Phase transition in the Bayesian estimation of the default portfolio
Phase transition in the Bayesian estimation of the default portfolio
复制标题
违约投资组合贝叶斯估计中的相变
DOI：
10.1016/j.physa.2019.123480
复制
发表时间：
2020
期刊：
影响因子：
3.3
通讯作者：
M.Hisakado and S.Mori
中科院分区：
文献类型：
--
作者：
Hisakado Masato;Mori Shintaro;M.Hisakado and S.Mori
违约概率估计是金融机构的一个重要环节。估计的难度取决于借款人之间的相关性。在本文中，我们介绍了一个分层贝叶斯估计方法，使用贝塔二项分布，并考虑了多年的情况下，时间相关性。当时间相关性通过功率衰减而衰减时，发生相变。当幂指数小于1时，PD估计器不收敛。由于历史数据有限，难以估计PD。相反，当幂指数大于1时，收敛性与二项分布相同。我们提供了一个条件，估计的PD和讨论的普适类的相变。我们研究了评级机构的经验违约数据历史及其傅立叶变换，以确认相关性衰减的形式。衰减历史的功率谱似乎是1/f，这对应于长记忆。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，参数可以正确估计。
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.