High breakdown point conditional dispersion estimation with application to S&P 500 daily returns volatility

We show that quasi-maximum likelihood (QML) estimators for conditional dispersion models can be severely affected by a small number of outliers such as market crashes and rallies, and we propose new estimation strategies (the two-stage Hampel estimators and two-stage S-estimators) resistant to the effects of outliers and study the properties of these estimators. We apply our methods to estimate models of the conditional volatility of the daily returns of the SEP 500 Cash Index series. In contrast to QML estimators, our proposed method resists outliers, revealing an informative new picture of volatility dynamics during "typical" daily market activity.