Multi-Period Defaults and Maturity Effects on Economic Capital in a Ratings-Based Default-Mode Model

In the last decade, portfolio credit risk measurement has improved significantly. The currentstate-of-the-art models analyze the value of the portfolio at a certain risk horizon, e.g. one year. Mostpopular has become the Merton-type one-factor model of Vasicek, that builds the fundament of thenew capital adequacy framework (Basel II) finally adopted by the Basel Committee On Banking Supervisionin June 2004. Due to this approach credit risk only arises from defaults, and the model providesan analytical solution for the risk measures Value at Risk and Expected Loss. One of the lessexamined questions in this field of research is, how the time to maturity of loans affects the portfoliocredit risk. In practice there is common agreement that credit risk rises with the maturity of a loan, butonly few solutions considering different maturities are discussed. We present two new approaches,how to cope with the problem of the maturity in the Vasicek-model. We focus...