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Theta

The Greeks Core Concept

Theta measures how much an option's price is expected to fall each day purely from the passage of time, with everything else held constant — commonly called "time decay."

What is Theta?

Theta is almost always a negative number for an option you own — an option loses a little value every single day just by getting closer to expiry, even if the underlying doesn't move at all. A Theta of −14.5 means the option is expected to lose about 14.5 points of value over the next day, all else equal. For a position where you've sold the option, Theta flips sign — time decay works in your favor, not against you, which is the whole basis of every credit-based strategy on this site.

How to read Theta

  1. For a bought option, Theta is a daily cost. It's the price of holding the position another day, separate from whatever the underlying does.
  2. For a sold option, Theta is a daily gain. Every day that passes without the underlying moving against you is a day you keep more of the premium collected.
  3. Theta is quoted per day, and typically assumes calendar days (including weekends), though the actual decay a trader experiences is concentrated on trading days.

Theta Example: Step-by-Step

Using the same setup as the Delta and Gamma pages: Nifty at 24,000, 7 days to expiry, 13% implied volatility. The at-the-money 24,000 call has a Theta of -14.512 per day.

  1. One day passes, with Nifty unchanged at 24,000.
  2. Theta predicts the option loses roughly 14.512 points of value, or ₹943.28 at a 65 lot size, purely from that one day passing.
  3. This is a genuine, checked estimate, not just a formula's output taken on faith — recomputing the option's full Black-Scholes price with one fewer day to expiry (holding spot and IV fixed) gives a very close, though not perfectly identical, actual price drop. The small gap is expected: Theta is a rate measured at a single instant, while a full day is not infinitesimally small.

Theta by Moneyness

Using the same Nifty setup across a range of strikes:

StrikeZoneCall ThetaPut Theta
23,400 Deep ITM (call) / Deep OTM (put) -7.956 -3.794
23,700 ITM (call) / OTM (put) -12.376 -8.161
24,000 ATM -14.512 -10.243
24,300 OTM (call) / ITM (put) -11.354 -7.032
24,600 Deep OTM (call) / Deep ITM (put) -5.750 -1.374

Like Gamma, Theta peaks at the at-the-money strike and falls off on both sides — at-the-money options have the most extrinsic (time) value to lose, so they have the most to decay each day. Unlike Gamma, though, call Theta and put Theta at the same strike are not identical (−14.512 vs −10.243 at the 24,000 strike) — a real difference driven by the risk-free rate term in the pricing formula, not a rounding artifact.

How Theta Accelerates Near Expiry

Holding spot, strike (at-the-money, 24,000), and 13% IV fixed, and only changing days to expiry:

Days to ExpiryATM Theta (per day)
30 -8.206
7 -14.512
1 -34.736

Theta grows sharply as expiry nears — from −8.2 per day at 30 days out to −34.7 per day at 1 day out, over a 4x increase. This is the same underlying mechanism behind Gamma's own acceleration near expiry (covered on the Gamma page): time value has less and less time left to be spread over, so it drains away faster and faster as the countdown to expiry shortens.

Theta for a Multi-Leg Position

Using the exact strikes from this site's own Iron Condor worked example (spot 24,000, 7 DTE, 13% IV):

LegStrikeOption ThetaPosition Theta
Sell Put 23,600 -6.707 6.707
Buy Put 23,400 -3.794 -3.794
Sell Call 24,400 -9.501 9.501
Buy Call 24,600 -5.750 -5.750

Summing the position Theta column: 6.707 − 3.794 + 9.501 − 5.750 = +6.665 per share, or roughly +₹433.21 per day at a 65 lot size. The net Theta is positive — this Iron Condor genuinely gains value every day that passes with Nifty staying roughly where it is, confirming with real computed numbers exactly why credit-based, range-bound strategies like this one are described as "theta-positive" or "income" trades.

Why Theta matters for strategies

Theta is arguably the single most defining feature separating the strategies on this site into two broad camps:

  • Net option buyers are theta-negative — a Long Call, Long Straddle, or Long Guts all lose value each day the underlying doesn't move enough, purely from time decay.
  • Net option sellers are theta-positive — a Short Straddle, Iron Condor, or Bull Put Spread all gain value each day the underlying stays roughly put, confirmed directly above for the Iron Condor.
  • This is the core trade-off behind every "collect premium" strategy on this site: theta-positive positions are paid for taking on the risk of a larger, faster move than the market currently expects.

Risks and things to watch

  • Theta decay is not linear and not guaranteed day-to-day. It accelerates sharply near expiry, as shown above, and a single large move in the underlying can easily overwhelm a day or more of theta gain or loss.
  • A theta-positive position isn't automatically a good trade. It's collecting a premium specifically because it's taking on real directional or volatility risk — the numbers above show the decay, not the risk of the underlying moving hard against the position.
  • Theta assumes everything else stays fixed, including implied volatility — a change in IV can easily swamp a day's worth of theta, which is exactly what Vega measures.

Frequently Asked Questions

Why is Theta negative for a bought option?
Because every option has a limited lifespan — as expiry approaches, there's less time left for the underlying to move favorably, so the option's time value erodes. That daily erosion is what Theta measures, and it's a cost for the buyer.
Why do option sellers want high Theta?
Because Theta flips sign for a sold position — the same daily decay that costs a buyer money is collected by the seller instead. A theta-positive strategy gains value each day the underlying doesn't move enough to work against it.
Is Theta the same for calls and puts at the same strike?
No — unlike Gamma, call Theta and put Theta at the same strike genuinely differ, driven by the risk-free rate term in the pricing formula. The difference is usually small for short-dated options but is real, not a rounding artifact.
Why does Theta accelerate so much near expiry?
Because time value has less and less time left to be spread across as expiry approaches, so it drains away faster — the same underlying dynamic behind Gamma's own acceleration near expiry.

Related concepts

Gamma
Also accelerates near expiry, for the same underlying reason.
Vega
What Theta assumes stays fixed — a change here can swamp a day's decay.
Weekly vs. Monthly Options
Why weekly options always sit on the steep, fast-decaying part of this curve.
See real Theta values on the actual chain

Check live Theta for any strike — not the example numbers above.

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