Learn/ Options/ Lesson 04

Options · Lesson 04 9 min read Intermediate

Theta and the shape of decay

Time value does not drain evenly. It drains along a curve, and the final week looks nothing like the first. Once you have seen the shape, half the folklore about expiry-week trading explains itself.

What theta measures

An option premium has two parts: intrinsic value, which is what the contract would be worth if expiry were right now, and time value, which is everything else. Time value is the market charging you for the possibility that things change before expiry.

Theta is the rate at which that second part disappears. It is quoted per day — a theta of −4 means the option loses about four rupees of value per day, all else being equal.

Those last four words carry the weight. Theta is what happens when nothing happens. It is not a prediction; it is the cost of the clock running.

The shape of the curve

The crucial fact is that time value does not fall in a straight line. It falls in proportion to the square root of the time remaining — which produces a curve that is nearly flat far out and then plunges.

Time value against days remainingIllustrative
Read the two marked points. Between day 30 and day 21 — nine days, a third of the life — the option loses about a sixth of its time value. In the last three days it loses roughly twice that. The same amount of calendar buys wildly different amounts of decay depending on where you are on the curve.

Theta is not a daily fee. It is an accelerating one, and the acceleration is the part that catches people.

This is why an option bought with three weeks left and held to the final day loses most of its time value in the final few sessions, and why the same position that felt stable for a fortnight can feel like it is evaporating on the Tuesday of expiry week. Nothing changed about the market. You moved along the curve.

The underlying, over those same daysIllustrative
Nothing happens. The underlying finishes almost exactly where it started. A holder of a long option lost money every single day of this chart, and no price move explains it.

Not every option decays the same way

The textbook curve describes an at-the-money option. Move away from the strike and the shape changes.

Two options, two shapesIllustrative
The dashed line is a far out-of-the-money option. It starts with far less time value to lose, and it bleeds away more steadily rather than holding up and then collapsing. Cheap options are not cheap because they are bargains — they are cheap because there is not much there.
  • At the money holds the most time value and suffers the sharpest final-week collapse.
  • Out of the money has less to lose and loses it more evenly. The percentage loss is brutal; the rupee loss is small.
  • Deep in the money is mostly intrinsic value, so theta barely touches it. It behaves closer to the underlying itself.

The two sides of the trade

Decay is a transfer, not an evaporation. Every rupee of time value a buyer loses, a seller collects. That symmetry is worth stating plainly because it is where the folklore goes wrong in both directions.

Buying means paying for time and needing the move to arrive before the clock does. You can be right about direction and still lose if you were early — a specific, common and avoidable way to be wrong.

Selling means collecting that decay, and the position makes money on quiet days by construction. The catch is the shape of what you have taken on: a steady small income against an occasional large loss. The income arrives daily and feels like skill; the loss arrives rarely and is the entire story.

Common mistake

Reading "options lose value over time" as "selling options is the easy side". Both statements are true and the conclusion does not follow. The seller is paid for decay because they are carrying the risk of the move. Theta is the rent, not the profit — and a single expiry can cost more rent than a year collects.

Read it yourself

Use the first curve for all three questions.

Practice
  1. Roughly what proportion of time value is left at 7 days remaining?
  2. Which single day on this chart destroys the most value?
  3. You buy a 30-day option and your view takes three weeks to play out. What has the clock cost you before direction is even considered?
Show answers

1. About half. The square-root shape means a quarter of the time remaining leaves roughly half the time value — which surprises most people, who expect a quarter.

2. The last one. The curve is steepest as it reaches zero, so the final session takes the largest single bite.

3. Roughly half the time value you paid, gone — with 9 days left the curve sits near 55. Your direction has to be right by more than that before you make anything. This is the calculation almost nobody does before buying, and it is the reason "I was right and still lost" is such a common sentence.

Terms used

Theta
Rate of loss of option value per day from the passage of time alone.
Time value
Premium above intrinsic value. Goes to zero at expiry, with certainty.
Intrinsic value
What the option would be worth if expiry were now.
At the money
Strike near the current price of the underlying. Most time value, fastest final decay.
Decay curve
The shape of time value against days remaining — flat, then steep.

Practise this on your own charts

The Options track works through 7 lessons like this one, each built around a drawn example and an exercise you complete yourself.

See the Options track