Speed
Speed was a third-order options Greek measuring the rate of change of gamma with respect to the underlying price, or equivalently the third partial derivative of the option's value with respect to price, indicating how quickly gamma itself accelerated or decelerated as the underlying moved.
In the hierarchy of options Greeks, speed occupied the third order: where delta measured price sensitivity, gamma measured how delta changed with price, and speed measured how gamma changed with price. Speed was therefore a measure of the curvature of gamma — the rate at which the already non-linear gamma profile bent further as the underlying moved through different price levels.
Speed was largest for options that were near-the-money and approaching expiry. The gamma of a near-expiry ATM option was high and peaked sharply at the strike. As the underlying moved away from the strike, gamma fell rapidly — and it was this rapid fall that speed captured. A large positive speed meant gamma was increasing quickly as the underlying moved in a particular direction; large negative speed meant gamma was falling rapidly.
For market makers on NSE managing large short-gamma books in Nifty or Bank Nifty options near expiry, speed was a relevant consideration during high-volatility trading sessions. When the index moved rapidly through multiple strikes in a single session — as happened during post-event volatility spikes — the gamma of each strike in the book changed rapidly. A risk model that ignored speed would misestimate how much the book's gamma was changing as the market moved, potentially leading to under-hedging during the most volatile periods.
The practical accessibility of speed as a Greek was limited. Most retail trading platforms in India did not display speed, and it was primarily tracked in professional options risk management systems used by institutional desks and algorithmic trading firms. For retail participants, understanding speed was more of a conceptual enrichment — recognising that even gamma was not constant but itself moved with the underlying — rather than an actionable number in day-to-day trading decisions.
The relationship between speed, gamma, and delta formed the core of third-order risk management. Traders who ran large gamma-scalping operations or managed complex multi-strike options books found that speed quantified the error in first-order gamma hedging, in the same way that gamma quantified the error in first-order delta hedging. Incorporating speed corrections into hedge ratios improved hedging precision for large moves in the underlying.