2024/11/11 by Hengxin Cui, Cui, Hengxin, Ken Seng Tan +3
Economics, Econometrics and Finance · Social Sciences · #Credit Risk and Financial Regulations #FOS: Economics and business #Insurance, Mortality, Demography, Risk Management #Risk Management (q-fin.RM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2411.06640
openalex publication_date 2024/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study large losses arising from defaults of a credit portfolio. We assume that the portfolio dependence structure is modelled by the Archimedean copula family as opposed to the widely used Gaussian copula. The resulting model is new, and it has the capability of capturing extremal dependence among obligors. We first derive sharp asymptotics for the tail probability of portfolio losses and the expected shortfall. Then we demonstrate how to utilize these asymptotic results to produce two variance reduction algorithms that significantly enhance the classical Monte Carlo methods. Moreover, we show that the estimator based on the proposed two-step importance sampling method is logarithmically efficient while the estimator based on the conditional Monte Carlo method has bounded relative error as the number of obligors tends to infinity. Extensive simulation studies are conducted to highlight the efficiency of our proposed algorithms for estimating portfolio credit risk. In particular, the variance reduction achieved by the proposed conditional Monte Carlo method, relative to the crude Monte Carlo method, is in the order of millions.