Where Does the Hedging Error Go? A Greek-by-Greek Decomposition for At-the-Money 0DTE Options under Heston

Zero-days-to-expiration (0DTE) options are intrinsically hard to hedge, and the sources of hedging error are poorly understood. In this paper, the error is broken into seven Greek terms (by building on Bergomi's expansion), under Heston, on 1015 SPY sessions. Gamma drives around 66% of the error's variance and Vega drives around 38%. The hedge loses 2.41 bp per session, with a Newey–West t statistic of −8.87. Under Heston, faster hedging can alleviate the effects of Gamma but cannot eliminate Vega. With the error fit to a + b√Δt, the floor is a, while the additional (hedgeable) portion is b√Δt. The floor is 86% of SPY's one-minute error and 85% of SPX's. Hedging every 10 s on tick data still leaves 93–98% of the one-minute error. SPX, QQQ, and NDX give the same ranking, and Gamma leads under every realistic parameter setting. The issue with 0DTE options and using them properly does not come down to technology and speed, but rather to risks, such as volatility, that faster delta hedging does not remove.