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Vega (ν)
Volatility sensitivity. Measures how much the option price changes when implied volatility moves by 1 percentage point.
Formula
ν = S · φ(d₁) · √T / 100
Variables
- ν
- Change in option price per 1% change in IV
- S
- Current stock price
- φ(d₁)
- Standard normal PDF at d₁
- T
- Time to expiration (years)
- /100
- Divides by 100 to express per 1% IV change (not per 100% change)
Worked Example
Inputs
- S
- $100
- φ(d₁)
- 0.3989
- T
- 0.25 (3 months)
Calculation Steps
- 1
√T = √0.25 = 0.5 - 2
Raw Vega = 100 × 0.3989 × 0.5 = 19.945 - 3
ν = 19.945 / 100 = 0.1995
Result: ν ≈ $0.20 — option gains $0.20 per 1% IV increase
Intuition
Vega is highest for longer-dated ATM options. After earnings, IV often drops 30-50% ("IV crush"), which can destroy long option positions even if the stock moves in your direction.