Использование марковских моделей со множеством состояний для прогнозирования вероятности дефолта заемщиков

Abstract

Introduction. After the crises, lenders realized the importance of assessing the risk of default on loan portfolios in various economic conditions. Modeling of credit risk assessment occurs mainly using internal ratings of banks based on probabilistic models of defaults of borrowers over a certain period of time. Theoretical models. Three models are considered. The first is a naive Markov model with R states. The transition matrix is given. The second is a Markov model with multiple states with covariates. Macroeconomic indicators are proposed as covariates. The third model is multinomial logit regression. Approbation of Markov models and multinomial regression on simulated and real data of borrowers’ defaults. We investigate the possibility of using multi-state Markov models to predict borrower defaults in financial institutions over time. Three approaches are considered for credit risk modeling. The first approach assumes that the transition probability matrix is constant over time, and the residuals of the Markov model and logistic regression are taken into account further when forecasting over the time horizon. The second one is supplemented by the Markov model, which takes into account the impact of default risks on migration, both individual factors of borrowers and the economic situation in the country. Using covariates, the models made it possible to simultaneously estimate the transition rate and the probability of erroneous classification of states. A multinomial logistic regression model is considered to compare the results obtained using multi-state Markov models. The proposed models are tested both on real and simulated data. Conclusion. The presented models show good predictive results with high accuracy of default estimates. The models reproduce the structure of the generated data quite well. The peculiarity of the multinomial regression model in predicting defaults is its adjustability, and Markov models estimate the probabilities of defaults. To implement the model, software R was used.