Journal of Credit Risk

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

Dirk Tasche

  • Modelling expected loss for covered bonds is challenging due to the absence of loss data. 
  • An approach based on separately modelling the asset values cover pool and issuer is explored.
  • The model is calibrated against probability of default and expected loss of cover pool and issuer.
  • The calibration is intricate due to the constraints imposed by the investors' dual recourse.


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.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here