The Greeks have given us feta cheese, philosophy, mathematics, and the Oedipal complex. They also tell us how much risk our option positions have.

There are ways of estimating the risks associated with options, such as the risk of the stock price moving up or down, implied volatility moving up or down, or how much money is made or lost as time passes. They are numbers generated by mathematical formulas. Collectively, they are known as the "greeks", because most use Greek letters as names. Each greek estimates the risk for one variable: delta measures the change in the option price due to a change in the stock price, gamma measures the change in the option delta due to a change in the stock price, theta measures the change in the option price due to time passing, vega measures the change in the option price due to volatility changing, and rho measures the change in the option price due to a change in interest rates.

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Delta

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 option's 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 doesn't change.