Does Gamma P&L Really Measure Convexity?

Decomposing option P&L into individual Greek contributions is a useful practice. The decomposition is typically derived from a Taylor expansion and serves both risk-management and research purposes. For example, some studies use gamma P&L as a measure of convexity and as a tool for analyzing the variance risk premium.

Reference [1] challenges this conventional interpretation. The authors argue that the gamma term, ½Γ(ΔS)², does not necessarily measure pure convexity. To support their argument, they compute the theoretical Black-Scholes gamma and compare it with an empirical gamma estimated from actual option price changes after removing delta and vega effects.

The authors pointed out,

…At the daily horizon, the ½*Γ_BS(∆S)² term loads primarily on vega contamination from negative spot–IV comovement rather than on convexity. The consequences are most direct for the variance risk premium literature that decomposes delta-hedged returns and attributes the ½*Γ_BS(∆S)² term to convexity exposure. If that term is dominated by vega contamination at the daily horizon, such attributions rest on a channel that is not identified….

…The broader implication is that Greek identification is horizon-specific. The Taylor channels do not scale uniformly with ∆t: delta, theta, vega, and gamma become observable at different rates, and cross-channel comovement can dominate the residual used to isolate a coefficient. A decomposition that is useful at one horizon can therefore fail at another unless the implied channel coefficients are checked directly.

The paper shows that correlations between theoretical and empirical gamma are close to zero at intraday horizons and become negative at daily horizons, ranging from -0.25 to -0.47.

In summary, the authors conclude that while the daily ½Γ(ΔS)² term can be calculated, it may largely reflect vega contamination arising from the leverage effect rather than pure convexity. Because spot and implied volatility are negatively correlated, volatility changes can be absorbed into the gamma term, distorting its interpretation.

Our experience is that the Greek P&L decomposition remains a useful approximation, particularly under normal market conditions. However, the paper’s findings reframe the conventional understanding of option convexity and the interpretation of gamma P&L.

Let us know what you think in the comments.

References

[1] Willeboordse, F. H. (2026), Does Gamma Survive the Close? Finance Research Letters, Article 110281.