Simulation-analytical approach for calculating VaR contributions in credit portfolios
提出两种模拟-解析方法，用于计算高斯Copula信用组合中单个债务人的风险价值贡献，解决了零概率事件条件期望的计算难题，数值实验表明该方法在精度和效率上优于传统蒙特卡洛模拟。
Risk capital allocation involves the decomposition of the overall portfolio risk in a credit portfolio into marginal risk contributions associated with individual obligors. The Value-at-Risk contribution (VaRC) measures how much each obligor contributes to the overall portfolio VaR. We propose two forms of simulation-analytical approach to calculate VaRC in Gaussian copula credit portfolios with correlation between probability of default (PD) and loss given default (LGD). Our method resolves the challenge of computing the expectation of the default loss of an individual obligor conditional on an event with zero probability mass. By employing ingenious analytical and simulation procedures, we recast the VaRC calculation to involve simulating the distribution function of the random portfolio loss, thereby avoiding numerical instabilities in the common kernel estimation method of computing expectations conditional on a zero-probability event. The inclusion of an analytical component in our algorithms helps reduce simulation effort when compared with the full simulation algorithms. Numerical experiments demonstrate that our proposed algorithms perform favorably well in terms of accuracy and computational efficiency, outperforming typical direct Monte Carlo simulation methods such as the iterative cross entropy method.