---
title: "Second order Greeks: vanna, volga, charm on Nifty options"
description: "Vanna, volga, charm, speed and colour on dated Nifty options: what each measures, where it is large, and how much it adds to a price and a hedge."
source_url: "https://www.rupeecase.com/learn/path-14/module-14-17-second-order-greeks"
---

[Path 14 17 of 17](/learn/path-14/)Second order Greeks: vanna, volga, charm, speed and colour[Path 14](/learn/path-14/)

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.

3By the end you can

1. Define vanna, volga, charm, speed and colour as slopes of the first order Greeks.
2. Read the sign and size of vanna and volga across the strikes of a dated Nifty chain.
3. Rebuild a price change from the Greeks, and size the hedge change that vanna and charm ask for.

Watch in the terminal: does the app hold my money or shares? A short tutorial on sample data.

## 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.

| Greek | Slope of | Also reads as |
| --- | --- | --- |
| Vanna | Delta against volatility | Vega against the index |
| Volga | Vega against volatility | Convexity in volatility |
| Charm | Delta against time | Delta decay |
| Speed | Gamma against the index | How gamma changes as the index moves |
| Colour | Gamma against time | How gamma changes as days pass |

The maths: Black 76 closed forms
With d1 and d2 as in the Black 76 formula, df the discount factor, phi the standard normal density, F the future, sigma the volatility and T the time in years:

vanna = − df x phi(d1)
x d2 / sigma

volga = vega x d1 x d2
/ sigma

speed = − (gamma / F) x
(1 + d1 / (sigma sqrt T))

charm, per year, for a call
= df x (r N(d1)
+ phi(d1) d2 / (2T))

colour, per year =
gamma x (r + (1 − d1 d2)
/ (2T))

Vanna is the same for a call and a put at one strike, because their deltas differ by a constant. This module and the Greeks calculator quote vanna and volga for one volatility point, and charm and colour for one calendar day. Charm and colour carry a one over T term, which is why they swell as expiry nears.

Read one more paragraph, 93 words
Why bother with them at all? For one option held to expiry the first order Greeks answer most questions. The second order ones matter when a position is hedged again and again. A delta hedge is rebuilt as the index, the volatility and the calendar move, and each rebuild trades the change of delta. Gamma explains the index part of that change. Vanna explains the volatility part and charm the calendar part. The Greeks calculator under this page has an expert mode that shows all five for any strike of a dated chain.

### 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.

Vanna changes sign at the forward

Out of the money option at each strike, its own implied volatility, change of delta for a bump of one vol point up and down, central difference. Per unit of the index, not per lot. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.
Read one more paragraph, 73 words
A short strangle sells both wings. The 23,800 call has a vanna of 0.0158 and the 22,700 put −0.0126, per unit and per vol point. Sold, their signs flip and mostly cancel: the strangle holds about minus 0.0032. A risk reversal, buying the call and selling the put, adds them to 0.0284. The same options, bought differently, give a book with almost no vanna or a book with a lot.

### 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.

Volga is a wing Greek

Out of the money option at each strike, its own implied volatility, change of vega in rupees for a bump of one vol point up and down. Per unit of the index. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.

### 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.

Delta decay quickens as expiry nears

Charm of the 23,800 call of the 30 Jun 2026 expiry at its implied volatility of 10 Jun 2026, change of delta for one calendar day, against the level of the future. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.

### 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?

| Per unit | Call | Put |
| --- | --- | --- |
| Strike | 23,800 | 22,700 |
| Implied vol, % | 14.38 | 15.74 |
| Price | 111.40 | 133.70 |
| Delta | 0.2443 | −0.2550 |
| Gamma | 0.000401 | 0.000375 |
| Vega | 17.05 | 17.45 |
| Vanna | 0.0158 | −0.0126 |
| Volga | 0.594 | 0.452 |
| Charm | −0.0056 | 0.0049 |

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.

3 terms this section turns on

From the module glossary; every term is in the Learn glossary too. Source: Module 14.17, Second order Greeks: vanna, volga, charm, speed and colour.

### 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.

| Greek | Strangle |
| --- | --- |
| Delta | 0.0107 |
| Gamma | −0.000775 |
| Vega | −34.50 |
| Vanna | −0.0032 |
| Volga | −1.045 |
| Charm | 0.0007 |

Read one more paragraph, 96 words
The strangle is close to delta neutral, at 0.0107. It is short gamma, short vega and short volga, and it holds almost no vanna or charm, because the call's and the put's signs oppose each other. A reader who only looked at delta and vanna would call this position quiet. It is short volga, so a jump in volatility costs it more than its vega says, and the module on hedging an option selling book returns to that exposure. What a table of position Greeks cannot say is how large a move the position survives.

