Speed

Speed is a third-order sensitivity that measures the rate of change of gamma with respect to changes in the underlying asset price. While gamma tells us how delta changes, speed tells us how that gamma changes, providing a measure of the convexity of the convexity.

It is essentially the third derivative of the option price with respect to the underlying asset price. In highly volatile cryptocurrency markets, speed is used by sophisticated traders to understand the stability of their gamma exposure.

If speed is high, it means the gamma of the position will change drastically with even small moves in the underlying, making risk management much more complex. It is often considered a secondary metric compared to delta and gamma, but it is crucial for managing tail risk and extreme market scenarios.

Traders monitoring speed can better prepare for situations where their gamma-hedging strategy might fail or become prohibitively expensive. It serves as a warning sign for potential non-linear risk amplification in a portfolio.