This paper explores the implications of producing forecast distributions that are optimized according to scoring rules that are relevant to financial risk management. We assess the predictive performance of optimal forecasts from potentially misspecified models for i) value-at-risk and expected shortfall predictions; and ii) prediction of the VIX volatility index for use in hedging strategies involving VIX futures. Our empirical results show that calibrating the predictive distribution using a score that rewards the accurate prediction of extreme returns improves the VaR and ES predictions. Tail-focused predictive distributions are also shown to yield better outcomes in hedging strategies using VIX futures.

翻译：本文探讨了根据与金融风险管理相关的评分规则优化预测分布的含义。我们评估了来自可能错误设定的模型的最优预测的预测性能，具体包括：i) 风险价值与预期亏损预测；ii) 用于涉及VIX期货的套期保值策略的VIX波动率指数预测。实证结果表明，使用奖励准确预测极端收益的评分来校准预测分布，可改善VaR和ES预测。同时，以尾部为重点的预测分布在使用VIX期货的套期保值策略中也能产生更好的结果。