What is the speed Greek and when does gamma slip?

Question

AcadiFi · Accepted Answer

Speed is the third derivative of option price with respect to spot, describing how gamma itself shifts as the underlying moves.

Unlock with Scholar — $19/month

Get full access to all Q&A answers, practice question explanations, and progress tracking.

Start 7-Day Free Trial Compare Plans

No credit card required for free trial

Consider a market-making firm named Brightside Options holding 8,000 short at-the-money calls on a tech ETF. Gamma is 0.085 per share, so a 1% spot move adds 6,800 shares of delta exposure. But speed is negative for short calls: as spot rises, gamma initially grows then falls past the strike. If speed is minus 0.0012, a 3% rally shrinks gamma by roughly 0.0036, meaning the realized delta change is less than a linear gamma estimate predicts, and the hedger may overbuy shares relative to actual exposure.

Speed matters most for high-gamma, near-strike books during rapid moves, for barrier options near knock-out levels, and for large institutional hedges where a two-Greek Taylor expansion is insufficient. Including speed improves P&L attribution and reduces slippage on dynamic delta hedges. For CFA Level II, the intuition is that vanilla risk reports truncate at delta-gamma-vega-theta, but professional books add speed, charm, vanna, and volga to capture curvature of curvature.

What is the speed Greek and when does gamma slip?

Master Level II with our CFA Course

Related Questions

Practice Questions