基于贝叶斯分析的中国商业银行内部欺诈分析

内部欺诈事件类型是中国商业银行最严重的操作风险类型。但由于操作风险本质特征和中国商业银行内部欺诈损失数据收集年度较短,数据匮乏,小样本数据容易导致参数结果不稳定。为了在小样本数据下进行更准确的度量,本文采用贝叶斯马尔科夫蒙特卡洛模拟方法,在损失分布法框架下,假设损失频率服从泊松-伽马分布,而损失强度服从广义帕累托-混合伽马分布,分析后验分布的形式,获得中国商业银行不同业务线的内部欺诈损失频率和损失强度的后验分布估计,并进行蒙特卡罗模拟获得不同业务线内部欺诈的风险联合分布。结果表明,拟合结果很好,与传统极值分析法相比,基于利用贝叶斯的分析获得的后验分布可以作为未来的先验分布,有利于在较小样本下获得较真实的参数估计,本方法有助于银行降低监管资本要求。

The Research on the Internal Fraud of Chinese Commercial BanksBased on the Bayesian Analysis

Internal fraud is the most important loss type of Chinese commercial banks and has caused a lot of losses.Since the nature characteristics of operational risk and the time of data collecting is short,loss data is deficiency,traditional methods are hard to derive stable parameters estimation with small sample.In order to calculate more accurate with little data,this paper uses the Bayesian Markov Chain Monte Carlo simulation to calculate the parameters.Under the framework of Loss Distribution Approach,we set the loss frequency Poisson distribution,the prior is Gamma distribution,while the loss severity is Generalized Pareto distribution,the prior distribution is mixture Gamma distribution,then we got the posterior distributions of loss frequency and loss severity of internal fraud of different business lines,with Monte Carlo simulation we get the integrated distributions of different business lines.The results are good and compared with tradition Extreme Value Theory method,Bayesian analysis is helpful to derive accurate and stable parameters and therefore the total loss with small sample,and using this method the bank can prepare lower operational capital.