Kolloquium: Estimating "Realized" Skewness using Convolutional Neural Networks

ABSTRACT: We propose a new estimator of low-frequency skewness that exploits high-frequency data through a direct functional mapping consisting of layers of convolutional neural networks followed by layers of MLPs. We show that the relevant high-frequency features converge to a continuous limit and that the latent skewness admits a continuous functional representation. This allows us to establish the unbiasedness of our NN estimator using classical universal approximation results and Rademacher complexity arguments. Monte Carlo experiments under stochastic volatility models, with and without jumps, show that the estimator reduces finite-sample bias relative to existing realized-skewness estimators and remains accurate under model misspecification. Empirically, our estimator exhibits temporal stability and delivers superior cross-sectional pricing performance in skewness-sorted portfolios. Another application finds no evidence that ESG-oriented firms exhibit lower crash risk. Overall, the results demonstrate how learning-based functionals can improve the estimation of nonlinear distributional characteristics from high-frequency data.