Theta

Theta measures how much an option loses in value as one day passes, all else equal. It is usually negative for a long option and positive for a short option. Theta is the price a long gamma holder pays, and the income a short gamma seller collects.

How it works

theta = change in option price for one day passing, with spot and implied volatility unchanged. Decay is not linear. It is slow on long-dated options and accelerates in the final weeks, especially for at-the-money strikes, where the remaining time value is largest. Out-of-the-money options carry a smaller theta in dollars, but lose a larger share of their value each day as expiry nears. Theta and gamma are two sides of the same trade: for a delta-hedged option, the daily theta roughly equals the gamma P&L the market expects from a move consistent with implied volatility.

Example

Hypothetical: an option is worth $4.00 with a theta of −0.05 per day. Five days later, with spot and implied volatility unchanged, it is worth about 4.00 − 5 × 0.05 = $3.75. On 20 contracts with a multiplier of 100, the decay is 20 × 100 × 0.05 = $100 per day.

On the desk

Traders translate theta into a break-even daily move: implied volatility divided by 16, since √252 is close to 16. At 16% implied, a delta-hedged long option needs moves of about 1% a day to pay its decay. Desks also check how weekends and holidays are treated in the theta their system reports.