IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v544y2020ics0378437119319430.html
   My bibliography  Save this article

Phase transition in the Bayesian estimation of the default portfolio

Author

Listed:
  • Hisakado, Masato
  • Mori, Shintaro

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.

Suggested Citation

  • Hisakado, Masato & Mori, Shintaro, 2020. "Phase transition in the Bayesian estimation of the default portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    • Handle: RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119319430
    DOI: 10.1016/j.physa.2019.123480
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119319430
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123480?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Defever, Fabrice & Imbruno, Michele & Kneller, Richard, 2020. "Trade liberalization, input intermediaries and firm productivity: Evidence from China," Journal of International Economics, Elsevier, vol. 126(C).
    2. Spyros Galanis, 2021. "Speculative trade and the value of public information," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(1), pages 53-68, February.
    3. Bernd Engelmann & Robert Rauhmeier (ed.), 2011. "The Basel II Risk Parameters," Springer Books, Springer, number 978-3-642-16114-8, December.
    4. W. Braddock Hickman, 1958. "Corporate Bond Quality and Investor Experience," NBER Books, National Bureau of Economic Research, Inc, number hick58-1.
    5. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    6. Paul Levine & Joseph Pearlman & Stephen Wright & Bo Yang, 2019. "Information, VARs and DSGE Models," School of Economics Discussion Papers 1619, School of Economics, University of Surrey.
    7. W. Braddock Hickman, 1958. "Index to "Corporate Bond Quality and Investor Experience"," NBER Chapters, in: Corporate Bond Quality and Investor Experience, pages 531-536, National Bureau of Economic Research, Inc.
    8. Mamageishvili, A. & Schlegel, J. C., 2019. "Optimal Smart Contracts with Costly Verification," Working Papers 19/13, Department of Economics, City University London.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Masato Hisakado & Kodai Hattori & Shintaro Mori, 2022. "Multi-dimensional Self-Exciting NBD Process and Default Portfolios," The Review of Socionetwork Strategies, Springer, vol. 16(2), pages 493-512, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fa, Kwok Sau, 2020. "A class of nonlinear Langevin equation with the drift and diffusion coefficients separable in time and space driven by different noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Liu, Changqing & He, Yigang & Peng, Guanghan, 2019. "The stabilization effect of self-delayed flux integral for two-lane lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Torres-Vargas, G. & Fossion, R. & Méndez-Bermúdez, J.A., 2020. "Normal mode analysis of spectra of random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Kowalski, A.M. & Plastino, A., 2019. "A nonlinear matter-field Hamiltonian analyzed with Renyi and Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    5. Cebreiros, Florencia & Clavijo, Leonardo & Boix, Elzeario & Ferrari, Mario Daniel & Lareo, Claudia, 2020. "Integrated valorization of eucalyptus sawdust within a biorefinery approach by autohydrolysis and organosolv pretreatments," Renewable Energy, Elsevier, vol. 149(C), pages 115-127.
    6. Algaba, Encarnación & Béal, Sylvain & Fragnelli, Vito & Llorca, Natividad & Sánchez-Soriano, Joaquin, 2019. "Relationship between labeled network games and other cooperative games arising from attributes situations," Economics Letters, Elsevier, vol. 185(C).
    7. Nunes, Maria Eugênia Silva & de Mello Silva, Érica & Martins, Paulo H.L. & Florencio, João & Plascak, J.A., 2020. "Dynamics of the one-dimensional isotropic Heisenberg model with Dzyaloshinskii–Moryia interaction in a random transverse field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    8. Wu, Jing Cynthia & Zhang, Ji, 2019. "A shadow rate New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    9. Aldakheel, F. & Ismail, M.S. & Hughes, K.J. & Ingham, D.B. & Ma, L. & Pourkashanian, M. & Cumming, D. & Smith, R., 2020. "Gas permeability, wettability and morphology of gas diffusion layers before and after performing a realistic ex-situ compression test," Renewable Energy, Elsevier, vol. 151(C), pages 1082-1091.
    10. Zhu, Wen-Xing & Zhang, Jing-Yu & Song, Ze-Rui, 2019. "Study on braking process of vehicles at the signalized intersection based on car-following theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1306-1314.
    11. Liu, Hong & Gao, Yuhang & Tisdell, Clement A. & Wang, Fei, 2020. "Are housing property rights important for fertility outcomes in China? Empirical evidence and policy issues," Economic Analysis and Policy, Elsevier, vol. 65(C), pages 211-223.
    12. Nagatani, Takashi, 2019. "Infection promotes species coexistence: Rock–paper–scissors game with epidemic on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    13. Jiang, Mengmeng & Westerholm, Maria & Qiao, Wei & Wandera, Simon M. & Dong, Renjie, 2020. "High rate anaerobic digestion of swine wastewater in an anaerobic membrane bioreactor," Energy, Elsevier, vol. 193(C).
    14. Borjas, George J. & Cassidy, Hugh, 2019. "The wage penalty to undocumented immigration," Labour Economics, Elsevier, vol. 61(C).
    15. Nataj, Sarah & Lui, S.H., 2020. "Superlinear convergence of nonlinear conjugate gradient method and scaled memoryless BFGS method based on assumptions about the initial point," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    16. Ishihara, Masamichi, 2020. "Derivation of density operators for generalized entropies with quantum analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 543(C).
    17. Ou, Hui & Wang, Tao & Tang, Tie-Qiao, 2019. "Analysis of trip cost in a two-lane traffic corridor with one entry and one exit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 65-72.
    18. Birol, Fatih & Okogu, Bright E., 1997. "Purchasing-Power-Parity (PPP) approach to energy-efficiency measurement: Implications for energy and environmental policy," Energy, Elsevier, vol. 22(1), pages 7-16.
    19. Sen, Parongama, 2020. "Scaling and crossover behaviour in a truncated long range quantum walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    20. Gargiulo, Nicola & Peluso, Antonio & Aprea, Paolo & Marino, Ottavio & Cioffi, Raffaele & Jannelli, Elio & Cimino, Stefano & Lisi, Luciana & Caputo, Domenico, 2019. "Chromium-based MIL-101 metal organic framework as a fully regenerable D4 adsorbent for biogas purification," Renewable Energy, Elsevier, vol. 138(C), pages 230-235.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119319430. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.