Unit 9 of 15 · Intermediate

Theta: the price of time

In one read

Theta is how much an option's value decays with the passage of one day, all else held equal. It acts on extrinsic value — the time-and-chance portion of the premium — draining it toward zero as expiry approaches. Theta is negative for the option buyer, who watches value bleed away each day the underlying sits still, and positive for the writer, who collects that decay. The decay is not linear: it accelerates as expiry nears, so an at-the-money option loses time value fastest in its final days. Weekends still count — three days of decay are priced in even though markets are shut for two of them. This unit reads theta on the same generic at-the-money call from the delta and gamma units, framing time value as rent the buyer pays and the writer collects, with no claim about which side wins.

Theta is what one day costs

Theta measures how much an option loses to the simple passage of one day, with everything else held still. It acts only on extrinsic value — the time-and-chance part of the premium — pulling it toward zero as the deadline approaches.

The sign depends on which side you are on:

  • For the buyer, theta is negative: hold a long option through a quiet day and it is worth a little less at the close, purely because a day is gone.
  • For the writer, theta is positive: they collect that same decay.

A common shorthand calls theta the seller's paycheck and the buyer's rent — the buyer pays for time, the writer is paid for providing it. That is a description of the mechanic, not a verdict on which side comes out ahead; theta is only one of four forces on the price.

A worked example

Take the same GENCO $100 call from the delta and gamma units — ATM, a month out. Suppose it carries $3.00 of extrinsic value and a theta of −$0.05 per day.

  • One quiet day passes, GENCO unchanged: the call is worth about $2.95. The buyer lost a nickel to time alone; a writer collected it.
  • Weekends still count. Going into a Friday close, roughly three days of theta are priced out over the weekend, even though the market is shut for two of them — the clock does not pause.

Now watch the curve steepen. With a month left, that decay is gentle. In the final days, the same ATM call sheds time value fastest — theta accelerates into expiry, so the last stretch is where the clock bites hardest.

See it in kestrel

Theta is easiest to isolate when little else is moving — the day where price drifts and time does the work. Run a real session and watch the tape:

npx kestrel.markets sim fomc-rate-decision-whipsaw

That runs a deterministic simulation over a generic index session — managed licensed data, no wall time, no signup, no card — and prints a certified proof URL. Kestrel advances the session on the tape's own clock (no wall time), so decay is applied by the record, not improvised. Recompute the whole thing on your own machine, byte for byte:

npx kestrel.markets certify https://kestrel.markets/proof/art_d29415f0cf502f4a218a9cba

Keep the clock one command away: drop the kestrel.markets MCP server into your client and the next session opens where this one left off — no account in between.

Recompute it

Every claim in this unit recomputes from a certified proof — no account, no card.

/proof/art_d29415f0cf502f4a218a9cba
Keep readingVega and implied volatility

Agent twin: /education/options/opt-theta/content.md