When you hear traders talk about the Greeks, they don’t mean Plato or Socrates.

They’re talking about the series of calculations that are used to determine the value of options. The calculations are designated by various letters of the Greek alphabet, from which they get their name.

On our agenda today is delta.

Best known as the fourth letter of the Greek alphabet (or seen in movies followed by the word “Force”), delta represents change. In options, that means the rate of change in the value of an option as related to the underlying instrument.

I know that seems like a mouthful, and it is, but bear with me and it’ll make a lot of sense shortly. (Plus you’ll sound like a genius among your friends.)

Every option, whether call or put, has a delta attached to it. Generally you can find this information on your broker’s Web site.

A call has a positive delta, and a put has a negative one.

If an option is at the money, usually the call option will be a delta of +.50 and the put option will be -.50.

Thus, if the GBP/USD is currently trading at 1.6400, the 1.64 call option has a delta of +.50 and the 1.64 August put option has a delta of -.50.

As the pair moves up in value (that is, the sterling appreciates against the dollar), the sterling calls will increase in value. As of this writing, they are trading at $2.51 x $2.63. With the delta at +.50, that tells us that for every penny the sterling increases in value (which would be measured as 100 pips), the option will increase 50 cents. Thus the delta is the measure of the rate of change in the value of the option as compared to the value of the underlying asset.

The reverse is also true. If the spot price fell 1 cent, or 100 pips, the value of the put option would increase by 50 cents.
We also have another inverse relationship to consider. If we are holding put options and the spot price increased, the value of the put option would FALL by 50 cents. Same is true of the call. A 100-pip or 1-cent decrease in the underlying spot price would make the option fall by 50 cents.

So if the pound is at 1.6400, and we are looking at the August 1.64 calls, let’s say we go ahead and we buy them right now at $2.63 ($263). We believe the sterling is going to rise and the options are going up in value. If the spot price goes to 1.6500, we can expect the call option to move up 50 cents in value to $3.01 x $3.13, giving us a return of 38 cents per position.

However, at that level, the delta has changed (actually it always changes as the price changes, but for the sake of simplicity we won’t go into that detail). At this point the delta is nearly +.60. So now for every cent the spot moves up, our option will increase by 60 cents. By the time that the call option is deep in the money, it will have a delta of 1.00. That means that for every 100 pips, or 1-cent move, in the spot, the option will move a corresponding 100 cents. The same is true for a deep in-the-money put. It will eventually reach its maximum delta of -1.00, at which point it will move in lockstep with the spot price.

How does this help us? Mainly in terms of entries and exits that we would like to plan in advance.

Planning Moves with Delta

Let’s go back to our British pound calls. When we last left them, we were at the purchase price of $2.63 ($263). We know that for the price to break even, we must see the underlying spot price move to 1.6663 by expiration. If it moves up, but less than $2.63, our position will be worth something, but it will still be a loss.

If we want our position to double, we can use delta to make the following calculation. A 1-cent move will increase our value by 50 cents to $3.13. Another 1-cent or 100-pip move will increase our option value by 60 cents to 3.73. That increases our delta to .65. Another 1-cent or 100-pip move will take us to $4.38.

That takes our spot to 1.6700. It is now 3 cents (or 300 pips) above our strike price and is valued with an additional $1.38 in time value to make up the whole price of $4.38.

If it never moves another pip or penny until expiration (where time value is zero), we would still have a 37 cent profit on the option – that’s simply taking the 3-cent or 300-pip move on the underlying spot and subtracting out our original $2.63 entry price.

But back to our example, we still have some time value and we are aiming for a double. Thus we need the option price to end at $5.26 ($526) or higher. At this point, our delta has reached +.70. Thus another 1-cent, 100-pip, move adds 70 cents to our $4.38 to make it $5.08. We are now only 18 cents shy of our target, and our delta has now risen to +.78, so we only need a move of 23 pips to get us to our target.

We have viewed a move of 423 pips (or approximately 4.25 cents) to produce it. But that isn’t all that goes into the equation. Time value has also deteriorated during this process and added some volatility.

Nevertheless, we can use delta to estimate our profit targets and keep them in line with current underlying movements of the market.

Hope that clears up some of the mystery about these Greek terms you hear tossed around.

Until next time,
Bill Jenkins

August 3, 2009

Bill Jenkins

Bill Jenkins, founder and managing editor of Master FX Options Trader, knows the Forex currency markets inside and out. After 20 years and a string of losses following other people's crack advice, Bill created his own system for cashing in on tiny currency fluctuations between the British pound and the U.S. dollar. Now you have a chance to benefit from his “lifetime” of hard-earned experience. As Agora Financial's resident currency specialist, Bill’s advice has led readers to gains of 33% in a week... 70% in four days... and 100% practically overnight. And we've broadened the service to include the euro, yen and other currencies in these volatile trading markets. When Bill is not helping people enjoy big wins with simple currency plays, he's a church minister and owns his own contracting business.

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