(the Greeks): Theta
Theta provides an indication of the sensitivity of an
option's fair value to small changes in the time left to expiration.
Theta is often expressed as the amount an option's price will decay in a
single day. Theta thus provides an estimate of how much an option's
theoretical value decreases when one day passes ďż˝ assuming there is no
move in the stock price and no change in the option's implied
Theta is used to estimate how much
of an option's extrinsic (i.e., time) value is whittled away by the
constant passage of time. Because an option loses time value as time
passes, theta is shown as a negative number. Time decay works against
option buyers but works in favor of option sellers (writers).
- For Long
calls and long puts: Theta is always negative;
- For Short
calls and short puts: Theta is always positive;
- For Stock:
Theta is zero, because a stock's value is not eroded by time;
options with fewer days left to expiration: Theta has a much greater
impact later in the life of an option, i.e., when it gets closer to
expiration. Note that time decay is not a linear function; it
accelerates as the option approaches expiry.
Theta decreases as options go in- or out-of-the money;
it is highest for at-the-money options. It also increases when implied
volatility goes down or when fewer days remain to expiration. A position
that consists of long options with a high, positive gamma value also has
the highest negative theta. Long gamma provides the fuel for an option
position to make money if the underlying starts to move substantially
(think of a long straddle); however, the price you pay for all that
power is theta. Theta will increasingly start to hurt your long position
the longer a stock remains (more or less) stationary, and the longer you
hold the position.
Theta is not the same for a
call and a corresponding put at the same strike price and with the same
expiration date: There is a difference which is accounted for by the
cost of carry for the underlying stock. When the cost of carry for the
stock is positive (i.e., when its dividend yield is less than the
interest rate), the call's theta will be higher than that of the put.
Conversely, a call's theta will be lower than that of its corresponding
put when the cost of carry for the stock is negative (i.e., when its
dividend yield is greater than the interest rate).
The fact that options are decaying assets is a vital
trading lesson that needs to be fully understood; it is particularly
relevant for those just starting out in options trading. As noted above,
an option's time decay is not linear: Theta accelerates faster and
faster the closer an option gets to expiration. Some traders thus
liquidate or roll out their positions when one month or less remains to
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