Model risk and regulatory capital

In this paper we propose a general framework for the quantification of model risk.This framework allows one to allocate regulatory capital to positions in a given market depending on the extent to which this market can be reliably modelled. The approach is based on computing worst-case risk measures over sets of models that are in some appropriate sense close to a nominal model. In general, any set of models could be used, but we illustrate how, in particular, past data can be used to constructsuch model sets in a statistically meaningful way. This empirically based approach allows us to decompose the model risk into estimation risk, misspecification risk, and identification risk. The method is general in the sense that it can be applied with any of the usual risk measures such as value-at-risk and expected shortfall.We present an application to stock portfolios and find that, for usually applied specifications, misspecification risk is much more important than estimation risk.The combination of estimation risk and misspecification risk that we find explains half of the multiplication factors employed by the Bank of International Settlements (BIS). The remaining other half can be attributed to additional misspecification and identification risk, and, possibly, other risk factors.