Parameter estimation of default portfolios using the Merton model and Phase transition

Masato Hisakado and Shintaro Mori

Papers from arXiv.org

Abstract: We discuss the parameter estimation of the probability of default (PD), the correlation between the obligors, and a phase transition. In our previous work, we studied the problem using the beta-binomial distribution. A non-equilibrium phase transition with an order parameter occurs when the temporal correlation decays by power law. In this article, we adopt the Merton model, which uses an asset correlation as the default correlation, and find that a phase transition occurs when the temporal correlation decays by power law. When the power index is less than one, the PD estimator converges slowly. Thus, it is difficult to estimate PD with limited historical data. Conversely, when the power index is greater than one, the convergence speed is inversely proportional to the number of samples. We investigate the empirical default data history of several rating agencies. The estimated power index is in the slow convergence range when we use long history data. This suggests that PD could have a long memory and that it is difficult to estimate parameters due to slow convergence.

Date: 2020-05
New Economics Papers: this item is included in nep-ecm and nep-rmg
References: Add references at CitEc
Citations:

Published in Physica A,vol. 563, 1 February, 2021, 125435

Downloads: (external link)
http://arxiv.org/pdf/2005.07967 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2005.07967

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().