Second order Greeks: vanna, volga, charm, speed and colour

Wednesday 10 Jun 2026. The Nifty 23,800 call of the 30 Jun expiry settled at 111.40 with a delta of 0.2443. A seller of 100 lots holds 24.4 lots of the future against it. Now suppose the index has not moved by the next morning, implied volatility is two points lower, and one day has passed. The call's delta is 0.0316 lower because of the volatility and 0.0056 lower because of the clock, so the hedge is 3.7 lots too large. The two effects are vanna and charm, and they belong to a family called the second order Greeks. This module defines them, shows where each is large on a dated Nifty chain, and checks what they add to a price estimate. Every figure comes from NSE end of day files, dated, so nothing here is live and nothing is a view on the next move.

The idea, plainly

What is a second order Greek?

A Greek is a slope of the option's value. Delta is the slope against the index, vega against volatility, theta against time. A second order Greek is the slope of one of those slopes. Gamma, the slope of delta against the index, is the familiar one. The others cross the variables: how delta moves when volatility changes, how vega moves when volatility changes, how delta moves as time passes.

Where does vanna bite?

Vanna is positive for out of the money calls, negative for out of the money puts, and near zero at the money, where d2 is near zero. Read it as a probability story. When volatility rises, an out of the money call becomes more likely to finish in the money, so its delta rises. An out of the money put becomes more likely to finish in the money too, so its delta, which is negative, falls. The same number says how fast vega changes as the index moves.

What does volga add?

Volga is vega's own slope, the convexity of the option in volatility. It is positive in the wings and close to zero at the money, where it is 0.003 here. A long out of the money option gains vega when volatility rises and loses it when volatility falls, so its gains in a volatility jump come faster than its losses in a volatility fall. That makes wing options long the volatility of volatility. On this chain the 24,400 call has a volga of 1.119, more than the 22,000 put at 0.874, though both sit about five percent from the forward. The skew gives the put a higher implied volatility, 17.59 percent against 14.57 for the call, and volga, vega times d1 times d2 over sigma, is divided by that volatility. Both options sit close to one and a half standard deviations out, where volga peaks, so the volatility in the divisor makes most of the gap. A short wing is the opposite: it is short volga, and a jump in volatility hurts it more than a vega estimate says.

How does charm behave?

An out of the money call's delta falls as time passes, because there is less time to reach the strike. An in the money call's delta rises toward one for the opposite reason. The change quickens as expiry nears, because charm carries a one over T term. For the 23,800 call the delta falls by 0.0056 over the next day, with 20 days left. The chart shows the same call with 20 days left and with two. Charm is counted here in calendar days, as the pricing engine behind the Greeks calculator does. Whether a weekend is one day of decay or three depends on how time is measured, and that is a modelling choice, not a fact of the exchange.

What about speed and colour?

Speed is how gamma changes as the index moves, and colour is how it changes as days pass. At the money, gamma grows as expiry nears, so colour is positive there. Out in the wings gamma shrinks, so colour is negative. That is the shape of a busy expiry: near the money everything about the hedge is getting bigger, further out it is fading. The Greeks calculator shows both in its expert mode.

Worked example: two options, 10 Jun 2026

What are their Greeks?

Units: gamma is per point of the future, vega is rupees for one vol point, vanna and volga are for one vol point, and charm is for one calendar day. The expiry had 20 days left and the future stood at 23,240.10. Each option is read at its own implied volatility from its settlement price. The vanna and volga here are central differences of delta and vega over one vol point, and charm follows from the vanna by the identity in the fold. They agree with the closed forms of the pricing engine to the digits shown.

What does a position look like?

Greeks add across the legs of a position, and the second order ones add like the first order ones. Sell one unit of the call and one of the put and the position Greeks are the negative of the sum of the two columns, in the units of the table above.

What does a shock do to the price?

Move the index up one percent, 232.4 points, and drop volatility by one point, with no time passing. Reprice each option exactly, then rebuild the change from the Greeks.

What if the shock is bigger?

Take the call alone and raise the stakes: the index up three percent, 697.2 points, volatility down three points. The exact change is 215.87. The five terms give 186.19, and 29.68 is left over, about one part in seven of the exact change. Most of it is speed. The speed of the call is 0.00000034 of gamma for each point of the future, 0.000034 for each 100 points, and one sixth of speed times the move cubed adds 18.99. With it the sum is 205.18 and 10.68 remains, from still higher terms. A Greek based estimate is a local one. The bigger the shock, the more terms it needs, and a full reprice is cheaper than a long series.

What does it do to a hedge?

Return to the 100 lots sold. A volatility fall of two points lowers the call's delta by 0.0316 a unit, which is 3.2 lots of the future to take off. One day passing lowers it by 0.0056, another 0.6 lots. Together the hedge is 3.7 lots too large against the 24.4 lots first held. The future's lot and the option's lot are both 65 units, so lots map one to one. I use numbers like these to see how much of a rebalance is mechanical. I do not use them to say what an option seller should do.

Where does this stop?

The Greeks size a known position. They do not say what the position is. NSE publishes open interest by participant category, not by strike or by who hedges, as the module on who is on the other side shows, so any story that turns vanna and charm into market wide hedging flow assumes a sign for the position. The vanna and charm flows module works that story through and says plainly where it is a model.

The common mistake

The claim: Vanna and charm show which way dealers must hedge, so they tell you where the index goes next. They show how the hedge of a known position changes. In the example the whole adjustment for 100 lots is 3.7 lots of the future. Whose position it is, and whether they hedge in the future at all, is assumed. Change the assumed sign convention and the same vanna gives the opposite flow. A Greek is a sensitivity of a price. It is not a forecast of the index, and I treat a flow story as a hypothesis about positions, never as a signal.

Key takeaways

• A second order Greek is the slope of a first order Greek.
• Vanna: positive for out of the money calls, negative for out of the money puts.
• Volga is near zero at the money and larger in the wings.
• Charm lowers the delta of an out of the money call each day.
• Gamma, vanna and volga terms together came within one rupee of the exact change.
• Vanna and charm size a known hedge. They do not forecast the index.

Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study