Speed (∂³V/∂S³)

Q: What is Speed in options trading?

Speed is the third derivative of an option's value with respect to the underlying price (∂³V/∂S³). It tells you how fast gamma itself is changing as spot moves. If gamma is the rate of change of delta, speed is the rate of change of gamma — sometimes called the 'gamma of gamma'. It is essential for dynamic hedging of large, gamma-concentrated positions.

Q: Why does Speed matter for hedging?

When hedging a portfolio with significant gamma, traders re-hedge delta as spot moves. Speed tells them how quickly gamma will change during that move. High speed means gamma shifts rapidly, so hedges go stale faster and need more frequent adjustment. Market makers with large at-the-money positions monitor speed to anticipate how their gamma profile will evolve intraday.

Q: How do I get Speed from the FlashAlpha API?

Call GET /v1/pricing/greeks with spot, strike, dte, sigma, type, and optional r and q parameters. The response includes a third_order object containing the speed field. The endpoint is available on the Free tier.

Q: Why does Speed matter for trading?

Speed is a third-order Greek that captures how gamma itself changes across the price axis. In tail events — sharp rallies or crashes — speed is often where the real P&L surprise comes from, because gamma itself shifts. Quant vol traders and tail-risk specialists actively manage speed; most retail manages it implicitly.

Q: When is Speed good versus bad for a trader?

Positive speed is good for long-option tail hedges — gains accelerate in extreme moves. Negative speed is bad for short-strangle strategies facing breakouts — the edge disappears when most needed. Near-zero speed means standard gamma exposure; typical retail trades.

Third-order Greek measuring how gamma changes with the underlying price — the "gamma of gamma".

Definition

The third partial derivative of option value with respect to the underlying spot price. Speed quantifies how rapidly gamma changes as spot moves, making it essential for dynamic hedging of portfolios with concentrated gamma exposure.

Formula

Speed = ∂Γ/∂S = -(Γ / S) × [ (d₁ / (σ√t)) + 2 ]

Where Γ is gamma, d₁ is the standard Black-Scholes d₁ term, σ is implied volatility, t is time to expiry, and S is spot price. Speed is typically a very small number and is quoted per unit move in the underlying.

Inputs

spot price strike price time to expiry implied vol

API Field

third_order.speed

Interpretation

Positive speed: gamma is increasing as spot rises. The option is becoming more convex — delta will accelerate faster on further up-moves.
Negative speed: gamma is decreasing as spot rises. The option's convexity is flattening — delta acceleration is slowing.
Near ATM: speed is near zero at the money (gamma peaks there). Speed is most significant for OTM options approaching the strike.
Dynamic hedging: high absolute speed means gamma is unstable — re-hedging intervals must be tightened to avoid delta slippage.

Why Speed Matters

Gamma tells you how much delta will change for a unit move in spot. But gamma itself is not constant — it peaks at the money and falls off as the option moves into or out of the money. Speed measures this curvature of gamma. For a market maker hedging a large book, speed determines how quickly their gamma hedge becomes stale after a spot move.

Consider a portfolio that is long gamma near the current spot. As price moves away, gamma declines (speed is the rate of that decline). If speed is large, the hedge deteriorates rapidly, forcing more frequent and costly re-hedging. Conversely, if speed is low, the gamma profile is stable and hedges last longer.

Speed is particularly relevant around major option expirations when gamma is highly concentrated at a few strikes. A small spot move can shift the gamma profile dramatically, and speed is the metric that quantifies that instability.

Get Speed via API

Endpoint

GET /v1/pricing/greeks

Tier

Free

Parameters

spot (required) — underlying price
strike (required) — option strike price
dte (required) — days to expiration
sigma (required) — implied volatility (decimal)
type (required) — call or put
r (optional) — risk-free rate (default 0.05)
q (optional) — dividend yield (default 0.0)

Response field

{
  "third_order": {
    "speed": number,
    "zomma": number,
    "color": number,
    "ultima": number
  }
}

curl -H "X-Api-Key: YOUR_KEY" \
  "https://lab.flashalpha.com/v1/pricing/greeks?spot=550&strike=560&dte=30&sigma=0.18&type=call"

import requests
r = requests.get(
    "https://lab.flashalpha.com/v1/pricing/greeks",
    params={"spot": 550, "strike": 560, "dte": 30, "sigma": 0.18, "type": "call"},
    headers={"X-Api-Key": "YOUR_KEY"}
)
print(f"Speed: {r.json()['third_order']['speed']:.8f}")

const params = new URLSearchParams({
  spot: 550, strike: 560, dte: 30, sigma: 0.18, type: "call"
});
const r = await fetch(
  `https://lab.flashalpha.com/v1/pricing/greeks?${params}`,
  { headers: { "X-Api-Key": "YOUR_KEY" } }
);
const d = await r.json();
console.log(`Speed: ${d.third_order.speed}`);

Why Speed Matters for Trading

TL;DR

Speed is how fast gamma changes with spot. Positive speed = gamma grows into moves = accelerating convex profits. Negative speed = gamma shrinks = vanishing edge.

What it measures: ∂Γ/∂S — third derivative of option value with respect to spot.
What it signals: The convexity of convexity. Whether your gamma position accelerates or decays.
Why we measure it: Big directional moves don't just change delta — they change gamma itself. Speed is the meta-convexity that matters in tail events.
Who uses it: Vol traders, tail-risk quants, gamma scalpers.

How to read Speed

Positive speed (long)

Gamma grows into the move
Accelerating convex gains
Sweet spot of long-option trades
Most valuable in tail events

Good for: long options, tail hedges

Negative speed (short)

Gamma shrinks into moves
Edge vanishes as it's most needed
Short-strangle failure mode
Pin breaks fast

Bad for: short strangles in breakouts

Speed near zero

Pure gamma exposure
No third-order effect
Typical ATM
Standard trading regime

Linear

Rules of thumb

Speed matters at the tails. Small moves have minimal speed impact. Large moves are where speed P&L shows up.
Pair with gamma. Gamma is first-order convexity; speed is how that convexity evolves.
Quant-level Greek. Retail rarely computes speed directly — managed via strike/DTE selection.
Relevant near gamma flip. Regime changes trigger speed P&L.
Size awareness. In tail events, speed losses on short-gamma books compound gamma losses.