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A deep in-the-money call may make an almost perfect proxy for the stock, for example the Microsoft (NASDAQ:MSFT) $20 strike call would cost $11.85, when it was already $11.80 in the money, so the option premium is only 5 cents. However the January 2013 $31 strike call would cost $2.49, even though it was only 80 cents in the money, so the option premium would be $1.69.

(click to enlarge)

Stock quotation and options chart by Yahoo! Finance.

Obviously if the price of the underlying MSFT stock moves up or down, these options are not both going to behave in exactly the same manner relative to the price of the underlying stock.

It's important to have a good idea about the future price behavior of options you trade. So here's the question: How much will the price of each option move if the stock moves $1? The answer depends on the delta of the option.

Definition: Delta is the amount an option price is expected to move when the underlying stock moves $1.

Delta is the fourth letter of the Greek alphabet, equivalent to 'd' and yes, the river deltas like that of Mississippi or the Nile are called that because they look like the Δ shape of the capital delta letter and they get wider as they approach the ocean deep.

This may help to remember that the delta of an option expands and approaches 1 as it gets deeper into the money.

Options have a delta, but does the stock have a delta? Well sort of, but the delta of a stock is always exactly 1, because a move of one dollar in the stock equals a move of exactly one dollar in the stock--which is rather obvious. What is not quite so obvious is that when you have a deep in-the-money option, its delta may be so close to 1 as makes no appreciable difference and hence our Microsoft January 2013 $20 strike call also has a delta of 1, meaning that if the stock moves $1, the option will also move $1 just like the stock.

On the other hand, the other option we looked at, the Microsoft January 2013 $31 strike call which cost $2.49 even though it was only 80 cents in-the-money. The delta on this option is 0.6, meaning that it will only move about 6o cents when the underlying stock moves $1.

Usually in-the-money options will move more than out-of-the-money options, and short-term options will react more than longer-term options to the same price change in the stock.

Options that are at-the-money usually have a delta close to 0.5, which reflects that there is a roughly equal probability of the stock moving up or down.

As expiration gets closer, the delta for in-the-money calls will approach 1. The delta of out-of the-money calls will approach zero and won't react at all to minor price changes in the stock. That's because if they are held until they expire, calls will either be exercised or they will expire worthless.

Adding up the delta of a position.

Here's one of the really interesting things that excites me about delta. (OK, I am a delta nerd, I know). You can add up the delta of existing positions to see exactly where you stand on a particular day.

Delta does not stand still and it changes over time and with changes in the price of the stock, not to mention changes in implied volatility which is basically the mark-up that option market makers attach to options to compensate them for risk. So delta will only give you a snapshot of the present moment, but that is still incredibly helpful if you want to make adjustments.

Look at this position statement from an IRA investor's account:

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Graphics from TradeKing

The investor has 30 Microsoft January 2013 calls, representing 3,000 shares, (the total delta for these options is actually 2971.80, which is just about close enough to 3000 to call delta equal to 1).

But he is also short 20 Microsoft May 19th 2012 $32 strike calls, which subtracts a delta of 920.86 from his position, because these calls have a delta of about 0.46, and because short calls are always a minus delta.

(This is almost the same as a covered call, except that the deep in-the-money call is used as a substitute for the stock. This type of covered call is known as a bull call spread.)

And then he owns 10 shares of Microsoft stock outright, so they have a delta of plus 10. Add the two pluses and the minus and his total delta in the position on the day in question is 2060.94, as shown in the illustration.

This means that if the stock goes up $1, he will gain $2060.94 even though he is short the 20 May $32 strike calls. So if the short calls expire worthless at $32 or less on May 19th, the investor will be happy to add $640 to his account total, but if the stock shoots up to, let's say, $34 at options expiration, he will still be over $2,000 better off than he is right now.

Also note that the investor can easily adjust his overall delta at any time by buying or selling more long or short calls, or may increase the delta simply by buying more of the underlying stock. In the example shown, the investor owns 30 long in-the-money calls, but is short only 20 close-to-the-money calls.

If the whole market moved upwards, carrying MSFT, which is a Dow Jones Industrial Average stock, upwards, and the price of the $32 calls increased, the investor might want to sell 5 more calls at the higher price to average up the sale price of the short calls if he thought the stock looked toppy, then buy them back again if the stock corrected. By selling those extra 5 short calls, he would reduce his overall delta, thus reducing his profits if the stock surged sharply upwards, but cutting his losses if it fell back again.

On the other hand, if the underlying stock corrected in line with the market and the investor felt it was oversold, he might want to take profits by buying back some of the short calls in anticipation of the stock rebounding and thus giving him another opportunity to sell them again for more.

Source: How To Avoid The Delta Blues With Microsoft In Your IRA