greeks
Speed
Third-order price Greek. Measures how Gamma changes as the stock moves. Important for understanding gamma risk on large portfolio moves.
Formula
Speed = -Γ · (d₁ + σ√T) / (S · σ · √T)
Variables
- Speed
- dΓ/dS — rate of change of Gamma per $1 stock move
- Γ
- Gamma of the option
- d₁
- Standard Black-Scholes d₁
- S
- Current stock price
- σ
- Implied volatility
- T
- Time to expiration (years)
Worked Example
Inputs
- Γ
- 0.0191
- d₁
- 0.478
- S
- $105
- σ√T
- 0.177
Calculation Steps
- 1
Numerator: -0.0191 × (0.478 + 0.177) = -0.0125 - 2
Denominator: 105 × 0.177 = 18.585 - 3
Speed = -0.0125 / 18.585 = -0.000673
Result: Speed ≈ -0.00067 — Gamma decreases as stock moves away from strike
Intuition
Speed tells you that gamma is not constant. An ATM option has peak gamma, but as the stock moves $5, gamma drops. Large dealers track speed to anticipate how their gamma hedge will deteriorate during volatile moves.