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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 current state-of-the-art models analyze the value of the portfolio at a certain risk horizon, e.g. one year. Most popular has become the Merton-type one-factor model of Vasicek, that builds the fundament of the new capital adequacy framework (Basel II) finally adopted by the Basel Committee On Banking Supervision in June 2004. Due to this approach credit risk only arises from defaults, and the model provides an analytical solution for the risk measures Value at Risk and Expected Loss. One of the less examined questions in this field of research is, how the time to maturity of loans affects the portfolio credit risk. In practice there is common agreement that credit risk rises with the maturity of a loan, but only 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 on the influence of the maturity in the theoretical framework of Merton and show solutions from empirical data of four rating agencies. Our results are close to the parameters, that are used in the maturity adjustment of Basel II and may help to get a better understanding on economic capital allocation of long-term loans.