money (I TM) options. Extrinsic value (also
called time value) is an option’s value over
and above its intrinsic value. Thus, the
price of an O TM option represents 100%
The extrinsic value of an option is essentially the market’s opinion of how likely it is
to be ITM at expiration, and by how much.
All else being equal, an O TM option that
the market thinks is more likely to end up
ITM will have a higher price—more extrinsic value—than an O TM option the market
thinks is less likely to go ITM.
THE CONE OF UNCER TAIN T Y
Time gives stocks the opportunity to move
up or down. All else being equal, the more
time is left until expiration, the more likely it is a stock may move up or down by a
larger amount from its current price. That
means a longer-term O TM option has a
greater likelihood of turning into an ITM
option. The less time is available, the less
likely it is the stock may move significantly.
See Figure 1.
So, in theory, an option with less time—
fewer days to expiration—has a lower extrinsic value than an option with more days to
expiration. Thus, theta measures how much
each day reduces an option’s extrinsic value.
Almost everything that goes into an option’s price moves in two directions. In the
short term, stock prices move up and down.
So does volatility. Over longer periods, even
dividends and interest rates change. But
one thing doesn’t change: time marches
on at a steady rate, and always in the same
direction, one day at a time. Like our mortal
selves, each flip of the calendar, from one
day to the next, takes an option one day
closer to its expiration date.
Yes, time passes, and that’s why options
have time decay—also known as theta—to
the detriment of option buyers and the benefit of option sellers. Theta is a theoretical
metric (a “greek”) that represents how much
an option’s price loses, or decays, as one day
passes to the next. And because of time’s
reliability, many option traders rely on theta.
But why do options prices decay in the
first place? Keep in mind that an option’s
price has two components: intrinsic and ex-
trinsic value. Intrinsic value is affected only
by where the stock price is
relative to an option’s strike
price. It’s either zero for
out-of-the-money (O TM)
options, or the difference
between the stock price and
the strike price for in-the-
Let’s look at a theoretical example of the
impact of theta on options pricing (Figure
2). Say the SPX was at 2738 at the end of
November 2018. The 2700 put with 90 days
to expiration was valued at $73.33. Roll the
calendar ahead a month. Assume the SPX is
still at 2738. With volatility unchanged, the
value drops to $62.01. Note that it dropped
$11.32 over the month, although nothing
changed except the passage of time.
Now roll the calendar ahead another
month. Keep all else unchanged, and the
value drops by $22.06, from $62.01 to $39.95.
One month after that, in our example, the
option has expired worthless, having lost
the remaining $39.95. Notice, though, that
over each 30-day period, theta was high-
er—first $11.32, then $22.06, then $39.95.
Theta isn’t linear. It increases as the option
In this example, at 90 days out, the daily
theta was $0.47. So, when the calendar
was rolled from 90 days left to 89 days left,
the theoretical value went from $73.33 to
$72.86. At 60 days out, theta was $0.56, and
with 30 days to go, theta was $0.78. If
you’re designing time-sensitive options
strategies, it’s important to remember that
theta isn’t linear.
More to the point, how can one single day
have such different impacts on options with
different days to expiration? Although time
is a constant in and of itself, as a percentage
of time before expiration, it continues to
grow as expiration nears. One day is 0.55%
of 180 days, 1.67% of 60 days, 3.33% of 30
days, and 6.67% of 15 days. If an option is
FIGURE 1: Probability cone. To view this study in the thinkorswim® platform from TD Ameritrade, go to
Analyze > Probability Analysis. For illustrative purposes only. Past performance does not guarantee future results. A
time left, the