Default Probability Prediction with Static Merton-D-Vine Copula Model

  • Václav Klepáč Mendel University in Brno
Keywords: merton model, default risk, d-vine copula, probability, ARMA-GARCH


We apply standard Merton and enhanced Merton-D-Vine copula model for the measurement of credit risk on the basis of accounting and stock market data for 4 companies from Prague Stock Exchange, in the midterm horizon of 4 years. Basic Merton structural credit model is based on assumption that firm equity is European option on company assets. Consequently enhanced Merton model take in account market data, dependence between daily returns and its volatility and helps to evaluate and project the credit quality of selected companies, i.e. correlation between assets trajectories through copulas. From our and previous results it is obvious that basic Merton model significantly underestimates actual level, i.e. offers low probabilities of default. Enhanced model support us with higher simulated probability rates which mean that capturing of market risk and transferring it to credit risk estimates is probably a good way or basic step in enhancing Merton methodology.


Aas, K., Czado, C., Frigessi, A. et al. 2009. Pair-copula constructions of multiple dependence. Insurance: Mathematics & Economics.

Altman, E. I. 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. The Journal of Finance, 23 (4), 589–609.

Beaver, W. 1966. Financial ratios predictors of failure. Journal of Accounting Research, 4, 71–111.

Campbell, J., Hilscher, J. and Szilagyi, J. 2008. In search of distress risk. Journal of Finance, 63, 2899–2939.

Goddard Consulting. 2011. Option Pricing – Monte-Carlo Methods [online]. Available at:

Hillegeist, S. A., Keating, E. K., Cram, D. P. and Lundstedt, K. G. 2002. Assessing the Probability of Bankruptcy. SSRN Electronic Journal. DOI: 10.2139/ssrn.307479.

Joe, H. 1996. Families of m-variate distributions with given margins and m(m + 1)=2 bivariate dependence parameters. In Rauchendorf, L., Schweizer, B. and Taylor, M. D. (Eds.). Distributions with mixed marginals and related topics.

Klepáč, V. and Hampel, D. 2015. Assessing Efficiency of D-Vine Copula ARMA-GARCH Method in Value at Risk Forecasting: Evidence from PSE Listed Companies. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 63 (4), 1287–1295. ISSN 1211-8516.

Klepáč, V. 2014. Assesing Probability of Default: Merton Model Approach. In PEFnet 2014. Brno: Mendel University in Brno, 76.

Leland, H. E. and Toft, K. B. 1996. Optimal Capital Structure, Endogenous Bankruptcy and the Term Structure of Credit Spreads. Journal of Finance, 51 (3), 987–1019.

Longstaff, F. A. and Schwartz, E. S. 1995. A Simple Approach to Valuing Risky Fixed and Floating Rate Debt. Journal of Finance, 50 (3), 789–819.

Market data by Patria Online. [online]. Available in paid version at:

MathWorks. 2014. MATLAB and Statistics Toolbox Release 2014b.

Merton, R. 1973. On the Pricing of Corporate Debt: The Risk Structure of Interest Rate. Journal of Finance, 29 (2), 449–470.

Míšek, R. 2006. Strukturální modely kreditního rizika. (Ph.D. thesis.)

Ohlson, J. A. 1980. Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research, 18 (1), 109–131.

R Development Core Team. 2015. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.

Schoutens, W. and Cariboni, J. 2009. Lévy processes in credit risk. Chichester, U. K.: John Wiley, 185 pp. ISBN 04-707-4306-9.

Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris, 8, 229–231.

Zmijewski, M. 1984. Methodological issues related to the estimation of financial distress prediction models. Journal of Accounting Research, 59–86.