Risk management in credit risk portfolios with correlated assets

We consider a structural model of credit risk in the spirit of Merton [Journal of Finance 29 (1974) 449], where a firm defaults when its market value falls below the value of its debts or a certain given threshold level. Models of this type have extensively been used for valuing default-risky securities. Our research now focuses on the effect which positive dependence between credit risks in a portfolio has on the risk of the lending institute. In order to allow for unexpectedly defaults, we suppose that the firm’s asset value follows a geometric Lévy process. The following two main results are obtained: a positive dependence in terms of association between the credit risks always leads to a higher risk for the lending institute than independent credit risks, where the risk of the institute can be measured by any of the following risk measures: variance, upper partial moments or risk sensitive measure. In a second part we investigate the influence of the portfolio structure. We suppose that a firm’s asset value is influenced by an idiosyncratic risk, a sector specific risk and a systematic risk. Sectors can be defined, e.g., by the type of industry or geographic region. We show that whenever a sector structure majorizes another, the risk for the lending institute increases. This proves in particular a positive effect of diversification.