小样本条件下操作风险度量中的参数估计研究

针对操作风险损失数据匮乏的特点,引入贝叶斯推断理论来保证小样本条件下模型参数估计的质量,将专家经验以先验分布的形式引入,从贝叶斯推断的视角构建了融入专家经验的操作风险损失频率模型、损失强度模型和风险度量模型。其中,损失频率建模中假设损失频率服从Poisson-Gamma分布,损失强度建模中应用极值理论对损失分布的“厚尾”特性进行描述,利用广义帕累托分布(GPD)对损失强度分布进行拟合,并打破GPD的位置参数和形状参数常数化的限制,视其为随机变量并假定两者服从不同的Gamma分布。实证结果证明: 与传统的MLE方法相比,在小样本的情况下,基于贝叶斯推断的MCMC方法对参数的估计更有效和稳定,较好地解决了在操作风险度量中由于损失数据不足给损失分布拟合带来的难题。

Research on Parameter Estimation for Operational Risk Measurement based on Small Sampling Data

To ensure the parameter estimation quality based on small sampling data, Bayesian inference theory was applied. Taking experts'' experience and opinion as the prior distributions of parameters, the way to assess the frequency distribution and severity distribution was developed from a Bayesian perspective. Poisson distribution was chosen as the loss frequency distribution, and Gamma Distribution was set as the prior distribution. Extreme Value Theory(EVT)was applied in loss severity modeling, and GPD was used to fit the loss distribution. Both the location parameter and scale were assumed to have the prior Gamma distribution separately. Methodology for estimating parameters of the loss distribution was extended from Maximum Likelihoods Estimation(MLE) to Markov Chain Monte Carlo(MCMC)method. Results reveal that compared with the MLE method, MCMC method, which is based on Bayesian Inference, provides more effective and stable estimation for parameters in circumstances of small sampling dada.