Why Theta Decay Isn't a Straight Line
The "$100 over 30 days" intuition is wrong
It's tempting to think of an option's extrinsic value the way you'd think of a gift card balance: $300 of time value, 30 days left, so it must lose about $10 a day. That's not how it works. Theta — the rate at which an option loses extrinsic value as a day passes, all else equal — is not constant over the life of a contract. It starts small, stays fairly modest for most of the option's life, and then accelerates sharply in the final couple of weeks before expiration. The shape isn't a straight line down; it's closer to a curve that steepens as it approaches zero.
Why the square root of time drives the curve
Under the Black-Scholes framework, an at-the-money option's extrinsic value is roughly proportional to the square root of the time remaining until expiration. That relationship is the whole story. A function shaped like the square root of time falls off slowly at first and drops faster and faster as time approaches zero — which means its rate of change (theta) does the opposite: small in magnitude early, then growing larger and larger as expiration closes in.
Concretely, going from 90 days to expiration down to 60 days removes a much smaller fraction of an option's remaining time value than going from 30 days down to 0. The calendar days lost are the same in both cases — 30 — but the dollar decay is not remotely the same, because the square-root curve is far steeper near the origin.
Moneyness changes the shape too
The acceleration effect is strongest for options that are at or near the money. Deep in-the-money options behave more like the underlying stock — most of their value is intrinsic, not extrinsic, so there's less time value left to decay in the first place. Deep out-of-the-money options have very little extrinsic value to begin with and their theta, while nonzero, is small in absolute dollar terms even as expiration nears — there just isn't much premium left to lose. The dramatic late-life theta acceleration you hear about is really an at-the-money phenomenon, which is exactly where a short premium seller's risk tends to concentrate.
Theta and gamma are two sides of the same coin
This is not a coincidence — theta and gamma are mathematically linked for a given option. The same forces that make theta accelerate into expiration also make gamma accelerate. An at-the-money option's gamma rises as time runs out, meaning its price becomes more sensitive to a move in the underlying at exactly the moment decay is fastest. That's the mechanism behind the well-known short-premium tension near expiration: theta is paying you more per day right when a single adverse move can do more damage per point than it could have a month earlier. Neither number tells the full story without the other.
What this means for how you size and time a trade
The practical takeaway is that "days to expiration" alone is a poor proxy for how much theta you're collecting or paying on a given day. Two positions with the same 30 days to expiration but different starting points on the decay curve — say, one opened 90 days out and one opened 45 days out — are earning theta at very different daily rates in that identical 30-day window. Traders who sell premium often prefer the 30-to-45-day window specifically because it sits on the steeper part of the curve without yet carrying the extreme gamma risk of the final days.
You can see this curve directly rather than approximate it: OptionScope's Greeks Matrix shows theta across a grid of strikes and expirations side by side, and the 3D Surface Plot traces how theta and gamma both bend as time to expiry shrinks toward zero — the acceleration described above, rendered rather than just described. For the most compressed version of this curve, the final trading day, see how it plays out in 0DTE options.