Phase transition in the Bayesian estimation of the default portfolio

Masato Hisakado and Shintaro Mori

Physica A: Statistical Mechanics and its Applications, 2020, vol. 544, issue C

Abstract: 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.

Keywords: Phase transition; Default correlation; Bayesian estimation; Empirical data analysis; Ising model; Long and intermediate memory process (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119319430

DOI: 10.1016/j.physa.2019.123480

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