IDEAS home Printed from https://ideas.repec.org/a/oup/jfinec/v22y2024i5p1421-1455..html
   My bibliography  Save this article

Composite Likelihood for Stochastic Migration Model with Unobserved Factor

Author

Listed:
  • Antoine Djogbenou
  • Christian Gouriéroux
  • Joann Jasiak
  • Maygol Bandehali

Abstract

We introduce the conditional maximum composite likelihood (MCL) estimation method for the stochastic factor ordered probit model of credit rating transitions of firms. This model is recommended for internal credit risk assessment procedures in banks and financial institutions under the Basel III regulations. Its exact likelihood function involves a high-dimensional integral, which can be approximated numerically before maximization. However, the estimated migration risk and required capital tend to be sensitive to the quality of this approximation, potentially leading to statistical regulatory arbitrage. The proposed conditional MCL estimator circumvents this problem and maximizes the composite log-likelihood of the factor ordered probit model. We present three conditional MCL estimators of different complexity and examine their consistency and asymptotic normality when n and T tend to infinity. The performance of these estimators at finite T is examined and compared with a granularity-based approach in a simulation study. The use of the MCL estimator is also illustrated in an empirical application.

Suggested Citation

  • Antoine Djogbenou & Christian Gouriéroux & Joann Jasiak & Maygol Bandehali, 2024. "Composite Likelihood for Stochastic Migration Model with Unobserved Factor," Journal of Financial Econometrics, Oxford University Press, vol. 22(5), pages 1421-1455.
    • Handle: RePEc:oup:jfinec:v:22:y:2024:i:5:p:1421-1455.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/jjfinec/nbad031
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or

    for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Drew Creal & Bernd Schwaab & Siem Jan Koopman & Andr� Lucas, 2014. "Observation-Driven Mixed-Measurement Dynamic Factor Models with an Application to Credit Risk," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 898-915, December.
    2. Koopman, Siem Jan & Lucas, Andre & Monteiro, Andre, 2008. "The multi-state latent factor intensity model for credit rating transitions," Journal of Econometrics, Elsevier, vol. 142(1), pages 399-424, January.
    3. Gourieroux, C. & Monfort, A., 2018. "Composite indirect inference with application to corporate risks," Econometrics and Statistics, Elsevier, vol. 7(C), pages 30-45.
    4. repec:hal:spmain:info:hdl:2441/4m4fqk908d9obqasu0uhft7t94 is not listed on IDEAS
    5. Azizpour, S & Giesecke, K. & Schwenkler, G., 2018. "Exploring the sources of default clustering," Journal of Financial Economics, Elsevier, vol. 129(1), pages 154-183.
    6. Bonhomme, Stéphane & Jochmans, Koen & Robin, Jean-Marc, 2017. "Nonparametric estimation of non-exchangeable latent-variable models," Journal of Econometrics, Elsevier, vol. 201(2), pages 237-248.
    7. C. Gourieroux & A. Monfort & V. Polimenis, 2006. "Affine Models for Credit Risk Analysis," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 494-530.
    8. White, Halbert, 1983. "Corrigendum [Maximum Likelihood Estimation of Misspecified Models]," Econometrica, Econometric Society, vol. 51(2), pages 513-513, March.
    9. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    10. repec:hal:spmain:info:hdl:2441/lpag9391598uoauqu4u9opq76 is not listed on IDEAS
    11. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
    12. Gagliardini, P. & Gourieroux, C., 2005. "Migration correlation: Definition and efficient estimation," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 865-894, April.
    13. Feng, D. & Gourieroux, C. & Jasiak, J., 2008. "The ordered qualitative model for credit rating transitions," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 111-130, January.
    14. Bonhomme, Stéphane & Jochmans, Koen & Robin, Jean-Marc, 2017. "Nonparametric estimation of non-exchangeable latent-variable models," Journal of Econometrics, Elsevier, vol. 201(2), pages 237-248.
    15. Gagliardini, Patrick & Gourieroux, Christian, 2014. "Efficiency In Large Dynamic Panel Models With Common Factors," Econometric Theory, Cambridge University Press, vol. 30(5), pages 961-1020, October.
    16. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    17. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2017. "Nonparametric estimation of non-exchangeable latent-variable models," Sciences Po publications info:hdl:2441/4m4fqk908d9, Sciences Po.
    18. Antje Berndt & Rohan Douglas & Darrell Duffie & Mark Ferguson, 2018. "Corporate Credit Risk Premia [Fallen angels and price pressure]," Review of Finance, European Finance Association, vol. 22(2), pages 419-454.
    19. Leland E. Farmer, 2021. "The discretization filter: A simple way to estimate nonlinear state space models," Quantitative Economics, Econometric Society, vol. 12(1), pages 41-76, January.
    Full references (including those not matched with items on IDEAS)

