Vega (sensitivity to implied volatility)
Vega is the option greek that measures how much an option's value changes for a one-point change in implied volatility, with price and time held constant. It is the same for a call and a put of equal strike and expiry, it is largest near the money, and it grows with the square root of time to expiry.
Senzoukria · Glossary · Updated September 2026
At a glance
- Definition
- ∂V/∂σ, usually quoted per 1 volatility point (0.01)
- Black-Scholes (q = 0)
- Vega = S·φ(d1)·√τ per 1.00 of volatility
- Sign
- Positive for long calls and long puts
Definition and formula
Vega is the partial derivative of the option value with respect to implied volatility. In Black-Scholes it equals S·e^(−qτ)·φ(d1)·√τ per unit of volatility, where one unit is 100 volatility points; dividing by 100 gives the usual quote, the premium change for a move from, say, 20% to 21%. Because the formula contains no call or put term, a call and a put with the same strike and expiry have the same vega, which is a direct consequence of put-call parity.
- Vega peaks close to the money and falls away in both wings.
- It rises with √τ: long-dated options carry far more vega than short-dated ones.
- Vega is not a greek letter at all; some texts call it kappa.
Worked example
With spot 100, implied volatility 20% and zero rates, the table gives Black-Scholes vega per volatility point. A 30-day at-the-money option worth 2.29 gains about 0.11 if implied volatility rises one point; the 7-day option gains about half as much, the 90-day option about 1.7 times as much.
| Contract | Days to expiry | Vega per vol point |
|---|---|---|
| Strike 100 (at the money) | 7 | 0.055 |
| Strike 100 (at the money) | 30 | 0.114 |
| Strike 105 (out of the money) | 30 | 0.082 |
| Strike 100 (at the money) | 90 | 0.198 |
Why short-dated options are about gamma, long-dated about vega
Gamma scales like 1/√τ and vega like √τ, so the balance between them shifts with maturity. A 0DTE option has almost no vega but very high gamma near the strike; a six-month option reacts much more to a change in implied volatility than to a one-point move in spot. When implied volatility drops after an event, the loss on long options is concentrated in the longer expiries, while the shortest expiries are dominated by where price settles relative to the strikes.
Reading errors and the Senzoukria view
- Vega assumes the whole curve moves by one point. In practice wings and the at-the-money point move by different amounts, which vega alone cannot describe; vanna and vomma cover part of that gap.
- Vega of a position is not the same as the option's value: a short straddle can have little premium left and still large negative vega.
- In Senzoukria the GEX overview shows a Total VEX tile labelled per vol-pt: the sum of open interest × vega × 100 across the chain's calls and puts, without a dealer sign. It describes the dollar sensitivity of the open-interest book to one volatility point, and it reads as not in chain when the provider publishes no vega.
Related
In the same section
- Extrinsic value
- IV calculation
- Zomma
- Vega exposure
- Variation margin
- Velocity logic
- Variance swap
- Vertical spread
This page in other languages
Frequently asked questions
- Why do a call and a put have the same vega?
- Put-call parity links them through a position in the underlying and a bond, neither of which depends on volatility. Any change in the call's value due to volatility must therefore be matched by the put of the same strike and expiry, so their vegas are equal in a European model.
- Is vega the same as vanna?
- No. Vega is the change in option value for a change in implied volatility. Vanna is the change in delta for that same change in volatility, which is what forces a delta-hedged book to trade the underlying when volatility moves.