Fitting a distribution to value-at-risk and expected shortfall, with an application to covered bonds

ABSTRACT 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 in existence,;investors never suffered losses due to missed payments from covered bonds. From;a risk management perspective, therefore, modeling 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 modeling 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 modeling. 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.