英文标题：
《Phase transition in the Bayesian estimation of the default portfolio》
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作者：
Masato Hisakado and Shintaro Mori
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最新提交年份：
2019
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英文摘要：
  The probability of default (PD) estimation is an important process for financial institutions. The difficulty of the estimation depends on the correlations between borrowers. In this paper, we introduce a hierarchical Bayesian estimation method using the beta binomial distribution and consider a multi-year case with a temporal correlation. A phase transition occurs when the temporal correlation decays by power decay. When the power index is less than one, the PD estimator does not converge. It is difficult to estimate the PD with limited historical data. Conversely, when the power index is greater than one, the convergence is the same as that of the binomial distribution. We provide a condition for the estimation of the PD and discuss the universality class of the phase transition. We investigate the empirical default data history of rating agencies and their Fourier transformations to confirm the form of the correlation decay. The power spectrum of the decay history seems to be 1/f, which corresponds to a long memory. But the estimated power index is much greater than one. If we collect adequate historical data,the parameters can be estimated correctly.
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中文摘要：
违约概率（PD）估计是金融机构的一个重要过程。估计的难度取决于借款人之间的相关性。在本文中，我们介绍了一种使用贝塔二项分布的分层贝叶斯估计方法，并考虑了一个具有时间相关性的多年案例。当时间相关性因功率衰减而衰减时，会发生相变。当幂指数小于1时，PD估计不收敛。由于历史数据有限，很难估计PD。相反，当幂指数大于1时，收敛性与二项分布的收敛性相同。我们提供了一个估计PD的条件，并讨论了相变的普适性类。我们研究了评级机构的经验违约数据历史及其傅里叶变换，以确认相关性衰减的形式。衰变历史的功率谱似乎为1/f，对应于长记忆。但估计的功率指数远大于1。如果我们收集足够的历史数据，就可以正确估计参数。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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