### 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.

| Rs a unit | Call | Put |
| --- | --- | --- |
| Exact change | 48.15 | −63.64 |
| Delta term | 56.77 | −59.26 |
| Vega term | −17.05 | −17.45 |
| Gamma term | 10.82 | 10.11 |
| Vanna term | −3.67 | 2.94 |
| Volga term | 0.30 | 0.23 |
| Sum of five | 47.17 | −63.43 |
| Left over | 0.98 | −0.21 |

Watch in the terminal: what does "Same money in NIFTY 50" mean? A short tutorial on sample data.
Read one more paragraph, 106 words
For the call, delta and vega alone give 39.72 against an exact change of 48.15. Add gamma, vanna and volga and the estimate reaches 47.17, within 0.98 of the exact figure. The vanna term is 0.34 of the size of the gamma term, so on a day when both the index and its volatility move, vanna is not a rounding error. The put shows the same pattern with the signs of delta and vanna turned: delta and vega alone give −76.71 against an exact −63.64. What remains is speed and higher terms. Multiply by 65 units to get the change for one lot.

### 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](/learn/path-15/module-15-8-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](/learn/path-15/module-15-12-vanna-and-charm-flows) works that story through and says plainly where it is a model.

Two terms to hold on to from 14.17

From the module glossary. Source: Module 14.17, Second order Greeks: vanna, volga, charm, speed and colour.
Appendix: charm from vanna, and why the numbers agree
The closed forms in the first fold give an identity between charm and vanna for one option, whether call or put:

charm x 365 = r x delta
− vanna x sigma
/ (0.02 x T)

The vanna here is per vol point, which is why the factor 0.02 appears: one hundredth for the vol point and two from the 2T of the closed form. Sigma is the volatility as a decimal. The table of the two options was built this way: vanna by a central difference of delta over one vol point up and down, charm from the identity. The shock tables reprice by moving the strike instead of the future, which Black 76 allows because the price scales with the future and the strike together. Speed uses the same trick on gamma. Each figure was checked against the pricing engine behind the Greeks calculator, which gives the closed forms directly.

## 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.

Where this section sits in module 14.17

Sections 1 to 4 of 4; the highlighted one is next. Source: Module 14.17, Second order Greeks: vanna, volga, charm, speed and colour.
**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](https://www.sebi.gov.in/reports-and-statistics/research/aug-2026/study-profitability-of-individual-traders-in-the-equity-derivatives-segment-fy25-fy26-_103835.html)

What does Second order Greeks: vanna, volga, charm, speed and colour cover?Delta, gamma, vega and theta are first drafts. Vanna, volga, charm, speed and colour say how they change. On a dated chain, each has a place where it matters. It works through The idea, plainly, Worked example: two options, 10 Jun 2026, The common mistake, Key takeaways. It is module 14.17 of Path 14, Options and Greeks, about 13 minutes of reading, free.

TTry it

## Greeks calculator, on the same example.
Delta to rho, and vanna to colour in expert mode, from one Black 76 engine. Dated NSE end of day data, nothing live, no orders.

**Greeks calculator**, Nifty, 10 Jun 2026, 30 Jun 2026 expiry.

[Open the greeks calculator](/learn/tools/greeks-calculator?chain=NIFTY_2026-06-10_2026-06-30)

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QQuick check

## 10 questions, 7 to pass.
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* **30**questions
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CCheck yourself

## Path 14 so far.
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Stop 17 of 17 on Path 14

Options and Greeks: every live stop, this module ringed. Source: RupeeCase Learn, Path 14.

1. [14.1The call option, told as a storyNot yet](/learn/path-14/module-14-1-call-option-explained)
2. [14.2The put option, told as a storyNot yet](/learn/path-14/module-14-2-put-option-explained)
3. [14.3Buyer or seller: payoffs, margin, win rate and expectancyNot yet](/learn/path-14/module-14-3-option-buyer-vs-seller)
4. [14.4Moneyness, intrinsic value and time valueNot yet](/learn/path-14/module-14-4-moneyness-intrinsic-and-time-value)
5. [14.5Five things that move an option's priceNot yet](/learn/path-14/module-14-5-what-moves-an-option-price)
6. [14.6Expiry and settlement: cash, physical, exercise and STTNot yet](/learn/path-14/module-14-6-expiry-and-settlement)
7. [14.7Delta: speed, hedge ratio and the probability shortcutNot yet](/learn/path-14/module-14-7-delta)
8. [14.8Theta: the time decay curve into expiryNot yet](/learn/path-14/module-14-8-theta-time-decay)
9. [14.9From a binomial tree to Black Scholes and Black 76Not yet](/learn/path-14/module-14-9-binomial-tree-to-black-76)
10. [14.10Put call parity and synthetic positionsNot yet](/learn/path-14/module-14-10-put-call-parity)
11. [14.11Gamma: why it grows so fast near expiryNot yet](/learn/path-14/module-14-11-gamma)
12. [14.12Vega: volatility exposure across weekly and monthly expiriesNot yet](/learn/path-14/module-14-12-vega)
13. [14.13Rho and interest rates in Indian optionsNot yet](/learn/path-14/module-14-13-rho)
14. [14.14Position Greeks for multi leg strategiesNot yet](/learn/path-14/module-14-14-position-greeks)
15. [14.15Dynamic delta hedging and the P&L identityNot yet](/learn/path-14/module-14-15-delta-hedging)
16. [14.16Gamma scalpingNot yet](/learn/path-14/module-14-16-gamma-scalping)
17. [14.17Second order Greeks: vanna, volga, charm, speed and colourNot yet](/learn/path-14/module-14-17-second-order-greeks#quiz)
18. [TPath test, 30 questionsNot yet](/learn/path-14/module-14-17-second-order-greeks#pathTestSection)

