is essentially the same.
Now, think about the range of values for the delta of a call option. Really far out-of-the-money call options would hardly move if the underlying asset were to increase by just a little. You could confidently say, therefore, that the delta for a way out-of-the-money call option would be close to zero. The further out-of-the-money you go, the closer the delta moves to zero.
What about in-the-money options? Well, assuming all other factors remain constant (especially volatility), it is fair to say that an option’s fair value would not increase at a faster rate than the underlying market. Right?
Sure, if the other factors changed (interest rates, volatility and dividends), it might be possible. But, holding all those factors steady, the option price would not increase at a faster rate than the underlying, given a solitary change in the underlying.
This means that the most the delta could be is +100 per cent, or +1.0. A delta of +1.0 means the fair value of the option will move “tick-for-tick” with the underlying. A 5-cent increase in NAB will result in a 5-cent increase in the fair value of that particular call option.
| Strike | Delta |
| $30.00 | 1.00 |
| $31.00 | 1.00 |
| $32.00 | 0.98 |
| $33.00 | 0.92 |
| $34.00 | 0.80 |
| $35.00 | 0.61 |
| $36.00 | 0.39 |
| $37.00 | 0.21 |
| $38.00 | 0.09 |
| $39.00 | 0.03 |
| $40.00 | 0.01 |
Have a look at the call option table for NAB (as of this article’s initial writing, at $35.40). Note that, the deeper you go in-the-money, the closer the delta will be to +1.0. That means that deep in-the-money call options tend to behave just like the underlying asset. (This is an interesting thought when you want to hedge a position.)
A general rule of thumb is that an at-the-money option will have a delta of close to +0.50. The underlying asset, by definition, will always have a delta of +1.0.
Delta will also change, given the amount of time left in an option. So, a $35.00 October call will have a different delta from a December call. We’ll discuss this concept later in the series.
We have now established that the delta is a measurement of how an option behaves, given a change in the stock, and that that measurement ranges between zero and +1.0 for all call options.
Put Option Deltas
So far, we have talked about call options only. What about puts? Wouldn’t they just be the same? A $35.00 call should have the same delta as a $35.00 put right? Certainly not!
Think about it. If a market rallies 10 cents, the fair value of our calls would increase by a multiple of the delta. Put options, however, would decrease in price. And, yes, you guessed it; each put would decrease by a multiple of its very own delta.
The delta for a put option is pretty much the same as the delta for a call option, apart from the fact that the put delta is a negative number, not a positive one. An at-the-money put delta will be close to –0.50 just as an at-the-money call delta will be close to +0.50. Out-of-the-money put deltas will approach zero, just like call options. In-the-money deltas for put options will approach –1.0 just as call deltas approach +1.0.
Now, have a look at this table again, this time with the put deltas. Have a closer look at the put and call deltas for any one strike price. Notice anything? Their absolute value (i.e., ignoring the negative sign) adds up to 1.0. This is not a coincidence, but it will be something to look at in a couple of weeks.
October NAB options
| Strike | Call Delta | Put Delta |
| $30.00 | 1.00 | 0 |
| $31.00 | 1.00 | 0 |
| $32.00 | 0.98 | -0.02 |
| $33.00 | 0.92 | -0.08 |
| $34.00 | 0.80 | -0.20 |
| $35.00 | 0.61 | -0.39 |
| $36.00 | 0.39 | -0.61 |
| $37.00 | 0.21 | -0.79 |
| $38.00 | 0.09 | -0.91 |
| $39.00 | 0.03 | -0.97 |
| $40.00 | 0.01 | -0.99 |
So, What?
So, what is the big deal? What do we do with the delta? Is it worth all the bother? In my opinion, it is. Understanding your delta allows you to understand risk because that is essentially what the delta is: A measure of risk relative to market movements.
Even when you do not know what your actual numerical delta is, you should know if your delta is negative or positive and know if your delta is large or small. It is simply a measure of risk.
Some professional options traders would not be able to tell you what their exact delta is, but they do understand how movement in the market affects their positions. Delta is simply a method of measuring this exposure.
The most important lesson regarding delta is that you should be thinking in terms of risk and how your position changes relative to the market.
Over the next three articles in this series, we will look at the whole concept of delta, including how to use it in real time, how to apply the delta to multiple positions and, most importantly, when just looking at your delta becomes dangerous. It’s exciting stuff.
*Reprinted (and modified) with permission from Guy Bower of www.guybower.com
