Finite Sample Optimality of Score-Driven Volatility Models

We study optimality properties in finite samples for time-varying volatility models driven by the score of the predictive likelihood function. Available optimality results for this class of models suffer from two drawbacks. First, they are only asymptotically valid when evaluated at the pseudo-true parameter. Second, they only provide an optimality result `on average' and do not provide conditions under which such optimality prevails. We show in a finite sample setting that score-driven volatility models have optimality properties when they matter most. Score-driven models perform best when the data is fat-tailed and robustness is important. Moreover, they perform better when filtered volatilities differ most across alternative models, such as in periods of financial distress. These results are confirmed by an empirical application based on U.S. stock returns.