The first and most commonly used greek is delta. For the record, and contrary to what is frequently written and said about it, delta is NOT the probability that the option will expire ITM. Simply, delta is a number that measures how much the theoretical value of an option will change if the underlying stock moves up or down $1.00. Positive delta means that the option position will rise in value if the stock price rises, and drop in value if the stock price falls. Negative delta means that the option position will theoretically rise in value if the stock price falls, and theoretically drop in value if the stock price rises.

The delta of a call can range from 0.00 to 1.00; the delta of a put can range from 0.00 to –1.00. Long calls have positive delta; short calls have negative delta. Long puts have negative delta; short puts have positive delta. Long stock has positive delta; short stock has negative delta. The closer an options delta is to 1.00 or –1.00, the more the price of the option responds like actual long or short stock when the stock price moves.

So, if the XYZ Aug 50 call has a value of $2.00 and a delta of +.45 with the price of XYZ at $48, if XYZ rises to $49, the value of the XYZ Aug 50 call will theoretically rise to $2.45. If XYZ falls to $47, the value of the XYZ Aug 50 call will theoretically drop to $1.55.

If the XYZ Aug 50 put has a value of $3.75 and a delta of -.55 with the price of XYZ at $48, if XYZ rises to $49, the value of the XYZ Aug 50 put will drop to $3.20. If XYZ falls to $47, the value of the XYZ Aug 50 put will rise to $4.30.

Now, these numbers assume that nothing else changes, such as a rise or fall in volatility or interest rates, or time passing. Changes in any one of these can change delta, even if the price of the stock doesnt change.

Note that the delta of the XYZ Aug 50 call is .45 and the delta of the Aug 50 put is -.55. The sum of their absolute values is 1.00 (|.45| + |-.55| = 1.00). This is true for every call and put at every strike. The intuition behind this is that long stock has a delta of +1.00. Synthetic long stock is long a call and short a put at the same strike in the same month. Therefore, the delta of a long call plus the delta of a short put must equal the delta of long stock. In the case of the XYZ Aug call and put. 45 + .55 = 1.00. Remember, a short put has a positive delta. (Note: delta can be calculated with different formulas, which wont be discussed here. Using the Black-Scholes model for European-style options, the sum of the absolute values of the call and put is 1.00. But using other models for American-style options and under certain circumstances, the sum of the absolute values of the call and put can be slightly less or slightly more than 1.00.)

You can add, subtract, and multiply deltas to calculate the delta of a position of options and stock. The position delta is a way to see the risk/reward characteristics of your position in terms of shares of stock. The calculation is very straightforward. Position delta = option theoretical delta x quantity of option contracts x number of shares of stock per option contract. (The number of shares of stock per option contract in the U.S. is usually 100 shares. But it can be more or less, due to stock splits or mergers.)

So, if you are long 5 of the XYZ Aug 50 calls, each with a delta of +.45, and short 100 shares of XYZ stock, you will have a position delta of +125. (Short 100 shares of stock = -100 deltas, long 5 calls with delta +.45, with 100 shares of stock per contract = +225. –100 + 225 = +125)

A way to interpret this delta is that if the price of XYZ rises $1, you will theoretically make $125. If XYZ falls $1, you will theoretically lose $125. IMPORTANT: These numbers are theoretical. In reality, delta is accurate for only very small changes in the stock price. Nevertheless, it is still a very useful tool for a $1.00 change, and is a good way to evaluate your risk.

An ATM option has a delta close to .50. The more ITM an option is, the closer its delta is to 1.00 (for calls) or –1.00 (for puts). The more OTM and option is, the closer its delta is to 0.00.

Delta is sensitive to changes in volatility and time to expiration. The delta of ATM options is relatively immune to changes in time and volatility. This means an option with 120 days to expiration and an option with 20 days to expiration both have deltas close to .50. But the more ITM or OTM an option is, the more sensitive its delta is to changes in volatility or time to expiration. Fewer days to expiration or a decrease in volatility push the deltas of ITM calls closer to 1.00 (-1.00 for puts) and the deltas of OTM options closer to 0.00. So an ITM option with 120 days to expiration and a delta of .80 could see its delta grow to .99 with only a couple days to expiration without the stock moving at all.

The delta of an option depends largely on the price of the stock relative to the strike price. Therefore, when the stock price changes, the delta of the option changes. Thats why gamma is important.