厚尾分布情形下的信用资产组合风险度量

Risk measurement for portfolio credit risk with risk factors with heavy-tailed distruibution

本文研究风险因子多元厚尾分布情形下的信用资产组合风险度量问题.用多元t-Copula分布来描述标的资产收益率分布的厚尾性,同时将三步重要抽样技术发展到基多元t-Copula分布的资产组合模型中,拓宽和丰富了信用资产组合风险度量模型.同时,并运用了非线性优化技术中的Levenberg-Marquardt算法来解决重要抽样技术中风险因子期望向量估计.模拟结果表明该算法比普通Monte Carlo模拟法的计算效率更有效,且能很大程度上减少所要估计的损失概率的方差,从而更精确地估计出信用投资组合损失分布的尾部概率或给定置信度下组合VaR值.

This paper develops an efficient simulation method to calculate credit portfolio risks when the risk factors have heavy-tailed distributions. In modeling heavy tails, the features of return on the underlying assets are captured by multivariate t-copula. Moreover, a three-step importance sampling （IS） technique is devel- oped in the t-copula credit portfolio risk measure model for further variance reduction. This broadens and enri- ches credit portfolio risk measure models. Simultaneously, the Levenberg-Marquardt algorithm associated with nonlinear optimal technique is applied to estimate the mean-shift vector of the systematic risk factors after the probability measure changes. Numerical results show that IS technique based on t-copula is more efficient and accurate than plain Monte Carlo simulation in calculating the tail probability of distribution of portfolio loss （ or VaR of credit portfolio risk under a given confidence level） and that the IS technique can decrease the vailanee of estimation on the tail probability to a great degree