First-order Greek · ∂V/∂σ

Vega: what a point of implied volatility is worth

Vega is the change in an option's value for a one-point change in implied volatility. It's how much you make or lose when the market reprices uncertainty, whether or not the underlying moves.

The formula

d₁ = [ ln(S/K) + (r + σ²/2)·T ] / (σ√T)
d₂ = d₁ − σ√T

Vega = S·φ(d₁)·√T

Black-Scholes, European options, no dividends. S spot, K strike, T years to expiry, r the risk-free rate, σ implied volatility, N(·) the standard normal CDF and φ(·) its density.

That's per 1.00 of volatility (100 points). Divide by 100 for the usual quote, value per vol point. It's the same for a call and a put with the same strike and expiry.

Where vega lives

Vega grows with √T and peaks near the money. Long-dated options carry far more vega than short-dated ones, the opposite of gamma, which is why "long vol" means different things at different tenors: a same-day option is a gamma trade, a one-year option is a vega trade.

Vega moves with the market

Implied volatility tends to rise when equity indices fall, so a long-vega position often gains on the way down. That relationship is why skew exists, and why vanna, the cross-sensitivity of delta to vol, matters for dealer flows.

Its relatives

Vanna: how delta changes when implied vol moves (equivalently, how vega changes with spot).
Vomma: how vega changes when implied vol moves.
Ultima: how vomma changes when implied vol moves.

SPX ATM implied volatility through the session, skew smile, expected move and skew in Zanshin Flow — Volatility through the session: ATM IV, the skew smile, skew and the expected move on SPX.

Questions

What does a vega of 0.25 mean?

Quoted per vol point, the option gains about 25 cents for each one-point rise in implied volatility and loses about 25 cents for each one-point fall.

Why do long-dated options have more vega?

Vega scales with the square root of time to expiry: a change in volatility compounds over a longer life, so it changes the option's value more.

Is vega a real Greek letter?

No. Vega isn't in the Greek alphabet; the name stuck by convention. It's sometimes written with the Greek letter nu or kappa.

Not financial advice. This article explains how options and dealer hedging work. It is not a recommendation to buy or sell anything.