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Journal number 3 ∘ Beka Gurgenidze
Estimating probability of default using aggregate data. The case of Georgia

Expanded Summary

Doi: 10.36172/EKONOMISTI.2022.XVIII.03.Beka.Gurgenidze

The concept of expected credit loss is one of the key components of International Financial Reporting Standards (IFRS 9). The computation of expected credit loss depends on modern credit risk analysis, in which estimation of default probabilities are essential. In order to analyze default probabilities there are three alternative sources of information: 1. estimation from historical data; 2. calibration from the value of market instruments; 3. determination by using expert judgement [Bolder, 2018: 497]. The models which use the first type of information are widespread and include Logit and Probit models, Cox proportional-hazards models, Neural Networks, etc. It has to be mentioned that in developing countries, including in Georgia, information related to individual borrowers in Credit bureaus is limited and incomplete. Therefore, the standard estimation of default probabilities using the incomplete data has some disadvantages. In addition to that, in developing countries the transition data among different credit classes is not available. However, the best information obtainable is an aggregate ratio observed over time, which shows the share of total observations in a particular ratings category at a point in time. In the situation described above, it is not possible to obtain standard maximum-likelihood estimates using the cohort approach.

Considering this, different authors proposed an old approach that uses aggregate proportions data to estimate credit transition matrices and default probabilities. In 2005, Jones suggested to estimate credit transition matrices based on aggregate loan category data. Using a generalized least squares, the author demonstrated estimation of Markov transition matrices for the United States using nonperforming loan data [Jones, 2005]. Simister employed maximum likelihood approach to estimate Markov transition matrices for Jamaica using aggregate loan category data [Simister, 2006]. In 2011, Kunovac employed Bayesian approach to estimate credit transition matrices using aggregate data for Croatian corporate loans [Kunovac, 2011].  According to Kunovac, the Bayesian estimator used in his paper has some important comparative advantages over the estimators previously used in the literature. It is notable, that the estimations of credit transition matrices that were mentioned above are based on the assumption of time-homogeneity of transition probabilities. Therefore, effects of different macroeconomic variables are not included in the estimated transition probabilities. Considering this, Vaněk proposed a straightforward and intuitive method to incorporate macroeconomic variables into the transition probabilities [Vaněk, 2016]. The mechanism proposed by Vaněk is useful especially in the context of lifetime expected credit losses calculation within the IFRS 9 requirements.

It has to be mentioned that, estimation of transition probabilities using aggregate proportions data has some limitations as well. For instance, consideration of different borrowers in one category or class and therefore, giving them the same probability of moving to default category or class is not very realistic. It can be the case that different borrowers in the same credit category may have different likelihood of moving to another category. Considering this limitation, this paper discusses an additional adjustment of default probabilities using the payment to income ratio (PTI) of individual borrowers. Namely, transition probabilities can additionally be adjusted by PTI in order to incorporate individual information of different borrowers. Using a generalized least squares, this paper provides estimates of default probabilities for Georgian retail loans. In addition to that, the paper discusses a simple and intuitive approach to link makroeconomic variables to default probabilities. The estimates of default probabilities based on the methodology discussed in this paper can be applied to stress testing purposes of the banking system. Besides, banks that have limited resources to estimate the default probabilities, can use the probabilities assessed by this approach to analyze credit risk. The methodology shown in the paper can also be applied to different loan products by currency type.

Keywords: probability of default; Markov transition matrix; credit risk