Speed
The rate of change of gamma — how gamma accelerates with price.
Speed is a third-order Greek that measures the rate of change of gamma with respect to changes in the underlying stock price. Just as gamma tells you how fast delta changes, speed tells you how fast gamma itself changes. If gamma is the acceleration of delta, then speed is the "jerk" — the rate at which that acceleration shifts as the stock moves.
Why It Matters
Speed matters most during large, fast moves in the underlying. When a stock gaps sharply, gamma does not remain constant — it changes, and speed tells you by how much. For traders with large gamma exposure, speed determines whether their gamma position strengthens or weakens as the stock moves away from the current price.
Market makers and institutional traders monitor speed to anticipate how their hedging needs will evolve during rapid price moves. If you have a large positive gamma position centered at $100, speed tells you how quickly that gamma evaporates as the stock moves to $110 or $90. For retail traders, speed is less commonly monitored directly, but understanding it helps explain why gamma-based strategies behave differently during small versus large stock moves.
How It Works
Speed is the third derivative of the option price with respect to the stock price, or equivalently, the first derivative of gamma with respect to the stock price.
How speed behaves:
- ATM options: Speed is near zero at the money. Gamma is at its peak at the strike, so the rate of change of gamma is minimal right at that point.
- Slightly OTM or ITM options: Speed is at its highest magnitude just away from the money. As the stock moves away from the strike, gamma begins to decline, and speed measures how fast that decline occurs.
- Far OTM or deep ITM options: Speed is small because gamma is already low and relatively stable.
Sign conventions:
- For a long call just above the strike, speed is typically negative — gamma decreases as the stock continues to rise above the strike.
- For a long call just below the strike, speed is typically positive — gamma increases as the stock rises toward the strike.
- The reverse applies for puts.
Speed and large moves: During a 5% stock move, gamma can change significantly. Speed helps you estimate the new gamma after a large move rather than assuming gamma stays constant. This is important for:
- Stress testing portfolio risk
- Understanding how protective hedges behave during crashes
- Estimating P&L on large overnight gaps
Speed and time to expiration: Short-dated options have higher speed because their gamma is more concentrated around the strike. This means gamma changes more dramatically with stock price movement when expiration is near.
Quick Example
You own an ATM call on a $100 stock with gamma of 0.04 and speed of -0.002. The stock rises $5 to $105. Using speed, you can estimate the new gamma:
New gamma = 0.04 + (-0.002 x 5) = 0.04 - 0.01 = 0.03
Your gamma has dropped from 0.04 to 0.03. This means the acceleration of your gains is slowing as the stock moves further from the strike. Without accounting for speed, you might assume gamma stays at 0.04 and overestimate your profits on continued upside.
If the stock instead dropped $5 to $95, the new gamma would be approximately 0.04 + (0.002 x 5) = 0.05 — gamma increases because the stock is approaching the put's ATM zone.