Theta and time decay

Every option has an end date. As that date gets closer, the option has less time for something useful to happen, so it is worth less. The fall in value that comes only from time passing is called time decay, and the Greek that measures it is theta.

Theta = the change in option price for one day passing, with everything else unchanged

Theta is shown as a negative number for the holder. A theta of −13 on a NIFTY call means that if NIFTY and implied volatility stay where they are, the call will be worth about ₹13 less tomorrow. The seller of that call gains the same ₹13.

Only time value decays

An option's premium has two parts (see intrinsic and time value):

• Intrinsic value: what the option would be worth if exercised now. A 24,800 call with NIFTY at 25,000 has ₹200 of intrinsic value.
• Time value: everything above that. It is the price of the chance that the option becomes more valuable before expiry.

Theta eats only time value. At expiry, time value is zero and the option is worth only its intrinsic value. At-the-money options are almost entirely time value, so they lose the most rupees to decay. Deep in-the-money and far out-of-the-money options have little time value and lose less in rupees, though a far option can still lose a large share of its small price.

Why decay speeds up near expiry

Time value does not shrink in a straight line. It follows roughly the square root of the time left. Going from 30 days to 29 removes very little; going from 2 days to 1 removes a lot. For an at-the-money NIFTY option with IV at 13% and NIFTY at 25,000, the illustrative numbers look like this:

A handy rule of thumb: an ATM option's daily theta is roughly its price divided by twice the number of days left. ₹180 with 7 days left gives about ₹13 a day. On the final day, the remaining time value disappears within hours.

A live example: decay through today

The ATM straddle is the clearest way to see theta, because the two deltas roughly cancel and what is left is mostly time and volatility. Here is today's NIFTY straddle:

On a quiet day the line drifts lower from the open: that is theta. If it rises instead, NIFTY has moved more than the options expected (gamma) or fear has gone up (vega). Compare the day's high and low with the time they happened: decay usually shows as a gradual slide with the low later in the day.

The straddle price also sets the expected move to expiry, which shrinks as decay eats the premium:

As expiry gets closer, the range narrows, because there is less time left for NIFTY to travel.

Weekends, holidays and intraday decay

Theta is quoted per calendar day, but markets are shut at weekends and on holidays. In practice, option prices tend to start pricing in the weekend's decay on Friday, so Monday's opening drop is often smaller than a full three days would suggest. Before a long weekend or a market holiday, the same effect is larger. The market holiday list shows the dates.

Within the day, decay is not perfectly even either. Option sellers often see premiums soften through the late morning and early afternoon on quiet days, and expiry-day decay is heavy in the last couple of hours. These are tendencies, not rules: a single news headline can reverse them.

Theta, implied volatility and the strike you pick

Theta is not set by time alone. Two other inputs change it:

• Implied volatility. Higher IV means a bigger premium, and a bigger premium has more to lose, so theta is larger in rupees. Options before results or the Budget carry high IV and therefore high theta, which is part of why sellers are drawn to them.
• Distance from the price. Far from expiry, out-of-the-money options decay slowly in rupees. In the final days, their small remaining value can vanish almost completely, so in percentage terms they lose the most. A ₹10 option with two days left can easily be worth ₹1 at expiry.

So a buyer of cheap far options faces a very high percentage decay, while a seller of them collects little premium for a risk that is rare but large. Neither side gets something for nothing.

Theta for buyers and sellers

• Buyers pay theta every day. They need the underlying to move far enough, fast enough, to beat decay. This is why buyers often prefer options with more time left, or exit before the final days.
• Sellers earn theta every day the market stays calm. But high theta comes with high gamma: the same ATM option that decays fastest on expiry day also reacts most violently to a move.
• Spread traders use different decay speeds. A calendar spread sells a near expiry that decays fast and buys a later one that decays slowly.

A worked example: the short straddle

A trader sells the NIFTY 25,000 straddle with 3 days left for about ₹236. Its combined theta is about −₹40 for a buyer, so the seller earns about ₹40 a day if nothing moves. If NIFTY stays near 25,000 for two days, the straddle might fall to around ₹136, a gain of about ₹100 per unit. If NIFTY instead jumps 300 points the next morning, the straddle could be worth around ₹320, well above the ₹236 collected, despite the decay. Theta pays only while the market cooperates. Read the intraday short straddle guide for how sellers manage this.

Common mistakes

• Thinking a falling premium means you were wrong on direction. A call can lose value with NIFTY flat or even slightly up, purely from decay.
• Buying weekly options early in the week and holding to expiry hoping for a move. Decay works against you every day you wait.
• Treating theta as guaranteed income. Sellers earn it only if the move stays smaller than the premium, and losses on a big move are not capped.
• Ignoring changes in IV. A rise in implied volatility can outweigh several days of theta.
• Comparing decay across expiries without adjusting. A monthly option and a weekly option at the same strike decay at very different speeds; compare each with its own days left.
• Forgetting trading costs. Capturing a few rupees of decay a day can be wiped out by brokerage, taxes and slippage if you trade often.