Theta: how time decay really works
Why an option loses value every day, why the loss speeds up in the last week, and what Arthfy's history says about selling time at different distances from expiry.
An option's price is intrinsic value (what it would be worth if it expired now) plus time value. Time value is the market's price for the chance that the option ends further in the money than it is today. At expiry it is zero.
What an option is worth as expiry approaches
| Days left | ATM call | Lost in the next day | 200-pt OTM call |
|---|---|---|---|
| 30 | 441 | 8.6 (1.9%) | 340.2 |
| 21 | 359 | 9.8 (2.7%) | 261.5 |
| 14 | 286 | 11.6 (4.0%) | 191.9 |
| 7 | 195 | 15.6 (8.0%) | 108.3 |
| 3 | 124 | 23.8 (19.2%) | 47.4 |
| 1 | 70 | 70.1 (100.0%) | 10.7 |
For an at-the-money option, time value shrinks roughly with the square root of the time left. That makes the daily loss grow as expiry approaches: about half of a 30-day at-the-money option's value is gone by the time a week remains, and the last few sessions take the rest. Out-of-the-money options lose most of their value earlier, then collapse to zero unless the price comes toward them.
Selling the NIFTY at-the-money straddle at different distances from expiry, since 2016
Read the worst cycle next to the average. Short-dated straddles collect the fastest decay and also sit closest to the strike when a large move arrives.
