You've learned Delta, Gamma, Theta, and Vega. You might even know Rho. But if you've ever wondered why professional market makers seem to have an edge you can't replicate, part of the answer lives in Greeks you've probably never heard of: Charm, Vanna, and Volga. These are the "second-order Greeks" — the sensitivities of sensitivities — and understanding them reveals a deeper layer of how options really behave.
This guide explains each without jargon, shows when they matter in Indian markets, and helps you decide whether to learn them or skip them.
1. Why Second-Order Greeks Exist
First-order Greeks (Delta, Theta, Vega) answer "how much does option price change per unit of X?" Second-order Greeks answer "how much does that Greek itself change per unit of Y?"
The intuition
If Delta is your speed and Gamma is your acceleration, Charm is how your speed changes purely due to time passing. Vanna is how your speed changes when road conditions (volatility) shift. Volga is how sensitive your sensitivity to road conditions is.
2. Charm — The Daily Decay of Delta
Charm = change in Delta per day from time alone. Also called "Delta decay" or DDeltaDTime.
Charm by Moneyness — NIFTY at 24,8007 DTE
| Strike | Moneyness | Current Delta | Charm/day |
|---|
| 24,400 | Deep ITM | 0.74 | +0.03 |
| 24,800 | ATM | 0.51 | +0.005 |
| 25,200 | OTM | 0.28 | -0.04 |
| 25,600 | Deep OTM | 0.09 | -0.02 |
ITM options drift toward Delta 1.0 (positive Charm). OTM options drift toward Delta 0 (negative Charm). ATM options are near-stationary. Effect grows in final week.
Practical implication: if you hold a short OTM call near expiry, your negative Charm is your friend — the call loses Delta (and value) just from time passing, even on flat days.
3. Vanna — Delta Meets Volatility
Vanna = change in Delta per 1% change in IV (or equivalently, change in Vega per ₹1 change in spot).
Example · BANKNIFTY iron condor before RBI
Vanna risk during IV regime shifts
Position Delta at entry+2 (near neutral)
Position Vanna-0.15 per leg, -0.6 net
RBI surprise dovish → BANKNIFTY +400, IV +3%-
Delta shift from direction+2 → -8 (Delta move)
Delta shift from Vanna (IV up)-0.6 × 3% = -1.8 additional
Total Delta now-9.8 (way off-neutral)
Vanna explains why delta-neutral positions drift off-neutral during IV spikes — even if the spot hasn't moved that much. Market makers pre-hedge Vanna before major events.
4. Volga — The Vega of Vega
Volga (or Vomma) = change in Vega per 1% change in IV. It is the second derivative of option price with respect to volatility.
Why it matters
A position's Vega isn't constant — it changes as IV moves. If you're short Vega (short strangle, iron condor), rising IV makes your Vega even more negative (Volga compounds the pain). If you're long Vega, falling IV reduces your Vega sensitivity faster than expected.
Volga is highest for OTM options and longer-dated positions. It is why butterfly spreads and ratio backspreads become unpredictable during volatility regime shifts — the second-order effects swamp the first-order hedging.
5. When These Greeks Actually Matter
Retail trader verdict: For most Indian retail traders — monthly iron condors, covered calls, cash-secured puts — Delta/Gamma/Theta/Vega give 95% of the information you need. Second-order Greeks are polish.
When you should learn them:
- You hold positions through RBI / budget / earnings (Vanna matters)
- You run systematic multi-leg strategies (Volga matters)
- You trade weekly options near expiry (Charm matters)
- You manage a book of 20+ concurrent positions (all matter)
Market maker insight: The reason institutional desks make money on tiny per-contract edges is that they hedge second-order Greeks explicitly. Retail traders who don't are leaking edge in ways they can't see. Understanding the concept, even if you don't compute them daily, makes you a better trader.
Master all Greeks in Strategy Lab
All first-order Greeks shown live. Second-order Greeks on our roadmap for advanced tier.
Open Strategy Lab →Frequently Asked Questions
What is Charm?
Charm (also called Delta decay or DDeltaDTime) measures how much an option's Delta changes per day from the passage of time alone. OTM options lose Delta as they decay (Charm is negative). ITM options gain Delta (positive Charm). Charm matters most in the final week of expiry when Delta shifts can be abrupt even without price movement.
What is Vanna?
Vanna measures the change in Delta per 1% change in implied volatility. Equivalently, it's the change in Vega per ₹1 change in spot. Vanna tells market makers how their directional exposure shifts when volatility changes — important during IV regime shifts (pre/post RBI, earnings, geopolitical events).
What is Volga?
Volga (also called Vomma) is the second derivative of option price with respect to volatility — essentially, the Vega of Vega. It measures how much Vega changes when IV changes. Volga is highest for OTM options and longer-dated positions. Market makers hedge Volga during volatility-of-volatility spikes.
Do retail traders need to know second-order Greeks?
For most retail traders in India, knowing the first-order Greeks (Delta, Gamma, Theta, Vega) is sufficient. Second-order Greeks (Charm, Vanna, Volga) are useful when: you hold positions through known events (RBI, earnings) where IV and direction both shift, or you run systematic strategies across multiple legs. For occasional traders, they're over-engineering.
How do market makers use these Greeks?
Market makers on Indian exchanges (NSE, BSE) run thousands of contracts. Small biases in Delta, Vega, or second-order Greeks compound to large losses. They use Charm, Vanna, and Volga to pre-hedge before expected regime shifts — for example, reducing Vanna exposure the week before RBI policy when IV and Delta can shift together unpredictably.
Can I see Charm, Vanna, Volga on my broker's platform?
Most retail Indian broker platforms (Zerodha Kite, Upstox, Angel One) show only Delta, Gamma, Theta, Vega. Advanced platforms and prop tools show second-order Greeks. The White Stallion Strategy Lab displays all first-order Greeks for every leg — second-order Greeks are on the roadmap for advanced users.
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