    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. Telg, Sean & Dubinova, Anna & Lucas, Andre, 2023. "Covid-19, credit risk management modeling, and government support," Journal of Banking & Finance, Elsevier, vol. 147(C).
    2. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    3. Anna Dubinova & Andre Lucas & Sean Telg, 2021. "COVID-19, Credit Risk and Macro Fundamentals," Tinbergen Institute Discussion Papers 21-059/III, Tinbergen Institute.
    4. Dimitris Gavalas & Theodore Syriopoulos, 2014. "Bank Credit Risk Management and Rating Migration Analysis on the Business Cycle," IJFS, MDPI, vol. 2(1), pages 1-22, March.
    5. Andersen, Torben G. & Fusari, Nicola & Todorov, Viktor & Varneskov, Rasmus T., 2019. "Unified inference for nonlinear factor models from panels with fixed and large time span," Journal of Econometrics, Elsevier, vol. 212(1), pages 4-25.
    6. Bravo, Francesco & Chu, Ba M. & Jacho-Chávez, David T., 2017. "Generalized empirical likelihood M testing for semiparametric models with time series data," Econometrics and Statistics, Elsevier, vol. 4(C), pages 18-30.
    7. Wang, Fa, 2022. "Maximum likelihood estimation and inference for high dimensional generalized factor models with application to factor-augmented regressions," Journal of Econometrics, Elsevier, vol. 229(1), pages 180-200.
    8. Chernov, Mikhail & Augustin, Patrick & Song, Dongho, 2018. "Sovereign credit risk and exchange rates: Evidence from CDS quanto spreads," CEPR Discussion Papers 12857, C.E.P.R. Discussion Papers.
    9. Anand Deo & Sandeep Juneja, 2021. "Credit Risk: Simple Closed-Form Approximate Maximum Likelihood Estimator," Operations Research, INFORMS, vol. 69(2), pages 361-379, March.
    10. Areski Cousin & Mohamed Reda Kheliouen, 2016. "A comparative study on the estimation of factor migration models," Working Papers halshs-01351926, HAL.
    11. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    12. Alena Audzeyeva & Xu Wang, 2023. "Fundamentals, real-time uncertainty and CDS index spreads," Review of Quantitative Finance and Accounting, Springer, vol. 61(1), pages 1-33, July.
    13. Eser, Fabian & Schwaab, Bernd, 2016. "Evaluating the impact of unconventional monetary policy measures: Empirical evidence from the ECB׳s Securities Markets Programme," Journal of Financial Economics, Elsevier, vol. 119(1), pages 147-167.
    14. Dimitris Gavalas & Theodore Syriopoulos, 2014. "Bank Credit Risk Management and Migration Analysis; Conditioning Transition Matrices on the Stage of the Business Cycle," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 20(2), pages 151-166, May.
    15. Christian A. Vossler, 2013. "Analyzing repeated-game economics experiments: robust standard errors for panel data with serial correlation," Chapters, in: John A. List & Michael K. Price (ed.), Handbook on Experimental Economics and the Environment, chapter 3, pages 89-112, Edward Elgar Publishing.
    16. Nguyen, Ha, 2023. "An empirical application of Particle Markov Chain Monte Carlo to frailty correlated default models," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 103-121.
    17. Bátiz-Zuk Enrique & Mohamed Abdulkadir & Sánchez-Cajal Fátima, 2021. "Exploring the sources of loan default clustering using survival analysis with frailty," Working Papers 2021-14, Banco de México.
    18. Ouyang, Ruolan & Chen, Xiang & Fang, Yi & Zhao, Yang, 2022. "Systemic risk of commodity markets: A dynamic factor copula approach," International Review of Financial Analysis, Elsevier, vol. 82(C).
    19. Siwen Zhou, 2021. "Exploring the driving forces of the Bitcoin currency exchange rate dynamics: an EGARCH approach," Empirical Economics, Springer, vol. 60(2), pages 557-606, February.
    20. Alain Monfort & Jean-Paul Renne, 2013. "Default, Liquidity, and Crises: an Econometric Framework," Journal of Financial Econometrics, Oxford University Press, vol. 11(2), pages 221-262, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

    Statistics

    Access and download statistics

    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:oup:jfinec:v:22:y:2024:i:5:p:1421-1455.. 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: Oxford University Press (email available below). General contact details of provider: https://edirc.repec.org/data/sofieea.html .

    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.