银行操作风险度量的非参数估计方法——基于最大熵原理

Nonparametric Estimation of Bank Operational Risk——Based on Maximum Entropy Principle

根据新巴塞尔资本协议的要求,银行应该为操作风险分配相应的资本金来御其风险。损失分布法是最常用的操作风险度量模型,但损失分布的参数估计方法受主观影响较大,容易造成结果的偏差和不确定性。基于此提出了基于最大熵原理的非参数估计方法来估计损失分布中损失程度分布。该方法直接通过求解数学规划问题得到概率分布,所得分布拟合程度更高并且结果客观;基于该方法计算了我国商业银行业的操作风险的大小和资本金数量,最后采用国际商业银行的操作风险损失数据对模型进了压力测试。实证结果显示基于最大熵的方法较好地拟合了操作风险损失分布,同时具有良好的鲁棒性和敏感性。

The New Basel Capital Accord requires banks to allocate risk capital to withstand operational risk.Loss Distribution Approach（LDA）,which is a frequency/severity approach,is widely used to quantify operational risk.While parameters estimation of distribution may caused uncertainty or biased results,which are influenced by the subjective hypothesis of probability distribution.In order to acquire high degree of distribution fit and objective results,a new nonparametric estimation method was proposed for loss severity distribution based maximum entropy（maxent）principle through solving mathematical programming problems.This paper empirically analyzes operational risk capital with operational risk data of Chinese commercial banks,in which Poisson and maxent distribution are respectively used to fit frequency and severity data.Finally,the validation of the model is tested by stress test approach.The empirical results reveal the model not only is consistent with data characteristics but also fits operational risk loss data,meanwhile it is robust and sensitive to loss data.