by Yasushi Takano and Jiro Hashiba of Mizuho-DL Financial Technology
Abstract: This paper proposes a novel numerical methodology for quantifying credit portfolio risk, based on the multi-factor Merton model. This methodology consists of two steps. The first step is a numerical algorithm for computing moment generating function very quickly. The second one is a fast Laplace inversion algorithm first introduced by de Hoog et al. The moment generating function computed in the first step is transformed into a loss distribution function through the second step. It is demonstrated that the risk measures such as VaR and CVaR obtained by this methodology are sufficiently accurate, for a wide range of portfolios. Furthermore, computation time depends on portfolio size quite moderately in this methodology. In fact, by using an ordinary personal computer, we can compute the credit risk of a portfolio with 1 million obligors only in a few minutes. We also present a fast algorithm for computing the risk contributions of obligors to VaR and CVaR.