Financial density forecasts: A comprehensive comparison of risk‐neutral and historical schemes |
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Authors: | Ricardo Crisóstomo Lorena Couso |
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Institution: | 1. Comisión Nacional del Mercado de Valores (CNMV), Madrid, Spain;2. National Distance Education University (UNED), Madrid, Spain;3. CaixaBank Asset Management, Madrid, Spain |
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Abstract: | 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 nonholistic 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, 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 GARCH‐based GJR‐FHS delivers the most consistent forecasts across the entire density range. In contrast, lognormal densities, the Heston model, or the nonparametric Breeden–Litzenberger formula yield biased predictions and are rejected in statistical tests. |
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Keywords: | ARCH models ensemble predictions forecast verification probabilistic forecasting risk‐neutral densities |
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