金融密度预测：风险中性和历史方案的综合比较
Financial density forecasts: A comprehensive comparison of risk-neutral and historical schemes
摘要：
我们研究了金融经济学中最常用的基准的预测能力。我们接近概率预测研究的常见警告-小样本，有限的模型和非整体验证-通过在超过21年的时间内对15个预测方案进行全面比较。所有密度的统计一致性，局部精度和预测误差进行评估。使用一个新的综合指标，综合预测分数（IFS），我们表明，风险中性密度优于基于历史的预测的信息内容。我们发现，方差伽马模型产生最高的样本外观察价格的可能性和最低的预测误差，而基于ARCH的GJR-FHS在整个密度范围内提供最一致的预测。相比之下，对数正态密度，赫斯顿模型或Breeden-Litzenberger公式产生偏差的预测，并拒绝在统计检验。
英文摘要：
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.
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