How much premium is left as an option ages?
What shape does time decay follow?
Time decay is the erosion of an option’s time value as expiration approaches. It is not linear: on at-the-money options it accelerates into the final weeks, while far out-of-the-money options decay more evenly. Theta is the number that puts a per-day figure on this decay for a single position.
The shape of the curve
For an at-the-money option, time value shrinks roughly with the square root of the time left: the premium with d days to go is today’s premium times the square root of (d ÷ today’s days to expiration). It is an approximation that holds while price and implied volatility stay put, but it captures the shape — a long, shallow slope and then a steep drop in the final weeks. Theta, the per-day figure, is the slope of this curve on one day.
What it means for picking an expiration
Because the early part of the curve is flat, a buyer who picks a longer expiration pays more in total but loses less of it per week in the first stretch. A seller who wants the steep part has to accept short expirations, and with them a much higher sensitivity to price moves near the strike. Choosing an expiration is therefore choosing where on the curve the position spends its life, not only how long it runs.
What bends the curve
The square-root curve assumes nothing else happens. A move away from the strike pushes the option in or out of the money, and out-of-the-money options decay along a flatter path of their own. A rise in implied volatility can add back more time value than a week of decay removed, and a drop can wipe out weeks of decay in one session. Use the curve as a baseline for the actual marks, not as a forecast.
The common misreading
Many traders assume that once half the time has passed, half the premium is gone. On an at-the-money option it is not: with half the days left, about 71 % of the time value is still there, and with a quarter of the days left about half remains. Expecting an even, straight-line decay overestimates what the first weeks deliver and underestimates how much is still at stake close to expiration.
Worked example
Hypothetical numbers for illustration, not a market quote and not a recommendation.
An example stock trades at 100 €, and the at-the-money call with 36 days to expiration costs 4.00 € per share, all of it time value. With the square-root approximation, and with price and implied volatility unchanged, the call is worth about 4 × √(18/36) = 2.83 € with 18 days left and 4 × √(9/36) = 2.00 € with 9 days left.
Half the time gone has removed only 29 % of the premium. Three quarters gone still leaves half of it, 200 € per contract. Fees are ignored.
Strategies where the term matters
- Cash-Secured Put — After a 30% drop, would the strike still be a price you actually want to pay?
- Short Iron Condor — Is the range you expect genuinely narrower than the move the market has priced in?
- Long Call Calendar — Is the near-term expiration expensive relative to the far one (a term structure in backwardation)?
Calculators for this term
Track it in your journal
Related terms
Every term in one place: the options glossary.
This material is general information about option strategies, written for a general audience. It is not investment advice, not a recommendation, and not financial analysis. Options can lose their entire value, and uncovered positions can lose more than the amount committed. Anything said about tax is general in nature and is no substitute for professional tax advice. Last reviewed: 2026-08-06.