What Is Vega?

Vega (ν) is the first derivative of option value with respect to implied volatility. In the Black-Scholes model, vega equals S phi(d1) sqrt(T), where phi() is the standard normal density. Vega is typically expressed as the dollar change in option value per 1% (one volatility point) change in IV - so a vega of 0.45 means the option gains $0.45 for each 1-point rise in IV (e.g., 14% to 15%).

What Is Vega in Options?

Vega is how sensitive an option price is to changes in implied volatility. Long options have positive vega (they gain when IV rises); short options have negative vega (they lose when IV rises). Vega is the structural Greek for volatility-driven P&L: it translates IV-surface moves into dollar P&L on a position.

Three intuitions for vega. First, vega is the dollar value of a 1-point IV change - the most commonly-quoted version on a trading desk. Second, vega is the price of taking a long-vol position: if you buy options expecting realized vol to exceed implied, the realized P&L is roughly your vega times the IV gap (volatility risk premium). Third, vega is exhaustive in long-dated options: nearly all the price sensitivity in a 1-year ATM option is vega, while delta and gamma matter less than for short-dated options.

Worked Example

SPY at $500, 60-day ATM call, IV 14%, rate 4%. Black-Scholes vega computation:

That is the per-share vega. Per-1%-IV-change scaling: divide by 100 to get $0.80 per 1-point IV move. So if SPY IV moves from 14% to 15% (one vol point higher), the call gains roughly $0.80 per share or $80 per contract. If IV moves from 14% to 20% (six points), gain is roughly 6 × $0.80 = $4.80 (ignoring vomma).

Vega Across Moneyness and Time

Vega peaks ATM and falls off in both wings - similar shape to gamma. The peak vega magnitude scales roughly with sqrt(T): a 1-year ATM option has roughly 2x the vega of a 90-day ATM option. This means long-dated options are dominated by vega exposure, while short-dated options are dominated by delta and gamma exposure. The vega term structure is a primary axis of vol-trading strategy.

Volatility itself does not strongly affect vega magnitude (in pure BS). What matters more is the smile and term structure: actual market vega differs from BS-implied vega because the surface is curved, not flat. Smile-adjusted vega (sometimes called "regime vega" or "scenario vega") accounts for the fact that a parallel IV shift across the surface is rare; more typically, IV moves with skew and term-structure character.

How Pricing Models Compute Vega

Vega-Neutral Construction

Building a vega-neutral position is the central skill of volatility trading. The idea: hold combinations of long and short options such that aggregate vega is zero, isolating exposure to gamma, theta, or skew while neutralizing first-order vol exposure. Standard constructions:

Vega Risk Management

Aggregate position vega is the most-watched volatility-risk metric in retail and prop trading. A long-vol book with $50K vega per 1%-IV-shift is exposed to $250K loss if IV drops 5 points (e.g., post-earnings). Vega-by-bucket (decomposing vega into tenor buckets and skew buckets) is the institutional method - a single aggregate vega number masks term-structure and skew exposures.

Three operational rules for vega. First, vega scales with sqrt(T) so long-dated positions accumulate vega faster than short. Second, vega is linear in spot up to a point - doubling spot doubles vega for ATM options, but not for deep OTM. Third, vega and vomma together describe non-linear vol exposure: large IV moves produce P&L that exceeds linear vega × IV-change because vomma kicks in.

Vega Across Asset Classes

Special Cases

Related Greeks

Vega is the first-order vol Greek. Vomma (also Volga) is its second derivative - vega convexity. Vanna is the cross-derivative with spot. Veta is the cross-derivative with time (vega's time decay). The three vega-cousins together describe how vega itself moves through state space.

Related Concepts

Vomma · Vanna · Veta · Vol of Vol · Volatility Skew · IV Crush · Heston · All 17 Greeks

References & Further Reading

View SPY IV vs realized vol history →

This page is part of the 17 Greeks reference covering every options Greek with formula, intuition, worked example, and how each pricing model computes it. Browse the full documentation.