Monday 2 Feb 2026 was the first session after the Union Budget, which was presented on Sunday 1 Feb. India VIX closed the Sunday at 15.10 and the Monday at 13.87. The Nifty rose 1.06 per cent on the Monday. Take one option instead of the index: the Nifty 26,000 call of the 24 Feb series. Its delta went from 0.113 to 0.137. Three things changed under it at once: the index, the implied volatility and the clock. Each moves delta through its own Greek. You know gamma. The other two are vanna and charm, and they are what people mean by "flows" after an event or into an expiry. This lesson measures both on a dated chain, then asks what the word flow is allowed to mean.
3By the end you can
- Split a change in delta into gamma, vanna and charm terms on a dated Nifty chain.
- Size a volatility flow in units of the index and in rupees crore from open interest.
- Say which part of a flow story is measured and which part is assumed.
The idea, plainly
Delta moves for three reasons
Delta is a hedge ratio. It says how many units of the future offset one unit of the option. It is not fixed. Three things move it, and each has a Greek.
- The index moves. The change in delta per point is gamma.
- Implied volatility moves. The change in delta per volatility point is vanna.
- A day passes. The change in delta per calendar day is charm.
Change in delta =
gamma x move in F
+ vanna x move in IV
+ charm x days gone
+ smaller terms
The units are those of the engine behind these lessons: Black 76 on the future, delta per unit of the index, vanna per one volatility point, charm per calendar day. Module E04 sets out all five second order Greeks.
The maths: vanna and charm in closed form
Write d1 and d2 as usual for Black 76, with the volatility sigma, the time T and the rate r.
Vanna = −e−rT x φ(d1)
x d2 / sigma
(per unit of sigma;
x 0.01 for one point)
Charm (call) = e−rT x
[ r x N(d1)
+ φ(d1) x d2 / 2T ]
Vanna is a cross derivative: how delta moves with volatility is also how vega moves with the future, so one formula gives both. Charm is minus the derivative of delta with respect to time to expiry, taken per year and divided by 365 for a day. With a small rate the first term of charm is close to zero, and what is left is the shape of the normal curve times d2. That is why charm changes sign with moneyness and grows as T shrinks.
The signs, once
Vanna of a call and of the put at the same strike is the same number. Above the future it is positive. A rise in volatility raises the chance of finishing in the money, so a call's delta rises and a put's delta moves toward zero. Below the future it is negative. Charm pulls the delta of an out of the money option toward zero as days pass, and an in the money call toward one. Near the strike the sign flips, and the closer the expiry, the sharper the flip.
Vanna changes sign at the strike, and the swing grows as expiry nears
From delta to flow
Someone who has sold the call holds futures against it. If the delta of the call changes by some amount per unit, their hedge changes by that amount times the units. That trade is the flow. NSE publishes open interest by strike. It does not publish who holds which side, as module A18 shows. So the size of a flow can be computed. The direction cannot be read. The size is the only honest number, and the sign is an assumption you label, as in module A19.
The size of a flow is measurable and its direction is assumed
Not the same unit as GEX
Module A19 sizes gamma exposure in rupees crore for a one per cent move of the index. A vanna figure is in rupees crore, or in units of the index, for one volatility point. The two answer different questions, so they are not added. A day can have a small gamma figure and a large vanna figure, or the reverse. Always carry the unit: units of the index, rupees crore, and the move that it is quoted for.
Where it bites
- After an event. Before a known event, implied volatility is bid up across strikes. After it, volatility falls, the crush of module I16. At a flat index that moves every delta by vanna times the fall.
- Into an expiry. With the index flat, days pass and charm moves every delta toward its limit. The nearer the expiry, the faster. A weekly with a few days left ages quickly.
- Both together. The session after an event is also a day closer to expiry, so vanna and charm act on the same morning. They can pull the same way or opposite ways, and the split in the example shows which won.
Settlement matters here too. Index options on NSE are European and cash settled, so their deltas run to zero or one at expiry and the hedges unwind with them. State the settlement regime of the expiry you study. Expiries before 7 Dec 2026 settle on the index close.
2 terms this section turns on
What the number leaves out
- The sign, as above.
- How often the hedger rebalances, and whether the hedge uses futures or other options.
- Where volatility fell. India VIX is a thirty day figure; the option in question may have moved by more or less.
- End of day open interest, which hides what was opened and shut during the day.
- The scale: the day's traded value in the future, to be compared before calling anything a driver.
Worked example: the 26,000 call over Budget Day, then the chain, then a weekly
On Budget Day the 26,000 call, with the future at 24853.5, had 48,61,480 units of open interest and an implied volatility of 14.64%, solved from its own settlement price. Its delta was 0.113, its gamma 0.00021 a point and its vanna 0.0163 for one volatility point. The next day the future stood at 25141.8, 288.3 points higher, and the option's volatility was 12.35%. The delta was 0.137, up 0.024 in all. Start with the volatility picture.
