This paper innovates in the risk management of insurance and banking capital by exploring efficient, accurate, and reliable algorithms for evaluating risk measures and contributions in copula credit risk models. We propose a hybrid saddlepoint approximation algorithm, which leverages a synergy of nice analytical tractability from the saddlepoint approximation framework and efficient numerical integration from the Monte Carlo simulation. Notably, the numerical integration over the systematic risk factors is enhanced using three novel numerical techniques, namely, the mean shift technique, randomized quasi-Monte Carlo simulation, and scalar-proxied interpolation technique. We also enhance the exponential twisting and cross entropy algorithms via the use of interpolation and update rules of optimal parameters, respectively. Extensive numerical tests on computing risk measures and risk contributions were performed on various copula models with multiple risk factors. Our hybrid saddlepoint approximation method coupled with various enhanced numerical techniques is seen to exhibit a high level of efficiency, accuracy, and reliability when compared with existing importance sampling algorithms.

本文通过探索高效、准确、可靠的算法来评估Copula信用风险模型中的风险度量和贡献，创新了保险和银行资本的风险管理。我们提出了一种混合鞍点近似算法，该算法利用鞍点近似框架的良好分析易处理性和蒙特卡罗模拟的高效数值积分的协同作用。值得注意的是，使用三种新颖的数值技术增强了系统风险因素的数值积分，即均值平移技术、随机准蒙特卡罗模拟和标量代理插值技术。我们还分别通过使用最佳参数的插值和更新规则来增强指数扭曲和交叉熵算法。对具有多个风险因素的各种联结模型进行了关于计算风险度量和风险贡献的广泛数值测试。与现有的重要性采样算法相比，我们的混合鞍点近似方法与各种增强的数值技术相结合，表现出高水平的效率、准确性和可靠性。