Deviation-Based Model Risk Measures

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.