混合泊松违约强度下信用资产组合风险度量

摘要

This paper uses the Poisson distribution with a linear combination of Gamma distributions to capture the dependence among the default indicators of different assets, and then proposes a multi-factor risk model for portfolios credit risk based on mixed Poisson default intensity.Our model is based on the idea that dependence among common risk factors can be transformed into the dependency among the default indicators of different assets, which broadens and enriches portfolio credit risk measurement models.By introducing important sampling techniques to the model for effective numerical simulation, this paper empirically examines the portfolio credit risk in four industries of China's financial markets.More specifically, the classic structural model and option pricing formula are firstly used to estimate the dynamic default probability of an obligor;the dynamic Poisson strength of each asset under the mixed Poisson model is secondly obtained by using the dynamic default probability of a single asset;then, the factor loading coefficients of common risk factors are estimated, to reflect the degree of dependence among different assets;finally, the important sampling method is applied into the mixed Poisson model, in order to implement the efficient Monte Carlo simulation for the loss distribution of the credit portfolio composed across different industries.The simulation results show that our algorithm is more efficient than the ordinary Monte Carlo simulation and can greatly reduce the variance of the estimated loss probability.%基于共同风险因子的相依关系转换为不同资产的违约示性函数的相依关系来刻画的思想, 利用参数为Gamma分布线性组合的Poisson分布来描述不同资产的违约示性函数的相依关系, 建立基于混合泊松分布的信用资产组合多因子的风险度量模型, 并引入重要抽样技术到模型进行有效数值模拟计算, 拓宽和丰富信用资产组合风险度量模型.进一步地, 结合中国金融市场四个产业的数据把混合泊松分布应用到实证研究中.在模型的构建过程中, 首先运用经典的结构模型和期权定价公式估计单个债务人的动态违约概率;再利用单资产动态违约概率得到混合泊松模型下每个资产的动态泊松强度;接着结合共同风险因子的值求得资产不同的因子载荷系数, 该因子载荷系数反映了不同资产间的相依结构程度;最后, 把重要抽样技术发展到混合泊松模型中, 对由不同产业组成的信用资产组合的损失分布进行有效Monte Carlo模拟.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.