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.
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.
Gamma
Gamma
is an estimate of how much the delta of an option changes when the
price of the stock moves $1.00. As a tool, gamma can tell you how
"stable" your delta is. A big gamma means that your delta can start
changing dramatically for even a small move in the stock price. Long
calls and long puts both always have positive gamma. Short calls and
short puts both always have negative gamma. Stock has zero gamma because
its delta is always 1.00 – it never changes. Positive gamma means that
the delta of long calls will become more positive and move toward +1.00
when the stock prices rises, and less positive and move toward 0.00 when
the stock price falls. It means that the delta of long puts will become
more negative and move toward –1.00 when the stock price falls, and
less negative and move toward 0.00 when the stock price rises. The
reverse is true for short gamma.
Theta
Theta,
a.k.a. time decay, is an estimate of how much the theoretical value of
an option decreases when 1 day passes and there is no move in either the
stock price or volatility. Theta is used to estimate how much an
option's extrinsic value is whittled away by the always-constant passage
of time. The theta for a call and put at the same strike price and the
same expiration month are not equal. Without going into detail, the
difference in theta between calls and puts depends on the cost of carry
for the underlying stock. When the cost of carry for the stock is
positive (i.e. dividend yield is less than the interest rate) theta for
the call is higher than the put. When the cost of carry for the stock is
negative (i.e. dividend yield is greater than the interest rate) theta
for the call is lower than the put.
Vega
Vega
(the only greek that isn't represented by a real Greek letter) is an
estimate of how much the theoretical value of an option changes when
volatility changes 1.00%. Higher volatility means higher option prices.
The reason for this is that higher volatility means a greater price
swings in the stock price, which translates into a greater likelihood
for an option to make money by expiration.
Rho
Rho
is an estimate of how much the theoretical value of an option changes
when interest rates move 1.00%. The rho for a call and put at the same
strike price and the same expiration month are not equal. Rho is one of
the least used greeks. When interest rates in an economy are relatively
stable, the chance that the value of an option position will change
dramatically because of a drop or rise in interest rates is pretty low.
Nevertheless, we'll describe it here for your edification.
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