Modeling Default Probabilities of the Chosen Czech Banks in the Time of the Financial Crisis

One of the most important tasks in the risk
management is the correct determination of probability of default
(PD) of particular financial subjects. In this paper a possibility of
determination of financial institution’s PD according to the creditscoring
models is discussed. The paper is divided into the two parts.
The first part is devoted to the estimation of the three different
models (based on the linear discriminant analysis, logit regression
and probit regression) from the sample of almost three hundred US
commercial banks. Afterwards these models are compared and
verified on the control sample with the view to choose the best one.
The second part of the paper is aimed at the application of the chosen
model on the portfolio of three key Czech banks to estimate their
present financial stability. However, it is not less important to be able
to estimate the evolution of PD in the future. For this reason, the
second task in this paper is to estimate the probability distribution of
the future PD for the Czech banks. So, there are sampled randomly
the values of particular indicators and estimated the PDs’ distribution,
while it’s assumed that the indicators are distributed according to the
multidimensional subordinated Lévy model (Variance Gamma model
and Normal Inverse Gaussian model, particularly). Although the
obtained results show that all banks are relatively healthy, there is
still high chance that “a financial crisis” will occur, at least in terms
of probability. This is indicated by estimation of the various quantiles
in the estimated distributions. Finally, it should be noted that the
applicability of the estimated model (with respect to the used data) is
limited to the recessionary phase of the financial market.

• Petr Gurný

• Credit-scoring Models
• Multidimensional Subordinated Lévy Model
• Probability of Default.

[1] W. Beaver, “Financial ratios as predictors of failures. Empirical
Research in Accounting: Selected Studies – 1966”, supplement to
Journal of Accounting Research, 4, 1966, pp. 71-111.
[2] E. I. Altman, “Financial Ratios, Discriminant Analysis and the
Prediction of Corporate Bankruptcy”. Journal of Finance, September,
1968, pp. 589-609.
[3] D. A. McFadden, “Comment on discriminant analysis versus logit
analysis”. Annals of Economic and Social Measurement, 1976, pp. 511–
523.
[4] A. Santomero and J. D. Visno, “Estimating the probability of failure for
commercial banks and the banking system”. Journal of Banking and
Finance 1, 1977, pp. 185–215.
[5] J. A. Ohlson, “Financial ratios and the probabilistic prediction of
bankruptcy”. Journal of Accounting Research 18, 1980, pp. 109–131.
[6] M. E. Zmijeski, “Methodological issues related to the estimation of
financial mistress prediction models”. Journal of Accounting Research
22, 1984, pp. 59–82.
[7] M. Queen, and R. Roll, “Firm mortality: using market indicators to
predict survival”. Financial Analysts Journal 3, 1987, pp. 9–26.
[8] T. Shumway, “Forecasting bankruptcy more accurately: a simple hazard
rate model”. Journal of Business 74, 2001, pp. 101–124.
[9] A. Peretsky and A. Karminsky, “Models for Moody’s bank rating”,
BOFIT Discussion Papers 17, 2008.
[10] R. Cont and P. Tankov, Financial Modelling with Jump Processes.
Chapman & Hall press, 2004.
[11] W. Schoutens, Lévy Processes in Finance: Pricing Financial Derivates.
Wiley, 2003.
[12] W. Green, Econometric Analysis. 6th ed. Prentice Hall, 2008.
[13] B. Engelmann and R. Rauhmeier, The Basel II Risk Parameters.
Springer Verlag, 2006.
[14] A. Resti and A. Sironi, Risk Management and Shareholders' Value in
Banking: From Risk Measurement Models to Capital Allocation
Policies. Wiley, 2007.
[15] A. Kyprianou, W. Schoutens and P. Wilmott, Exotic Options Pricing
and Advanced Lévy Models. Chichester: Wiley, 2005.
[16] D. Applebaum, Lévy Processes and Stochastic Calculus. Cambridge
University Press, 2004.
[17] O.E. Barndorff-Nielsen, T. Mikosch and S.I. Resnick, Lévy processes.
Theory and Applications. Boston: Birkhäuser. 2001.
[18] R.B. Nelsen, An Introduction to Copulas. 2nd ed. Springer, 2006.
[19] J. Rank, Copulas. From theory to application in finance. Risk books,
2007.
[20] G.¨Cherubini, E. Luciano and W. Vecchiato, Copula Methods in
Finance. Wiley, 2004.
[21] J. A. Hanley and B. J. McNeil, “The Meaning and Use of the Area under
a Receiver Operating Characteristics (ROC) Curve”. Radiology, 1982,
pp. 561-557.
[22] P. Gurný and T. Tichý, “Estimation of PD implied by scoring model for
Czech banks”. Proceedings of the 12th International Conference on
Finance and Banking. Silesian University in Opava, 2010, pp. 79-88.