Model Risk Measures: A Review and New Proposals on Risk Forecasting

In financial decisions, model risk has been recognized as an important source of uncertainty. The revision of the Basel II suggests that financial institutions quantify and manage their model risk. Focusing on risk forecasting literature, we identify two main approaches to quantify model risk: the worst-case and loss function. The first approach includes measures with a similar structure to deviation measures, which are applied to a set of forecasts obtained by different models. For the second approach, monetary risk measures are employed under a loss or error function, from some forecasting procedure. Based on the untapped features of model risk for both approaches we suggest new proposals, which include measures to quantify upside and downside model risk, and average costs associated with risk overestimation and underestimation. We also conduct an empirical assessment of model risk measures using Value at Risk (VaR) and Expected Shortfall (ES) forecasting. We verify, using worst-case measures, that model risk tends to increase before crisis period and, according to loss function measures, model risk values increase in the crisis period. We also conclude that a model with good performance to risk forecasting (lower realized loss) does not indicate this model has lower model risk. Furthermore, we highlight insights into future research directions regarding this topic.