Charm, Vanna and Volga

The main Greeks, delta, gamma, theta, vega and rho, describe how an option's price responds to changes in its inputs. Second order Greeks describe how those sensitivities themselves change. Gamma is the best known second order Greek: it measures how delta changes with price. Three others matter a lot to professional traders: charm (how delta changes with time), vanna (how delta changes with volatility, or equivalently how vega changes with price) and volga (how vega changes with volatility). They explain why a hedged book drifts out of balance and help explain some market flows.

Summary#

Charm: delta decay#

As time passes, option deltas drift even if the price and volatility do not change:

• Out of the money options: delta drifts toward 0.
• In the money options: delta drifts toward 1 (calls) or minus 1 (puts).

Charm matters for dealers who hedge large option books: as expiration approaches, their hedges must change predictably, which some analysts link to flows around monthly option expiries.

Vanna: delta and volatility#

Vanna measures how delta changes when implied volatility changes. Equivalently, it measures how vega changes when the underlying moves.

• When implied volatility rises, out of the money option deltas increase (they become more likely to finish in the money) and in the money deltas decrease.
• For equity indices, implied volatility usually falls when markets rise. Through vanna, that changes option deltas, and dealers adjusting hedges may buy or sell the underlying.

Analysts sometimes describe "vanna flows": after a volatility spike fades, falling implied volatility can reduce the delta of puts that dealers are short, leading dealers to buy back hedges and support prices. These effects are debated and hard to measure. See Dealer Gamma Exposure.

Volga: vega convexity#

Volga measures how vega changes as implied volatility changes. Positions with positive volga gain more vega when volatility rises, so they benefit from large swings in volatility.

• Out of the money options have high volga relative to at the money options.
• Volga helps explain the volatility smile: traders demand extra premium for out of the money options partly because of their volatility convexity. See Volatility Smile and Skew.

In FX options markets, traders use the "vanna volga" method to adjust model prices for smile effects.

Why these Greeks matter#

Other higher order Greeks#

• Speed: how gamma changes with price.
• Color: how gamma changes with time.
• Zomma: how gamma changes with volatility.
• Ultima: how volga changes with volatility.

These matter mainly for large, complex books and exotic options.

Do retail traders need them?#

For most individual traders, delta, gamma, theta and vega cover what matters. Knowing charm helps explain why positions behave differently near expiry, and vanna helps explain why out of the money options react strongly to volatility changes. See Managing Portfolio Greeks.

Frequently asked questions#

What is charm in options?#

The rate at which an option's delta changes as time passes, also called delta decay.

What is vanna?#

The sensitivity of delta to changes in implied volatility, or equivalently the sensitivity of vega to changes in the underlying price.

What is volga?#

The sensitivity of vega to changes in implied volatility, sometimes called vomma or vega convexity.

Next, learn how traders neutralise direction in Delta Hedging.