In practice, risk forecasts are obtained by risk measures based on a given probability measure on a measurable space. In our study, we consider the probability measures as alternative scenarios, which refer to, for instance, different distribution assumptions, models, or economic situations. Using an improper probability measure can affect risk forecasting and lead to wrong financial decisions. In this context, we propose a Deviation-based approach for quantifying model risk associated with choosing an inappropriate probability measure for risk forecasting. This measuring approach provides us with information about how far our risk measurement process could be affected by model risk. We provide examples of Deviation-based model risk measures defined in the literature. Moreover, we are proposing new alternatives to quantify model risk, for example, Gini and Extended Gini-type model risk measures. We provide a practical example using Value-at-risk (VaR) and Expected Shortfall forecasting to illustrate our approach. Our results indicate that using an inadequate probability measure (distribution assumptions) can largely affect risk forecasting. We verify that model risk estimates present skewness and heavy tail, have significant auto-correlation and do increase in periods that coincide with the highest variability of returns.

实际上，基于可测量空间上的给定概率度量，通过风险度量获得风险预测。在我们的研究中，我们将概率测度视为替代方案，例如，它涉及不同的分布假设，模型或经济状况。使用不正确的概率度量会影响风险预测并导致错误的财务决策。在这种情况下，我们提出了一种基于偏差的方法，用于量化与选择不适当的概率度量进行风险预测相关的模型风险。这种衡量方法为我们提供了有关模型风险可能影响我们的风险衡量过程的信息。我们提供了文献中定义的基于偏差的模型风险度量的示例。此外，我们正在提出新的替代方法来量化模型风险，例如，基尼系数和扩展基尼系数类型的风险度量模型。我们提供了一个使用风险价值（VaR）和预期短缺预测的实际示例来说明我们的方法。我们的结果表明，使用不充分的概率测度（分布假设）会在很大程度上影响风险预测。我们验证模型风险估计值存在偏斜和尾巴很重，具有显着的自相关性，并且在与收益率最高变异性一致的期间内确实有所增加。