Revisiting local expansions for zero days-to-expiry option pricing

The rapid growth in trading volumes of zero days-to-expiry (0DTE) options has underscored the need for accurate and flexible pricing models tailored to ultra-short-term maturities. This paper revisits a semi-analytical framework for pricing 0DTE European options by combining local-in-time expansions of the log-return characteristic function with jump-diffusion models. More precisely, we compare Edgeworth and Gram–Charlier Type A expansions, both incorporating higher-order moment corrections to better capture skewness and kurtosis in return distributions. The model also allows for general jump specifications, and we show that incorporating tempered stable jump distributions substantially improves pricing accuracy relative to Gaussian jumps, even in the presence of a rich continuous component. This highlights the relevance of flexible jump modeling in capturing the short-term dynamics of 0DTE options. Further gains are achieved by applying minimal filtering procedures to the data tails, which reduce pricing errors while preserving the shape of the implied volatility curve, especially around the at-the-money region. The proposed methodology is validated on intra-daily SPX 0DTE options and extended to DAX and Euro Stoxx 50 contracts, demonstrating robustness across markets. Our findings emphasize the importance of local expansions and flexible jump modeling in capturing the dynamics of very short-horizon option markets.