Fitting a Distribution to Value-at-Risk and Expected Shortfall, with an Application to Covered Bonds

Covered bonds are a specific example of senior secured debt. If the issuer of the bonds defaults the proceeds of the assets in the cover pool are used for their debt service. If in this situation the cover pool proceeds do not suffice for the debt service, the creditors of the bonds have recourse to the issuer's assets and their claims are pari passu with the claims of the creditors of senior unsecured debt. Historically, covered bonds have been very safe investments. During their more than two hundred years of existence, investors never suffered losses due to missed payments from covered bonds. From a risk management perspective, therefore modelling covered bonds losses is mainly of interest for estimating the impact that the asset encumbrance by the cover pool has on the loss characteristics of the issuer's senior unsecured debt. We explore one-period structural modelling approaches for covered bonds and senior unsecured debt losses with one and two asset value variables respectively. Obviously, two-assets models with separate values of the cover pool and the issuer's remaining portfolio allow for more realistic modelling. However, we demonstrate that exact calibration of such models may be impossible. We also investigate a one-asset model in which the riskiness of the cover pool is reflected by a risk-based adjustment of the encumbrance ratio of the issuer's assets