LFIN DP 2025 / 03

Efficient Monte Carlo estimation of credit concentration risk / Matteo Barbagli, Frédéric Vrins. 

> In this paper we address the explicit exclusion of credit concentration risk from the Pillar 1 minimum capital requirements formulas of the Basel framework. Leveraging on a well established Gaussian multi-factor model, we introduce a novel control variate estimator of value-at-risk (VaR), suitable for measuring sector concentration risk under the Pillar 2 guidelines. This estimator integrates the precision of Monte Carlo simulations with the speed and simplicity of the Large Pool approximation, aiming for a more efficient quantile estimation tool. We conduct numerical experiments in a two systematic factor setup to test the validity of our methodology, achieving consistent variance reduction compared to the benchmark Monte Carlo estimator. Our results are robust across various pool parameters and increasing number of Monte Carlo simulations.