Theta is the change in an option's price from one day passing, with everything else unchanged. It is negative for options owned and positive for options sold, and it grows sharply in the final weeks, most of all for at-the-money strikes.
An option's price is part intrinsic value (what it would be worth if exercised now) and part time value. Theta measures how fast the time value drains away. An option buyer pays it every day; an option seller collects it, in exchange for carrying the risk of a move.
An at-the-money call on a $100 stock at a flat 30% implied volatility, with the stock held at $100 (model prices):
| Days to expiration | Call price | Theta per day | Per contract |
|---|---|---|---|
| 60 | $5.17 | -$0.046 | -$4.56 |
| 45 | $4.44 | -$0.052 | -$5.19 |
| 30 | $3.59 | -$0.062 | -$6.24 |
| 21 | $2.98 | -$0.074 | -$7.36 |
| 14 | $2.42 | -$0.089 | -$8.90 |
| 7 | $1.70 | -$0.124 | -$12.38 |
| 1 | $0.63 | -$0.319 | -$31.87 |
More than half the 60-day option's value is gone with two weeks left, and the final seven days take the last $1.70, a third of the 60-day price.
Time value scales with the square root of time remaining, not with time itself. Going from 60 to 59 days barely changes the square root; going from 2 days to 1 cuts it by almost a third. The result is a decay curve that is nearly flat early and steep at the end, steepest for at-the-money strikes. Far out-of-the-money options have less time value to lose, so their theta is smaller in dollars: the 110 call in the same example decays about $0.035 a day at 30 days against $0.062 for the at-the-money call.
The decay a short option collects is payment for the gamma it owes: the risk that a move changes the position faster than expected. Both grow together into expiration, which is why "more theta" is never free. The shortest expirations pay the most per day and carry the most risk per dollar of movement. Owners of options face the mirror image: long gamma, paid for with negative theta.
A spread's theta is the sum of its legs, with sold legs counting as positive. The 95/90 bull put credit spread on the example stock collects about $0.043 a day on the sold 95 put and pays about $0.023 on the bought 90 put, a net of about $0.019 a day, close to $2 per contract. A debit spread usually runs negative theta while it is out of the money, since its long leg is closer to the money than its short one.
Models differ on whether theta counts calendar or trading days, and quoted prices tend to anticipate weekends before they arrive, so a Friday-to-Monday drop is often smaller than three days of theta. The practical conventions for premium sellers, entering around 30 to 45 days to expiration and closing or managing by about 21, aim at the middle of the curve where decay is meaningful and gamma still moderate. The reasoning is in choosing an expiration.
Theta is how much an option's price changes from one day passing, with the stock and volatility unchanged. It is negative for options owned and positive for options sold.
Time value scales with the square root of the time left, so each day removes a larger share of what remains as expiration approaches. An at-the-money 30-day option on a $100 stock decays about $0.06 a day; with one day left it decays about $0.32.
No. The decay a seller collects is payment for gamma risk, the chance that a move changes the position quickly. Both grow together into expiration, so higher theta always comes with more risk per move.