Time decay, and the gamma that comes with it

An option's price has two parts. Intrinsic value is what it would be worth exercised right now: for a $45 put with the stock at $42, that's $3. The rest is extrinsic value, or time value, the amount the market pays for the possibility that things change before expiration. Time value goes to zero on expiration day, for every option, in every market. Theta is the rate at which it goes: how much an option is expected to lose per day, holding everything else still.

Why it exists

With 30 days left, a lot can happen; with three days left, much less. The chance that a $45 put on a $50 stock finishes in the money is meaningful over a month and small over an afternoon. The option's price tracks that chance, so it falls as the calendar advances. A seller who has already collected the premium watches the option they're short lose value while the stock sits still. That's the tailwind: the only mechanism in options that pays you for nothing happening.

Why it speeds up

Decay isn't linear. For an at-the-money option, time value scales with roughly the square root of the time remaining, so the last 30 days lose more than the 30 before them, and the last week loses more than the three before it. A $2.00 at-the-money option with 60 days left might be worth $1.40 at 30 days and $0.60 with five days to go. The seller of that option earns most of the premium in the final stretch.

Options well out of the money decay differently. Their time value is smaller to begin with and most of it drains earlier, so by the last two weeks there's little left to earn and the option is mostly waiting to expire or to get run over.

What comes attached

Theta is the payment for gamma. Gamma is how fast an option's delta changes when the stock moves, and it's largest for the same options that carry the most theta: near the money, near expiration. So the position that earns the most per day is also the one most exposed to a sudden move. On a Tuesday with two days left, a short at-the-money put on a $50 stock might earn $15 of decay and lose $250 on a $3 drop. Nobody pays theta for free. They pay it because you're carrying the risk that the stock moves before the clock runs out.

That trade-off is behind a common convention: sell around 45 days out and close or roll around 21 days, capturing the middle of the decay curve while staying away from the end, where gamma is highest and the remaining premium is small. It isn't a law. It's one way of choosing where on the curve to sit, and the right answer depends on how much gamma you're willing to hold for the theta on offer.

Weekends and the calendar

Theta is measured in calendar days, so an option loses value over the weekend while the market is closed. Market makers know this and usually price part of the weekend's decay into Friday afternoon quotes, so the "free theta" of holding over a weekend is smaller than it looks and the Friday close isn't the bargain it seems.

Keeping it in proportion

Theta is real, it's steady, and it's the reason selling premium has a positive expected return in most months. It's also small next to the size of a bad move. A portfolio earning $80 a day in theta can give back two months of it in a morning. Count the theta; size for the gamma.