India VIX jumped on Budget Day and gave back most of it the next session
Splitting the move in delta
Take the first order terms at the Budget Day chain. Gamma times the 288.3 point rise in the future adds 0.060. Vanna times the fall in the option's own volatility changes delta by −0.037. One day of charm takes off a little more. What is left is the smaller terms and the change in the rate. The total is 0.024.
The index move beat the volatility fall, so delta rose even as volatility dropped
The maths: why a first order split leaves a remainder
A Greek is a slope at one point. Delta is a curved function of three inputs, so a slope times a change is a straight line laid on a curve. The error grows with the size of the move and with how bent the curve is there. The next terms are gamma's own slope, speed, the bend in vega with volatility, volga, and cross terms such as the effect of the index move on vanna. The change in the rate between the two chains adds a small amount. Here the remainder is about a quarter of the total, which is large because the index moved by about one per cent and the strike sits well above the future. Treat a first order split as a sketch of the order of magnitude and of the signs, and reprice in full when the sizes matter.
Read 2 more paragraphs, 117 words
Why is the volatility fall of this one option more than the fall in VIX? VIX is a thirty day figure for the whole index. This option sits well above the future, and on that session the volatility of strikes above the future fell by more than the headline figure. Its own volatility moved from 14.64% to 12.35%. The split uses that change, because the option's delta responds to its own volatility.
So on that day vanna was real, and it lost. The volatility fall alone would have cut the call's delta. The rise in the index more than covered it. A trader who watched only vanna would have had the wrong sign for the day.
How big was the volatility flow
Now use VIX as the scale of a whole-chain thought experiment: hold the index flat and let volatility fall by the 1.23 points that VIX fell. The 26,000 call's delta shifts by about vanna times the fall. Across its 48,61,480 units that is 97,435 units of the index, worth Rs 242 crore at the future. That is for one strike. Here is every strike within a few per cent of the future, calls and puts together, for one more point of volatility.
The vanna exposure sits just above the future, where open interest is heavy
Read one more paragraph, 83 words
The bars above the future are open interest times a vanna that is large there. Below it, the sign flips. A writer who hedges every day trades the future by the size of each bar: buying where the bar is positive when volatility rises, selling when it falls. A buyer who hedges trades the opposite way. Which of them holds the open interest at a strike is the assumption, and it makes this a model with a label, not a record of anything.
Charm into a weekly expiry
On 10 Jun 2026 the 16 Jun weekly had 6 days to run. The 23,500 call of that series, with a future at 23229.3 and an implied volatility of 14.41%, had a delta of 0.268 and 65,49,140 units of open interest. Leave the index and the volatility where they are and let time pass.
Charm bites harder each day: the dip deepens and narrows toward the strike
Appendix: reproducing the bars in a spreadsheet
You need three columns from the F&O end of day file: the strike, the settlement price and the open interest, plus the future, the rate and the days to expiry. Solve each option's implied volatility from its settlement price. Compute delta at that volatility and again at one point higher. The difference is the vanna for one point. Multiply by open interest in units, which is already contracts times the lot, so do not multiply by the lot again. For charm, compute delta again with one day less and subtract. Sum calls and puts at each strike. Then write down the sign you assumed. The first three steps are measurements, the last is a choice.
Read one more paragraph, 120 words
With six days left the drift is a small step each day. With one day left, a call a little out of the money can lose most of its delta in a single day if the index does not move. At that point charm is a rate, and the true change over the day is capped by the delta the option has left, so read the tall one day curve as a sign of speed, not as a forecast of size. A writer of that call, long futures against it, sells futures as the day wears on. A buyer who hedged with short futures buys them back. Which of the two holds the open interest is again the missing input.
The common mistake
The claim: India VIX fell after the Budget, so vanna flows forced dealers to buy the index, and that is why it rose.
Look at 2 Feb 2026. VIX did fall, by 1.23 points, and the index did rise, by 1.06 per cent. But for the 26,000 call the vanna term changed delta by −0.037 while the index move added 0.060. Whether a fall in delta means buying or selling depends on the side the hedger holds, and no file says. Even with the sign fixed, the volatility flow at that strike was about Rs 242 crore. Set that against the day's traded value before calling it a cause.
Key takeaways
- Delta moves with the index, with volatility and with time: gamma, vanna and charm.
- Vanna is the change in delta for one volatility point; charm is per day.
- A volatility fall at a flat index still shifts every delta.
- NSE open interest gives the size of a flow; no file gives its sign.
- On 2 Feb 2026 the index term beat the vanna term for the call studied.
- Charm pulls out of the money deltas toward zero, faster as expiry nears.
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