Speed —
How Gamma changes for a ₹1 move in the underlying.
Quick answer: Speed measures how much an option's Gamma changes when the underlying moves by ₹1 — the third derivative of price with respect to spot, which tells you how quickly your acceleration (Gamma) itself shifts as Nifty travels.
Simple explanation
Delta is speed, Gamma is acceleration, and Speed (the Greek) is how that acceleration changes as Nifty moves — think of it as the 'jerk' of the option. It tells you how the Gamma hump slides and reshapes as the underlying travels away from the strike. Speed matters most for large moves and near expiry, when Gamma is tall and changes rapidly across strikes, so Delta-hedges built on today's Gamma go stale after a big move.
Speed — visual
How Speed behaves
Speed is an S-shaped curve that crosses zero near the at-the-money strike — positive on one side and negative on the other — describing how the Gamma peak shifts and decays as spot moves away from the strike.
Detailed explanation
What Speed measures — the third derivative
Speed is the rate of change of Gamma with respect to the underlying price (∂Gamma/∂S), which makes it the third derivative of the option price with respect to spot. If Delta is the option's velocity and Gamma its acceleration, Speed is the 'jerk' — how the acceleration changes as the underlying moves. It describes how the tall, narrow Gamma peak slides across strikes and loses height as Nifty travels away from the money.
Why Gamma is not constant across a move
Traders often approximate a move using Delta plus Gamma. But Gamma itself changes as spot moves, and Speed quantifies that. On a large Nifty move — say 200 points on a Budget day — the Gamma you started with is not the Gamma you finish with. Speed tells you how much your acceleration decayed or grew during the move, so a Delta-plus-Gamma estimate that ignores Speed will misprice the P&L of a big swing.
Why it matters near expiry and for big moves
Near a Nifty or Bank Nifty weekly expiry, the Gamma hump is extremely tall and narrow around the ATM strike. That means Gamma changes violently over small distances, so Speed is large. A short-Gamma seller who is run over on a fast move finds that not only is Delta accelerating (Gamma), but the acceleration itself is shifting (Speed) — the classic 'the position kept getting worse faster than I expected' experience on expiry day.
Practical role in hedging books
Delta-Gamma hedging assumes Gamma is locally stable. Speed measures the error in that assumption. Market makers and structured-product desks running large Nifty option inventories use Speed to judge how often a Delta-Gamma hedge must be re-struck after the underlying moves — high Speed means the hedge decays quickly and needs frequent adjustment, especially in the final expiry sessions.
Formula
Speed formula
Speed = ∂Gamma/∂S = ∂³V/∂S³ = −Gamma/S · (d₁/(σ√T) + 1)
A third-order Greek: the derivative of Gamma with respect to spot (third derivative of price wrt the underlying). Signed and S-shaped, crossing zero near the money; largest and most volatile near expiry when Gamma is tall.
Practical example (Nifty)
Illustrative — Nifty spot 24500, lot size 75
Nifty is at 24,500, one day to a weekly expiry. Your 24,500 CE has Gamma 0.008 and a meaningful Speed. Nifty gaps up 150 points to 24,650 on strong global cues. A naive Delta-plus-Gamma estimate would keep applying Gamma of 0.008 across the whole move, but Speed means Gamma actually falls as the option moves in-the-money — say to 0.005 by 24,650. So the Delta rose fast at first and then decelerated. A trader who Delta-hedged assuming constant Gamma over-hedged the tail of the move; one who accounted for Speed sized the adjustment correctly and avoided being whipsawed on the pullback.
Practical trading impact
- Speed tells you your Gamma will not stay constant through a large Nifty move — acceleration itself shifts as spot travels.
- It is largest near expiry, when the Gamma hump is tall and narrow, so big weekly-expiry moves reshape Gamma sharply.
- Delta-plus-Gamma P&L estimates for large swings are inaccurate unless Speed is considered.
- High Speed means Delta-Gamma hedges go stale quickly after a move and need re-striking, especially on expiry day.
Common mistakes
- Assuming Gamma is constant through a big move and mis-estimating the P&L of a large Nifty swing with Delta plus Gamma alone.
- Ignoring Speed on expiry-day short-Gamma positions, then being surprised that losses accelerated non-linearly on a fast move.
- Confusing Speed (Gamma vs spot) with Color (Gamma vs time) — both reshape Gamma but for different reasons.
- Over- or under-hedging after a large move by applying the pre-move Gamma across the whole distance travelled.
Professional usage
Option market makers and Delta-Gamma hedgers on Nifty and Bank Nifty treat Speed as the correction term that tells them how quickly their Gamma hedge decays as spot moves. On expiry day, when Gamma is tall and Speed is large, they re-strike hedges frequently and size adjustments to the changing, not the initial, Gamma. Volatility desks also use Speed to price the curvature of large-move scenarios that a simple Delta-Gamma approximation would misstate.
Key takeaway
Speed is the jerk of an option — how your acceleration (Gamma) changes as Nifty moves. It is negligible for small moves far from expiry but decisive for large moves near a weekly expiry, where ignoring it makes Delta-Gamma hedges and big-swing P&L estimates simply wrong.
Frequently asked questions
What is Speed in options trading?
How is Speed different from Gamma?
What is the difference between Speed and Color?
Why does Speed matter near expiry?
Is Speed important for retail traders?
Is Speed a second- or third-order Greek?
How does Speed affect Delta-Gamma hedging?
Why did my short option lose faster than Gamma predicted on a big Nifty move?
Sources & references
Last reviewed 7 July 2026. Educational content only — not investment advice.