Why does gamma trading profitability depend on volatility clustering?

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AcadiFi · Accepted Answer

Long gamma profits when realized volatility exceeds implied volatility at purchase. Gamma scalping captures 0.5*Gamma*(dS)^2 each rebalance, which integrates over the holding period to 0.5*Gamma*sigma_R^2*S^2*T. Theta decay, on the other hand, equals 0.5*Gamma*sigma_I^2*S^2*T for an at-the-money option. Net P&L = 0.5*Gamma*S^2*T*(sigma_R^2 - sigma_I^2).

Vol clustering (GARCH effects) means volatility is persistent: high-vol days cluster, as do low-vol days. A long gamma trade held during a cluster of high-vol days can earn far above the average. Conversely, during low-vol regimes, theta grinds down positions. The risk profile is asymmetric—lots of small losses during calm periods, occasional large gains during storms.

For Windrose's 1-month SPY gamma position, implied vol = 18%, realized over month = 24%: P&L from scalping minus theta ≈ 0.5 * Gamma * S^2 * (1/12) * (0.24^2 - 0.18^2) = positive. But if realized vol is 15%, P&L is negative. The Sharpe ratio of long gamma depends critically on vol-of-vol and vol mean reversion.

Practical considerations: (1) rebalancing frequency matters—too frequent incurs transaction costs, too infrequent misses gamma capture; (2) jumps hurt short gamma disproportionately (convexity gain bounded below by -option premium, unbounded above); (3) implied vol tends to rise when realized spikes, so vega from being long options provides secondary gain. Windrose should size positions by vol-of-vol and hold through regime transitions, not bail out after a quiet week.

Why does gamma trading profitability depend on volatility clustering?

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