  We investigate the forecasting ability of the most commonly used benchmarks
in financial economics. We approach the usual caveats of probabilistic
forecasts studies -small samples, limited models and non-holistic validations-
by performing a comprehensive comparison of 15 predictive schemes during a time
period of over 21 years. All densities are evaluated in terms of their
statistical consistency, local accuracy and forecasting errors. Using a new
composite indicator, the Integrated Forecast Score (IFS), we show that
risk-neutral densities outperform historical-based predictions in terms of
information content. We find that the Variance Gamma model generates the
highest out-of-sample likelihood of observed prices and the lowest predictive
errors, whereas the ARCH-based GJR-FHS delivers the most consistent forecasts
across the entire density range. In contrast, lognormal densities, the Heston
model or the Breeden-Litzenberger formula yield biased predictions and are
rejected in statistical tests.
