Efficient algorithms for calculating risk measures and risk contributions in copula credit risk models

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.