Option time decay (theta): why premium melts near expiry

A very common message from new option buyers goes like this: "Nifty didn't fall, it was flat all day. Why is my call down 20%?" Nothing went wrong with the market. Time passed, and time is part of what you pay for when you buy an option.

Two parts of every option price

• Intrinsic value: what the option would be worth if it expired right now. A 24,800 call with Nifty at 25,000 has ₹200 of intrinsic value per unit. An out-of-the-money option has none.
• Time value: everything above intrinsic value. It is what buyers pay for the possibility of a bigger move before expiry.

On expiry day, time value is zero. An out-of-the-money option is made entirely of time value, which is why so many of them end at nothing. The daily loss of time value, if nothing else changes, is called theta.

Why the melting speeds up

Time value does not fall in a straight line. For an at-the-money option it is roughly proportional to the square root of the days left. Halve the time and you lose only about 30% of the value, not 50%. The rest comes off later, in a rush, as expiry gets close.

Rule of thumb for an at-the-money option Time value ≈ 0.4 × index level × implied volatility × √(days left ÷ 365). It's an approximation that ignores interest rates and dividends, but it shows the shape of decay well.

Watch the premium melt

An at-the-money Nifty option where the market doesn't move at all. Slide towards expiry.

Days to expiry

30

Implied volatility

13%

Nifty level

Premium today (approx.)₹373

Lost by tomorrow if flat₹6.3

That's per day1.7%

The numbers, side by side

Nifty at 25,000, implied volatility 13%, at-the-money option, market perfectly flat:

With 7 days to go, the option still has about 48% of the value it had with 30 days to go. In other words, more than three weeks of waiting took about half, and the last single week takes the other half.

What this means for buyers and for sellers

If you buy options, you need the move to come soon enough and big enough to beat the decay. Being right about direction but late can still lose money. That's not a reason to avoid options; it is a cost to count, just like brokerage.

If you sell options, decay works in your favour each day, which is why selling looks attractive. The other side of it: your gain is capped at the premium received, while a sharp move against you can cost many times that. Collecting small, steady decay and then giving it back in one bad session is a well-known pattern.

Weekly expiries are almost all time value Options with a few days left are cheap because most of their time value is already gone. Cheap is not the same as low risk: a small price can still go to zero, and it can do so in hours on expiry day.

What theta cannot tell you

• Theta assumes nothing else changes. In reality, price movement (delta) and changes in implied volatility (vega) often matter more on any one day.
• The formula here is for at-the-money options. Deep in-the-money and far out-of-the-money options decay in different patterns.
• Implied volatility usually drops after a big event such as results or a budget. That can cut an option's price sharply even if the market moved the way the buyer wanted.

Implied volatility for the index is summarised by India VIX. The India VIX post shows how to turn it into a Nifty range.