CHING'S MARKOV CHAIN MODELS
RETAIL MORTGAGES
C. Liu, M. Hassan, R. Nassar and M. Guo (2012). Multivariate Markov Models for Retail Mortgages Based On Correlation Analysis. Academy of Banking Studies Journal, 11(2), 23-45.
https://www.abacademies.org/articles/volume-11-issue-2.pdf
In Liu et al. (2012), the authors consider the problem of the correlation between different credit products. They present multivariate Markov chain model, higher-order Markov chain model and higher-order multivariate Markov chain model to analyze the relationship between the payment behaviors of retail mortgage loans and consumer credit cards in different situation. An early warning system for bank credit portfolios can then be built by monitoring the correlation between credit products payment.
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In Liu et al (2012), the authors found that the bank management of the importance of the correlation between retailed mortgage loans and personal credit cards, both of which are usually offered by a local bank to the same group of consumers in the area. Since multivariate Markov chain models have been successfully used in representing the behavior of multiple data sequences generated by the same source, it is suggested to be used to analyze and quantifying the correlation that has been long observed by the credit risk management personals in banking.
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The original sequences are a sequence of probability distribution vector for the retail mortgage and a sequence of probability distribution vector for personal credit cards. The transient states are past due and prepayment states. And the absorbing states are the default state contributed by permanent events such as death. Applying the parsimonious multivariate Markov chain model in Ching et al. (2002, 2006) and the parsimonious high-order Markov chain model in Ching et al. (2006), the correlation between credit products payment can be estimated efficiently by solving the linear programming systems.
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The authors in Liu et al. (2012) used the three models to predict mortgage loan health distribution by analyzing the delayed cross-products transition process. And they concluded that the proposed models offer the bank management quantitative methods to analyze and predict its loans’ behaviors. Also, this modeling approach could help the bank management in making strategic financial decisions. Furthermore, the measurement of correlation using the parsimonious high-order multivariate Markov chain model offers a reliable method to analyze data for small-to-medium size local commercial banks, which, in most cases, do not have adequate resources for implementing comprehensive large computation systems.
W. Ching, E. Fung, M. Ng (2002). A Multivariate Markov Chain Model for Categorical Data Sequences and Its Applications in Demand Prediction. IMA Journal of Management Mathematics, 13:187-199.
https://ieeexplore.ieee.org/document/8142556
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W. Ching and M. Ng (2006) Markov chains models, algorithm and application. Springer.