Second Order Option Greeks: Charm, Vanna and Vomma
Second order greeks measure how the first order greeks themselves change. Charm is the rate at which delta decays with time, vanna is how delta responds to a change in implied volatility, and vomma is how vega responds to a change in implied volatility.
Delta, gamma, theta, vega and rho describe an option position. Second order greeks describe how those first numbers drift as the market moves. For a retail trader on NSE, the practical goal is recognising these effects when a position behaves oddly, not trading them directly.
Why a Second Layer of Greeks Exists
Every greek is a sensitivity. Delta measures premium against spot, vega against implied volatility, theta against the passage of time. Because those sensitivities are themselves unstable, they have their own sensitivities.
Gamma is the second order greek everyone already knows, since it measures how delta changes with spot. Charm, vanna and vomma complete the picture by mixing time and volatility into the same idea. Market makers who hedge continuously care, because a mispriced second order effect turns into a real hedging loss.
Charm: Delta Decay Over Time
Charm is the change in delta for the passage of one day, holding spot and volatility fixed. It is sometimes written as delta bleed.
An out of the money Nifty 24,500 call with spot at 24,000 sees its delta drain towards zero as expiry closes in, while an in the money call sees delta climb towards 1. Charm is the speed of that drift. It matters most for hedged books held over a weekend or a long holiday break, because delta shifts while the market is shut and no hedge can be adjusted.
Vanna: Delta Sensitivity to Implied Volatility
Vanna is the change in delta for a one point change in implied volatility. The same number is also the change in vega for a one point move in spot, since the cross derivative works both ways.
When India VIX spikes, the delta of far out of the money puts rises, because a wider expected range makes those strikes look reachable. Traders running skew positions, such as risk reversals, live with vanna as a core exposure. If your short strangle suddenly looks directional after a volatility jump even though Nifty barely moved, vanna is the explanation.
Vomma: Vega Sensitivity to Implied Volatility
Vomma, sometimes called volga, is the change in vega for a one point change in implied volatility. It is vega convexity.
At the money options have high vega but low vomma, so their vega is stable. Out of the money options have lower vega and higher vomma, so their vega grows as volatility rises. That convexity is one reason the volatility smile exists and why wing options get bid up in a panic far more than a plain vega figure suggests.
A Quick Comparison Table
| Greek | What it measures | Changes which greek | Where it shows up |
|---|---|---|---|
| Gamma | Delta change per unit of spot | Delta | Expiry day scalping, hedge frequency |
| Charm | Delta change per day | Delta | Positions held over weekends and holidays |
| Vanna | Delta change per volatility point | Delta and vega | Skew trades, VIX spikes |
| Vomma | Vega change per volatility point | Vega | Volatility smile, wing options |
Higher order terms exist too. Speed measures gamma change with spot, colour measures gamma decay with time, and zomma measures gamma change with volatility. They belong to quant desks, not a two lot Bank Nifty position.
What a Retail Trader Should Actually Do
Knowing these names is more useful than calculating them. Most Indian broker platforms do not display charm, vanna or vomma, and hedging them needs continuous execution that retail costs make impractical.
- Use them as diagnostics. A delta shift after a volatility move is usually vanna, one after a quiet weekend is usually charm.
- Treat them as a warning that short option positions carry risks a payoff diagram never shows.
- Size positions so a surprise in vega or delta does not force an exit at a bad price.
- Keep daily attention on delta, theta and vega, which you can see and manage.
One misconception is worth correcting. Second order greeks are not exotic add-ons for complicated structures. They already sit inside a plain short straddle, quietly changing your delta and vega while you watch only the premium.
Frequently Asked Questions
Is gamma a second order greek?
Yes. Gamma is the second derivative of option value with respect to spot, so technically it belongs in the same family as charm, vanna and vomma. It gets grouped with the first order greeks only because traders use it so routinely.
Which second order greek hurts a weekend position most?
Charm, usually. Two or three calendar days pass with no chance to adjust, so delta drifts and a hedged book can open Monday with directional exposure it did not have on Friday afternoon.
Do Indian broker platforms show vanna and vomma?
Rarely. A few third party option scanners compute them, but standard NSE option chains stop at the five main greeks. You can also derive them from a Black-Scholes calculator that exposes partial derivatives.
Does vanna explain why my short strangle turned directional?
Often it does. A jump in implied volatility changes the delta of both wings unevenly, so net delta drifts even if Nifty closes flat.
Key Takeaways
- Charm is delta decay per day, vanna is delta change per volatility point, vomma is vega change per volatility point.
- They exist because first order greeks are unstable.
- Charm matters over weekends, vanna during volatility spikes, vomma in the smile.
- Retail traders should use them to explain surprises rather than to build trades.
- These risks are already inside plain short option positions, not just exotic structures.
