Zero-DTE And Weekly Options

An option that expires in 30 days loses value gradually, and a trader watching it can reasonably treat "a day" as a small, roughly equal-sized slice of what's left. An option expiring today cannot be thought of that way. In its final hours the same option can lose more value in twenty minutes than it lost all week, and the size of a single tick in the stock starts to matter far more than the trader's view of where the stock is going.

A sand timer, not a straight ruler

A ruler shows the same amount of distance for every inch. A sand timer doesn't: the sand falls at a roughly constant rate, but the last grains determine the outcome in a way the first grains never could — one final grain decides whether the timer has run out. Option decay near expiry behaves like the sand timer, not the ruler: time is running out at a constant clock speed, but the option's sensitivity to that remaining time is not constant at all — it explodes as the timer empties.

Why the last hours dominate

$$\Theta \approx -\tfrac{1}{2}\sigma^{2}S^{2}\Gamma, \qquad \Gamma = \frac{\phi(d_1)}{S\sigma\sqrt{T}}$$

In plain English: theta (the daily bleed) is paid to compensate for gamma (the curvature that lets a hedged position profit from any wobble in the stock), and gamma itself grows as $\sqrt{T}$ shrinks in the denominator. As expiry approaches, the option needs less absolute stock movement to swing between worthless and valuable, so both its curvature and its decay rate accelerate together.

Worked example 1: theta at one day versus one month. Take an at-the-money option on a $100 stock, $\sigma=20\%$, $r=0$. With 30 days left, Deriving The Black-Scholes PDE shows $\Gamma=0.0695$ and daily theta of about $0.038. With one day left, $T=1/365=0.00274$, $\sigma\sqrt{T}=0.01047$, so $\Gamma=0.3989/(100\times0.01047)=0.381$, and annualised theta is $-0.5\times0.04\times10{,}000\times0.381=-76.2$, or $76.2/365=0.209$, i.e. $0.209 per day. That's over five times the daily decay of the 30-day option, on the exact same stock and volatility — the calendar didn't change, only how close to zero the clock had run.

Worked example 2: decay inside the final day. The rough at-the-money value formula is $V \approx 0.4\,S\,\sigma\sqrt{T}$. With a full trading day left ($T=1/365$), $V\approx0.4\times100\times0.2\times0.0523=0.42$, i.e. $0.42. With just 30 minutes left in a 6.5-hour session, that's $30/390=0.0769$ of a trading day, so $T=0.0769/365=0.000211$ and $\sqrt{T}=0.01452$, giving $V\approx0.4\times100\times0.2\times0.01452=0.12$, i.e. $0.12. The option lost roughly 72% of its remaining value in the final half hour alone, purely from time passing with the stock near the strike.

Try nudging the stock a dollar either side of $100 in the payoff above — with so little premium left, a move that would barely register on a 30-day option is the difference between the option finishing worthless and finishing meaningfully in the money.

Watch a single path near the strike late in its life: because gamma is so large, a stock that drifts back and forth by even a dollar swings the option between nearly worthless and meaningfully in the money, over and over, in the last hour.

What this means in practice

Zero-DTE (same-day expiry) and weekly options turn the "last day" from a once-a-month event into a daily one. Market makers quoting them size their books smaller per strike, rebalance far more frequently, and treat the realised path of the stock — not just its starting and ending price — as the main source of P&L, because gamma scalping opportunities and pin risk (see Pin Risk At Expiry) recur every single session instead of once a cycle.