Vega
Sensitivity of option price to a 1.00 (i.e. 100 percentage point) change in volatility. Identical for European calls and puts on the same strike and expiration. Most broker platforms divide by 100 to show "$/1% vol move."
When to use: Use to size volatility exposure on long or short option positions. Long calls and puts both have positive vega — they gain when implied volatility rises. Short positions have negative vega.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Vega | Vega | Change in option price per 1.00 (i.e. 100%) change in volatility | $ |
| S | Stock Price | Current price of the underlying | $ |
| Strike | Strike Price | Exercise price of the option contract | $ |
| Rf | Risk-Free Rate | Continuously compounded annual risk-free rate as a decimal | % |
| Sigma | Volatility | Annualized volatility of the underlying as a decimal (e.g. 0.25 for 25%) | % |
| T | Time to Expiration | Time to expiration in years (e.g. 0.25 for 3 months) | years |
Real-Life Examples
Example 1: ATM Vega, 30% Vol, 90 Days
Stock at $100, $100-strike 90-day option, r = 4%, σ = 30%.
Given
Step-by-Step
A 1.00 (i.e. 100-percentage-point) rise in volatility increases the option price by ~$19.75. Per-1%-vol-point convention: ~$0.197. ATM options have the highest vega.
Frequently Asked Questions
Differentiating put-call parity with respect to σ: the right-hand side (S − K·e^(−rT)) has no σ dependence, so ∂C/∂σ = ∂P/∂σ. Vega is a property of the strike and expiration, not the option type.
For ATM options with the most time to expiration. Vega scales with √T, so longer-dated options carry more volatility risk; deep ITM and OTM options have lower vega because their value is dominated by intrinsic value or near-zero probability.
Divide by 100. The output here is per 1.00 (100%) move in σ; brokers conventionally display the per-1%-point figure (vega ÷ 100), which is more intuitive for the typical 1-2 vol-point swings traders experience.