High-dimensional simulations of portfolio credit risk

Credit risk is one of the most important types of risk that any financial institution must face with. In the financial world, the essence of control relies on how well the model mimes reality and on the precision of the computational methods used. In this thesis, we consider the most common credit risk models: “CreditRisk+” of Credit Suisse Financial Product, and the Gaussian and t-copula models. All of them belong to the Bernoulli mixture models, used in literature for tractability reasons, and for their generical modeling approach. We, therefore, focus on Bernoulli mixture models, without loss of generality. We consider the case of homogeneous portfolios, i.e. exchangeable Bernoulli mixture model. We aim to quantify the credit risk related to the obligors’ default. To satisfy this target, we calculate the proper risk metrics as tail loss probability and conditional loss for the Bernoulli mixture models. The problem relies on how to conduct and set the simulation to calculate these risk indicators: the naïve Monte Carlo simulation in rare event settings is problematic as the number of repetitions should increase enormously to get reliable estimates of metrics. This work proposes to overcome the common pitfall of the naïve approach, following the new efficient simulation proposed by Bașoğlu, Hörmann, and Sak. This innovative algorithm combines the importance sampling based on cross-entropy, and inner replication using the geometric shortcut, and we apply it to all three models described. An overview analysis is based on the computation of Value-at-Risk (VaR) showing the improvements in the benchmark methods for the credit risk models.