A0731
Title: New robust conditional quantile-based volatility, skewness and kurtosis
Authors: Laura Garcia-Jorcano - Universidad de Castilla-La Mancha (Spain)
Angel Leon - University of Alicante (Spain)
Trino Niguez - University of Westminster (United Kingdom) [presenting]
Abstract: The aim is to introduce a novel and computationally efficient method to estimate time-varying skewness and kurtosis of daily stock returns using quantile-based techniques. The proposed two-step approach first estimates return quantiles using the CAViaR model, then fits a cubic polynomial to derive conditional skewness and kurtosis via non-linear transformations of the estimated coefficients. Classical quantile-based measures of unconditional skewness and kurtosis are revisited, and their limitations are highlighted relative to moment-based definitions. Recent contributions propose alternative quantile-based measures aligned with moment theory. Building on this, closed-form expressions are derived for these measures under a cubic distribution and propose new robust quantile moment-based (RQM) measures. These are shown to offer improved empirical performance. The resulting time-varying skewness and kurtosis series are benchmarked against those obtained via maximum likelihood methods. The method provides a practical, interpretable, and robust alternative for modeling higher-order moments directly relevant to risk management and asset allocation.
