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:
d1 = [0 + (0.04 + 0.142/2)(60/365)] / (0.14 sqrt(60/365)) = 0.00819 / 0.05676 = 0.144phi(d1) = 0.395- Vega = 500 × 0.395 × sqrt(60/365) = 500 × 0.395 × 0.405 = 80.0
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
- Black-Scholes: closed-form vega
S phi(d1) sqrt(T). Same vega for calls and puts (because both have the same N(d1)-derived sensitivity). - Heston (stochastic volatility): there is no single "vega" because Heston has multiple volatility-related parameters:
v0(initial variance),theta(long-run variance),nu(vol-of-vol),kappa(mean reversion),rho(correlation). The Heston "vega" most often quoted ispartial V / partial sqrt(v0)- sensitivity to instantaneous volatility. Cross-vegas to the other Heston parameters describe sensitivities to vol-of-vol regime, mean-reversion speed, and skew dynamics. - SABR: vega is decomposed into three pieces: sensitivity to
alpha(the stochastic-vol level, the closest analog to BS vega), tonu(vol-of-vol), and torho(skew control). Practitioner SABR vega often refers to the alpha-derivative. - Local volatility (Dupire): in pure LV there is no vol parameter to differentiate against - the vol surface is the input. Practitioners compute LV vega by parallel-shifting the entire input IV surface and re-pricing.
- Jump diffusion: standard diffusion vega plus jump-component vega (sensitivity to jump intensity and jump-distribution parameters). For Bates (Heston + jumps), there are additional vegas to the jump terms.
- Monte Carlo: vega is computed by pathwise differentiation or by re-running with bumped vol (finite-difference). For exotic options, MC vega is the production method.
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:
- Calendar spread (sell front, buy back): approximately vega-neutral if sized correctly across expirations. Isolates exposure to vega term structure.
- Risk reversal (long OTM call, short OTM put): approximately vega-neutral. Isolates exposure to skew (rho in SABR).
- Butterfly spread: small vega exposure. Isolates exposure to vomma (vol convexity, vol-of-vol).
- Diagonal spreads: tunable vega exposure. Used to express directional vol-term-structure views.
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
- Equity indices: vega scales straightforwardly with sqrt(T). Term-structure dominated by the volatility risk premium.
- Single-stocks: vega is jumpy because earnings introduce regime breaks. Pre-earnings vega is heavily corrupted by event premium, decaying via IV crush.
- FX options: Garman-Kohlhagen vega closely matches BS form. FX skew is generally symmetric (smile-like), making butterfly vega the dominant non-flat structure.
- Commodity options: upward-sloping skew (calls trade richer than puts) reverses the equity-index vega-skew interaction.
- Treasury options: vega is dominated by yield-curve regime; cross-vega between rate and vol is significant.
Special Cases
- Deep ITM/OTM: vega approaches zero. The option is no longer sensitive to vol because its outcome is essentially decided.
- Long-dated ATM: vega dominates. A 5% move in IV can be the largest single-day P&L driver.
- Short-dated ATM: vega is small but non-zero. Gamma and delta matter more.
- Pre-earnings options: reported vega understates the actual sensitivity to the earnings-day IV crush. Use scenario analysis with explicit pre/post IV regimes.
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
- Hull, J. (2018). Options, Futures, and Other Derivatives, 10th ed. Pearson.
- Gatheral, J. (2006). The Volatility Surface: A Practitioner's Guide. Wiley.
- Natenberg, S. (2014). Option Volatility and Pricing, 2nd ed. McGraw-Hill.
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.