Path 14 in reading time: 149 minutes over 17 modules

Minutes of reading per module, this one in amber. Source: RupeeCase Learn, Path 14.

    Explore next

## Put the module to work.

* [Free module 16.16Skew dynamics: sticky strike against sticky delta13 min read](/learn/path-16/module-16-16-skew-dynamics)
* [ToolOption payoff builderLegs on a dated Nifty chain, breakevens and charges](/learn/tools/payoff-builder)
* [Free module 14.11Gamma: why it grows so fast near expiry8 min read](/learn/path-14/module-14-11-gamma)
* [Free module 14.15Dynamic delta hedging and the P&L identity10 min read](/learn/path-14/module-14-15-delta-hedging)
* [Free module 15.12Vanna and charm flows around expiries and events12 min read](/learn/path-15/module-15-12-vanna-and-charm-flows)
* [QuestionWhat are vanna and charm?A short answer with a dated chart](/learn/questions/vanna-and-charm)

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SSources

## Go to the source.
6 sources, NSE the most cited

The publisher of each source listed below. Source: Module 14.17 source list.
1. [NSE, equity derivatives contract specifications (European exercise, cash settlement, lot size)](https://www.nseindia.com/static/products-services/equity-derivatives-contract-specifications) NSE
2. [NSE, derivatives end of day reports: the F&O bhavcopy these figures are built from](https://www.nseindia.com/all-reports-derivatives) NSE
3. [NISM, Series VIII Equity Derivatives, test objectives (option pricing, volatility and option strategies)](https://www.nism.ac.in/revamp-nism/test-objectives-revised-nism-series-viii-equity-derivatives-certification-examination/) NISM
4. [SEBI Investor, Understanding derivatives](https://investor.sebi.gov.in/understanding_derivatives.html) SEBI
5. [Black (1976), The pricing of commodity contracts, Journal of Financial Economics 3](https://doi.org/10.1016/0304-405X(76)90024-6) Paper
6. [Haug, The Complete Guide to Option Pricing Formulas, 2nd edition (closed forms of the Greeks)](https://www.mheducation.com/highered/product/complete-guide-option-pricing-formulas-haug/M9780071389976.html) Book

GTerms

## 5 terms from this module.
Second order GreekThe slope of a first order Greek: vanna, volga, charm, speed and colour are the common ones.
VannaHow delta changes when implied volatility changes. It is also how vega changes as the index moves. Quoted here for one vol point.
VolgaHow vega changes when implied volatility changes, the convexity of an option in volatility. Larger in the wings than at the money.
CharmHow delta changes as a day passes. It lowers the delta of an out of the money call and raises that of an in the money call.
Speed and colourSpeed is how gamma changes as the index moves. Colour is how gamma changes as days pass.
[All 230 terms in the glossary](/learn/glossary)

[Question people askWhat are vanna and charm?A short answer with a dated chart](/learn/questions/vanna-and-charm)[Related module14.11 Gamma: why it grows so fast near expiry8 min, Intermediate](/learn/path-14/module-14-11-gamma)[Related module14.15 Dynamic delta hedging and the P&L identity10 min, Advanced](/learn/path-14/module-14-15-delta-hedging)[Pillar guideDerivatives and Quant115 modules across paths 12 to 19](/learn/derivatives)

Education only, not investment advice, a research report or a recommendation to buy, sell or hold any security. RupeeCase (QC Alpha Technologies Pvt Ltd) is not registered with SEBI as an investment adviser or research analyst. Contracts and prices shown are for illustration only, come from NSE end of day files at least 30 days old, and are not recommendatory. Derivatives trading carries a high risk of loss.