Importance This research outlines an economic and mathematical model of the overdue loan debt. The model is based on copula functions allowing to simulate a non-Gaussian distribution of financial risks and credit risk, in particular. Objectives The research models a joint distribution of overdue debt series in order to forecast the credit risk exposure. Relying upon the forecast, we intend to evaluate the efficiency of methods used to make provisions for possible losses and subsequently determine a reasonable approach to accruing the provision. Methods We examine whether hierarchical copula models can be applied to build the joint distribution of overdue loan debt series in relation to banking institutions. It is considered as the basis for making further estimates of the overdue loan debt. Results We build and evaluate a multivariate copula model of overdue loan debt with the hierarchical structure. Based on the modeled multivariate correlation, we forecast indicators of the overdue loan debt, which could be used as estimated provisions for credit losses. The estimated provisions turn to be sufficient for covering the real amount of overdue debt, being, in most cases, much less than that indicated in Regulation of the Central Bank of the Russian Federation № 254-П, On Rates of Provisions for Loan Losses. Conclusions and Relevance The multivariate copula model of the overdue loan debt can underlie effective risk management systems in credit institutions.
Bologov Ya.V. Otsenka riska kreditnogo portfelya s ispol'zovaniem kopula-funktsii [Assessing the risk exposure of the credit portfolio using the copula function]. Moscow, Sinergiya Press Publ., 2013, 22 p.
Fantazzini D. [Credit risk management]. Prikladnaya ekonometrika = Applied Econometrics, 2008, vol. 12, iss. 4, pp. 84–137. (In Russ.)
Fantazzini D. [An econometric analysis of financial data in risk management]. Prikladnaya ekonometrika = Applied Econometrics, 2008, vol. 10, iss. 2, pp. 105–138. (In Russ.)
Fantazzini D. [Modeling of multidimensional probability distributions with copula functions]. Prikladnaya ekonometrika = Applied Econometrics, 2011, vol. 2, iss. 2, pp. 98–134. (In Russ.)
Nelsen R.B. An Introduction to Copulas. New York, Springer, 2006, 269 p.
Aas K., Czado C., Frigessi A., Bakken H. Pair-Copula Constructions of Multiple Dependence. Insurance: Mathematics and Economics, 2009, vol. 44, iss. 2, pp. 182–198. URL: Link
Czado C., Brechmann E.C., Gruber L. Selection of Vine Copulas. In: Copulae in Mathematical and Quantitative Finance. Springer-Verlag Berlin Heidelberg, 2013.
Travkin A.I. [Designing paired-copula constructs on the basis of empirical tails of copula: Evidence from the Russian market of shares]. XV Aprel'skaya mezhdunarodnaya nauchnaya konferentsiya po problemam razvitiya ekonomiki i obshchestva: materialy konferentsii [Proc. Sci. Conf. The 15th April International Scientific Conference on Development Issues of the Economy and Society]. Moscow, NRU HSE Publ., 2015, vol. 1, pp. 387–400.
Hering C., Hofert M., Mai J.-F., Scherer M. Constructing Nested Archimedean Copulas with Lévy Subordinators. Journal of Multivariate Analysis, 2010, vol. 101, iss. 6, pp. 1428–1433. URL: Link
Hofert M., Scherer M. CDO Pricing with Nested Archimedean Copulas. Quantitative Finance, 2011, vol. 11, iss. 5, pp. 775–787.URL: Link
Hofert M., Mächler M., McNeil A.J. Archimedean Copulas in High Dimensions: Estimators and Numerical Challenges Motivated by Financial Applications. Journal de la Société Française de Statistique, 2013, vol. 154, iss. 1, pp. 25–63.
Hansen B.E. Autoregressive Conditional Density Estimation. International Economic Review, 1994, vol. 35, iss. 3, pp. 705–730.
Bolstad W.M. Introduction to Bayesian Statistics: Second Edition. John Wiley & Sons, 2007, 464 p.