Charm (Delta Decay)

Q: What is charm in options?

Charm is the rate at which delta changes with the passage of time, holding the underlying and volatility fixed. It is also called delta decay or delta bleed. OTM options lose delta toward zero as expiry nears; ITM options gain delta toward one.

Q: Why does charm matter for delta hedging?

Because a hedge sized to today’s delta is wrong tomorrow even if the market does not move. In the example a 24,400 Nifty call’s delta falls from 0.20 to 0.09 over four flat days, so a hedger must reduce the futures hedge by more than half to stay neutral. In expiry week this drift dominates.

Q: Is charm positive or negative?

It depends on the option. For an OTM call charm is negative (delta falls toward zero); for an ITM call it is positive (delta rises toward one). For puts the signs mirror, with delta moving toward zero for OTM puts and toward minus one for ITM puts. At the money charm is close to zero.

Q: How is charm related to theta?

Charm equals minus the derivative of theta with respect to the underlying price. Theta measures how much value time removes from the option; charm measures how much directional exposure it removes. Both are small far from expiry and large near it.

Delta does not sit still even when the market does. Charm is the overnight drift that leaves a hedged book unhedged by morning.

In short: charm is the second-order Greek measuring how delta changes with the passage of time, holding the underlying price and volatility fixed. It is the time-derivative of delta, or equivalently the price-derivative of theta. Out-of-the-money options lose delta as expiry approaches (their delta decays toward zero); in-the-money options gain it (toward one). Charm is small far from expiry and large in the final days, especially for strikes near the money.

The intuition

Delta is roughly the probability that an option finishes in the money. With Nifty at 24,000, a 24,400 call with a week left might have a 20% chance; the same call with one day left, and Nifty still at 24,000, has almost none. Nothing happened to the index, yet the option’s delta fell from 0.20 toward zero. That drift, delta changing purely because the calendar moved, is charm. For an in-the-money option the drift runs the other way: as time runs out the option becomes more certainly a stand-in for the underlying, and its delta rises toward one.

Charm matters to anyone who hedges. A market maker short that 24,400 call and long futures to cover its 0.20 delta wakes up each day with less delta to cover, and must sell futures to stay flat. Across a whole book, charm is a predictable flow that the market sees around the open and into expiry.

Formula

Charm = ∂Δ / ∂t = −∂Θ / ∂S

Under Black-Scholes, charm for a call = −N′(d₁) × [2(r − q)T − d₂σ√T] ÷ [2Tσ√T], the same expression applies to a put. It is usually quoted per day, by dividing by 365.

Charm is near zero at the money (where delta is pinned around 0.5 whatever the time left), negative for OTM calls and ITM puts (delta drifting toward zero or −1 respectively), and changes sign across the strike; its magnitude grows sharply as T shrinks.

Worked example (illustrative numbers)

Suppose NIFTY is at 24,000 and implied volatility stays at 13%. Model deltas and daily charm for the 24,400 call as the days run down, with the index unchanged:

Days to expiry	24,400 call price	Delta	Charm per day
14	₹112	0.295	−0.009
7	₹48	0.200	−0.020
3	₹11.5	0.088	−0.039
1	₹0.40	0.008	−0.028

Between day 7 and day 3, delta falls by 0.11 with the index flat; on one lot (65 units) that is 7.3 units of Nifty exposure that simply evaporated. A desk short 100 lots of this call, hedged long 1,300 units of futures at day 7, must sell about 730 units by day 3 just to stay neutral, and nearly all the remainder by expiry. Multiply across every OTM strike on the chain and the direction of the charm flow in expiry week becomes visible: hedgers of OTM calls sell, hedgers of OTM puts buy, as those deltas decay.

Delta decay with the index flat. The slope of this curve is charm; it steepens into expiry.

Why it matters to an options trader

Hedges go stale overnight. A delta-neutral book at the close is not neutral at the open; charm is the overnight drift and is largest in expiry week.
It is the counterpart of theta. Theta is how much value time removes; charm is how much delta it removes. A seller collecting theta on OTM options is also collecting a steady fall in their directional exposure.
It drives expiry-day flow. Hedgers of large OTM strikes adjust in a predictable direction as those deltas decay, part of the mechanics behind pinning near heavy strikes.
It interacts with vanna. Vanna is delta’s drift with volatility; charm its drift with time. Together they describe how a book’s delta moves when the index does not.

Common mistakes

Hedging delta once and holding. On weekly expiries the delta of OTM positions can halve in two sessions with no move.
Confusing charm with gamma. Gamma is delta’s change with price; charm is its change with time. A flat day has zero gamma effect and full charm effect.
Reading charm far from expiry. With a month left it is negligible; the numbers that matter appear in the last five sessions.
Ignoring the sign at the money. Charm is close to zero exactly at the money and flips sign across it; a strike that crosses spot changes the direction of the drift.

Indian-market specifics

Nifty has a weekly expiry every Tuesday, so some part of the chain is always in its final sessions, where charm is largest; the Sensex weekly on Thursday creates a second such window.
NSE index options trade until 15:40 on expiry day under the current timing circular, so the last hour of charm-driven hedging runs ten minutes beyond the cash close.
Settlement is at the underlying’s closing value (closing-auction based since August 2026; last-30-minute VWAP of continuous trading from 7 December 2026), and a strike’s delta converges to zero or one against that figure; the sharpest charm appears on near-the-money strikes in the final half-hour.
Broker platforms generally display delta, gamma, theta and vega but not charm; it has to be computed from a pricing model, or read as the day-over-day change in delta on an unchanged index.

FAQ

What is charm in options?

The change in delta per day with the market unchanged.

Why does charm matter for delta hedging?

A hedge set today is stale tomorrow; the drift is largest near expiry.

Is charm positive or negative?

Negative for OTM calls, positive for ITM calls; mirrored for puts.

How is charm related to theta?

Charm is the price-sensitivity of theta; both grow near expiry.

See the Greeks by strike before expiry week

The option Greeks page explains each Greek with live examples from the latest close. In the app, the Option Chain page shows delta, gamma, theta and vega per strike, so day-over-day delta on a flat index can be read directly.

Option Greeks Nifty option chain

Related terms

Delta, what charm erodes
Theta, the value side of the same decay
Vanna, delta’s drift with volatility
Second-Order Greeks, the family charm belongs to