The Greeks at expiration

When the timer hits zero

At expiration, the Greeks behave very differently from how they look earlier in the option's life. The smooth curves we've been drawing collapse into something sharper. Two Greeks die (theta and vega). One Greek becomes a step function (delta). And one Greek does something that earns expiry its 'knife fight' reputation (gamma).

Theta hits zero. Theta represents the bleed of extrinsic value over time. When time runs out, there's no more time-value to bleed. Theta's job is done. The option is now worth exactly its intrinsic value — the difference between stock price and strike, if positive, or zero if the option is OTM.

Vega hits zero too. Vega measures sensitivity to implied volatility, but at expiry there's no future for IV to assume. The option's worth is now decided purely by where the stock closed. IV is irrelevant. Vega = 0.

Delta becomes a step function. Before expiry, delta climbed smoothly through the strike on its S-curve. At expiry, the smoothness vanishes. If the stock closes above the call strike by even one cent, delta is exactly 1 (the option is ITM, worth the difference). If it closes below by one cent, delta is exactly 0 (the option expires worthless). There's no middle ground — and no smooth transition between the two states.

Gamma 'goes vertical' at the ATM strike. Gamma is the rate of change of delta. If delta is jumping from 0 to 1 at the strike in an instant, then gamma at that point — in theory — is infinite. In practice, this means a stock tick of $0.50 around an ATM strike on expiry afternoon can swing a position from worthless to fully ITM. Short-option positions that look 'safe' at noon can blow up by 4 PM. Long-option holders sometimes win huge if a late move pushes them across the line.

Practical implication for retail traders. If you hold options into the final hour of expiry day, you are essentially trading a binary outcome around the strike. Brokers know this and increasingly require equity options to be closed before expiry if cash isn't available to assume assignment. If you trade weeklies, the safer habit is to close positions on Thursday or Friday morning — well before the gamma spike. The traders who profit from the expiry spike are typically market makers running large delta-hedged books, not retail with single positions. Knowing the Greeks at expiry helps you decide when to step out of a trade rather than ride it into the kink.

Recap: at expiry, theta = 0, vega = 0, delta = 0 or 1 (step), gamma = vertical spike at ATM. Expiry day is the most asymmetric trading day.