Introductory Context
"Gamma measures how much delta changes per ₹1 move in the underlying. Always positive for long options. ATM options have highest gamma. Gamma accelerates near expiry creating explosive ATM moves on expiry days. Gamma is the reason buyers benefit more from large moves than expected and sellers suffer more than expected from the same moves."
The Precise Definition and the Convexity Benefit
Gamma = Change in delta ÷ Change in underlying price.
For a Nifty ATM call with delta 0.50 and gamma 0.003: a 100-point Nifty rise changes delta from 0.50 to 0.50 + (0.003 × 100) = 0.80.
The convexity of positive gamma — illustrated with a 200-point move in each direction from an ATM call (delta 0.50, gamma 0.003):
• 200-point Nifty rise: delta increases continuously from 0.50 to ~0.80. Average delta ≈ 0.65. Gain = 0.65 × 200 = ₹130 per unit
• 200-point Nifty fall: delta falls from 0.50 to ~0.20. Average delta ≈ 0.35. Loss = 0.35 × 200 = ₹70 per unit
On the same 200-point move: gaining ₹130 when correct, losing only ₹70 when wrong. This asymmetry — gaining more on wins than losing on losses of the same magnitude — is the gamma-driven convexity of long options. It is a primary structural advantage of buying options over buying the underlying directly.
Gamma Sign Conventions
Long calls: positive gamma. Long puts: positive gamma. Short calls: negative gamma. Short puts: negative gamma. Options buyers always have positive gamma (both calls and puts benefit from large moves through accelerating delta). Options sellers always have negative gamma.
Gamma Across Strikes and Time
ATM options have highest gamma because the transition zone between likely-OTM (delta near 0) and likely-ITM (delta near 1) creates maximum uncertainty and therefore maximum sensitivity. Deep ITM or OTM options have low gamma — the outcome is more predictable, small moves change probability much less.
Gamma increases dramatically as expiry approaches. ATM gamma with 25 days to expiry: approximately 0.001. With 5 days: approximately 0.003. With 1 day: approximately 0.008. This expansion means that in the final days of an expiry cycle, ATM options behave explosively — small underlying moves cause large, fast delta changes.
Gamma Risk on Expiry Tuesday
The extreme gamma of ATM options on expiry Tuesday creates both opportunity and danger. A 50-point Nifty move on Monday changes an ATM call's delta by 0.001 × 50 = 0.05. The same move on Tuesday changes delta by approximately 0.008 × 50 = 0.40 — eight times larger. Tuesday positions must be sized smaller and managed more actively than any other day.
Long Gamma vs Short Gamma — The Fundamental Trade
• Long gamma (options buyer): profits from large moves beyond what delta predicts. Pays theta every day. Profits when realised volatility exceeds implied.
• Short gamma (options seller): suffers from large moves. Collects theta every day. Profits when realised volatility is below implied.
The gamma-theta trade-off is the central dynamic of options markets. Buyers pay theta to access gamma convexity. Sellers collect theta but bear gamma risk. The question for any trade: will realised volatility be high enough to justify the theta cost (buyer's view) or low enough to let theta exceed gamma losses (seller's view)?
Gamma is not just a technical Greek — it is the mechanism that gives options their unique risk-reward profile. The convexity it creates makes options fundamentally different from the underlying. Understanding gamma is understanding why options behave the way they do on large-move days, near expiry, and in high-volatility events.