0DTE Option Pricing

The market for ultra short-term (zero days-to-expiry or 0DTE) options has grown exponentially over the last few years. In 2023, daily volume in 0DTEs reached over 45% of overall daily options volume. After briefly describing this exploding new market, we present a novel pricing formula designed to capture the shape of the 0DTE implied volatility surface both out-of-the-money (through discontinuities in the dynamics of the underlying) and at-the-money (through continuous volatility dynamics driven, in particular, by leverage and the volatility-of-volatility). The latter result hinges on an Edgeworth-like expansion of the conditional characteristic function of the continuous portion of the underlying’s price process. The expansion shifts probability mass from an otherwise locally Gaussian return density by adding time-varying skewness (through leverage) and time-varying kurtosis (through the volatility-of-volatility). The expansion is local in time and, therefore, naturally suited to price ultra short-tenor instruments, like 0DTEs. We document considerable price improvements as compared to state-of-the-art specifications. We also provide suggestive results on nearly instantaneous predictability (through leverage and the volatility-of-volatility) by estimating 0DTE return/variance risk premia