Speed (Third-Order Greek)
Rate of gamma change vs. price
What is Speed (Third-Order Greek)?
Speed (Third-Order Greek) Speed is a third-order option Greek that measures the rate of change of gamma with respect to changes in the underlying asset's price. It is mathematically the third partial derivative of the option price with respect to the underlying price. Speed tells you how quickly your gamma exposure changes as the stock moves, which is critical for managing large options portfolios where gamma itself is not constant. How it works: Gamma measures how fast delta changes, but gamma itself is not static. Speed quantifies this next level of curvature. When speed is positive, gamma increases as the stock price rises; when negative, gamma decreases. Speed is highest for at-the-money options near expiration, where gamma is already large and changing rapidly. For a single option, speed is typically small, but for portfolios with thousands of contracts, speed-driven gamma changes can create significant hedging demands. For example, suppose a market maker is delta-neutral and gamma-neutral on a large SPY options book. If SPY moves up $2, the gamma on the book changes due to speed. With a positive speed of 0.002, the book picks up 0.004 of gamma per contract as SPY rises, meaning the delta hedge now needs to be adjusted more aggressively for each additional dollar of movement. Ignoring speed would cause the hedger to underestimate how quickly gamma builds during a rally. Speed matters most for institutional traders and market makers managing large, complex portfolios. Retail traders rarely need to monitor speed directly, but understanding the concept explains why options market dynamics become non-linear during large price moves. When speed is high, hedging activity accelerates with each incremental price change, potentially amplifying market moves. This is one reason why large directional moves tend to feed on themselves near option expiration dates.
Complete Definition
Speed is a third-order option Greek that measures the rate of change of gamma with respect to changes in the underlying asset's price. It is mathematically the third partial derivative of the option price with respect to the underlying price. Speed tells you how quickly your gamma exposure changes as the stock moves, which is critical for managing large options portfolios where gamma itself is not constant. How it works: Gamma measures how fast delta changes, but gamma itself is not static. Speed quantifies this next level of curvature. When speed is positive, gamma increases as the stock price rises; when negative, gamma decreases. Speed is highest for at-the-money options near expiration, where gamma is already large and changing rapidly. For a single option, speed is typically small, but for portfolios with thousands of contracts, speed-driven gamma changes can create significant hedging demands. For example, suppose a market maker is delta-neutral and gamma-neutral on a large SPY options book. If SPY moves up $2, the gamma on the book changes due to speed. With a positive speed of 0.002, the book picks up 0.004 of gamma per contract as SPY rises, meaning the delta hedge now needs to be adjusted more aggressively for each additional dollar of movement. Ignoring speed would cause the hedger to underestimate how quickly gamma builds during a rally. Speed matters most for institutional traders and market makers managing large, complex portfolios. Retail traders rarely need to monitor speed directly, but understanding the concept explains why options market dynamics become non-linear during large price moves. When speed is high, hedging activity accelerates with each incremental price change, potentially amplifying market moves. This is one reason why large directional moves tend to feed on themselves near option expiration dates.
Frequently Asked Questions
What is the Speed Greek in options?
Speed is a third-order Greek measuring how gamma changes as the underlying price moves. It is the third derivative of option price with respect to the underlying. Speed is most relevant for large portfolios where changes in gamma require dynamic hedging adjustments.
When does Speed matter in options trading?
Speed is most significant for market makers and institutional traders managing large options books. It matters most near expiration when gamma is highest and changing rapidly. Retail traders rarely need to track speed, but it explains why large price moves near expiration can become self-reinforcing.
How is Speed different from Gamma?
Gamma measures how delta changes with price, while Speed measures how gamma itself changes with price. Think of it as the acceleration of acceleration: delta is the first derivative of price, gamma is the second, and speed is the third. Speed captures the non-linearity that gamma alone misses.
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