Credit portfolio losses with climate change factors

In this work, we consider the problem of computing risk measures of a credit portfolio via the evaluation of the characteristic function of the loss variable. We propose a new methodology to obtain the characteristic function of the loss distribution when the dependence structure is driven by either the Gaussian or t-copula model. This new approach relies on a quadrature method based on Shannon wavelets and the cardinal sine function. It works out extremely well for the one-factor and the multi-factor model when, in the second case, a moderate number of risk factors are considered. Then, we compare with some of the state-of-the-art methods to perform the same task, and we get much better results in terms of execution time and accuray. As quadrature methods are affected by the curse of dimensionality, we further introduce a simulation approach to evaluate the characteristic function in the case of multi-factor models with many risk factors. The simulation is based on lowdiscrepancy Monte Carlo sequences. A broad set of numerical examples illustrate the efficiency of our methodology. We conclude our work with a real portfolio where the exposures are taken from the European Investment Bank, and we incorporate climate change-related factors into the analysis. This study highlights the practical relevance of our methodology for assessing credit risk in portfolios exposed to emerging environmental challenges.