Lesson 14 of 20 · 6 min

Theta: the shape of decay

Theta is the value an option loses per day when nothing else changes, and nothing else never happens.

Theta measures the passage of time. Specifically it is the change in the option's price for one day less remaining, holding every other input fixed.

In the base case theta is −$0.053 per day. So the $3.02 call, with everything else unchanged, should be worth about $2.97 tomorrow. Check it against the model at 29 days: $2.968. Theta is accurate over one day, and increasingly inaccurate over longer stretches for a reason lesson 15 covers.

Theta is negative for long options and positive for short ones. This is the most reliable directional statement in the whole track: extrinsic value converges to zero at expiry, so it can only fall on average. It is also the only Greek whose direction of travel is known in advance. Nobody knows whether the underlying will rise; everybody knows tomorrow will be one day closer.

Two practical notes. Theta is usually quoted per calendar day, so a weekend costs roughly three days of decay while the market is closed and nothing can move in your favour. And theta as printed assumes constant volatility, so on a day when implied volatility also falls, the observed loss is theta plus the vega effect, and attributing all of it to time is a common misreading.

Theta is largest in dollar terms for at-the-money contracts, because they have the most extrinsic value to lose. The 110-strike call in the base case has a theta of only −$0.023, less than half the at-the-money figure, simply because it has less to give up.

Key terms

Theta: The change in an option's price per day of elapsed time, holding all other inputs fixed. Negative for long options.
Decay: The loss of extrinsic value as expiry approaches. Guaranteed to reach zero, uneven on the way.
Calendar versus trading days: Theta is normally quoted per calendar day, so decay continues across weekends and holidays when the underlying cannot move.

Worked example

Theta's prediction and the model's price

Base case: underlying 100, strike 100, rate 4%, volatility 25%. Underlying held at 100 throughout.

30 days: price, theta: $3.02, −$0.053
Theta's prediction for tomorrow: $2.97
Model price at 29 days: $2.97
21 days: $2.51
14 days: $2.03
7 days: $1.42

Theta is right about tomorrow every time, and it is a bad guide to next month, because theta itself doubles over the period.

Check yourself

The base-case call is worth $3.02 with a theta of −$0.053. If nothing changes, what is it worth in ten days — and why is $2.49 not the right answer?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.