Application of Fourier Inversion Methods to Credit Portfolio Models with Integrated Interest Rate and Credit Spread Risk

Most credit portfolio models currently used by the banking industry rely on Monte Carlo simulations for calculating the probability distribution of the future credit portfolio value, which can be quite computer time consuming. Adding market risk factors, such as stochastic interest rates or credit spreads, as additional ingredients of a credit portfolio model, the computational burden of full Monte Carlo simulations even increases and the need for efficient methods for calculating credit risk measures becomes even more obvious. In this study, based on a version of the well-known credit portfolio model CreditMetrics extended by correlated interest rate and credit spread risk, it is analyzed whether the use of characteristic functions and inverse Fourier transformation can be an efficient tool for calculating risk measures in the context of integrated credit portfolio models. Unfortunately, the characteristic function of the credit portfolio value at the risk horizon can not be calculated in closed-form, but has to be computed by Monte Carlo simulations. However, this method can be much faster than a full Monte Carlo simulation of the future credit portfolio distribution. The accuracy of the method depends on the composition of the portfolio.