Speed (third-order option greek)
Speed is the third-order option greek that measures how fast gamma changes when the underlying price moves. It is positive when spot is below the strike and rising toward it, negative once spot has passed the strike, and it is the reason a gamma figure measured at today's price cannot be carried unchanged to another price.
Senzoukria · Glossary · Updated September 2026
At a glance
- Definition
- ∂Γ/∂S = ∂³V/∂S³
- Black-Scholes
- Speed = −(Γ/S)·(d1/(σ√τ) + 1)
- Units
- Change in gamma per 1 unit of underlying price
Definition and formula
Gamma is the rate at which delta changes with spot; speed is the rate at which gamma itself changes with spot. In Black-Scholes it equals −(Γ/S) × (d1/(σ√τ) + 1). Gamma forms a hump centred slightly below the strike, so speed is positive on the left side of the hump, zero at its peak and negative on the right side. For a trader this means that the gamma of a strike grows as price approaches it and fades after price crosses it.
Worked example
With spot 100, implied volatility 20%, 30 days to expiry and zero rates, the 105 call has a gamma of 0.0496 and a speed of +0.0066. If spot rises to 100.5, the first-order estimate gives 0.0496 + 0.5 × 0.0066 = 0.0529, and the exact gamma is 0.0528. A strike below spot behaves the other way: the 97 call has a speed of −0.0064, so its gamma falls as spot rises away from it.
- Speed is largest for short-dated options, where the gamma hump is narrow and steep.
- A first-order speed estimate works for small moves only; for larger moves gamma must be recomputed.
Why it matters for gamma exposure
A gamma exposure total is computed at one spot price. Because every leg's gamma changes with spot at a rate given by its speed, the total at a price 1% higher is not the total at today's price. Two approaches exist: hold each leg's gamma fixed and accumulate it by strike, which ignores speed entirely, or reprice the chain at each hypothetical spot, which captures speed and all higher-order effects at once. The second approach is what a gamma profile by price does, and the two can place the zero-gamma level at different prices.
In Senzoukria
Senzoukria does not display speed as a number. Its GEX module offers both views described above: the Net GEX by strike chart with its Cumulative toggle keeps each strike's exposure at today's spot, while the Gamma profile by price recomputes Black-Scholes gamma at 81 hypothetical prices across ±8% of spot and rescales each leg's published exposure, so the change of gamma with price is built into the curve. When the two flips differ, the chart overlay labels the profile's crossing separately rather than merging the two readings.
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Frequently asked questions
- Do traders actually hedge speed?
- Rarely as a separate number. Large option books reprice their gamma across a grid of spot scenarios, which captures speed implicitly. Speed is mostly useful to understand why a gamma figure is only valid near the price where it was computed.
- Why is speed negative for an at-the-money option?
- Because the gamma hump peaks slightly below the strike in Black-Scholes. At a spot equal to the strike, price is already just past the peak, so a further rise lowers gamma a little.