A Markov Chain Study on Mortgage Loan Default Stages
Ying-Shing Lin, PhD
Dept. of Accounting Information Systems.
National Kaohsiung First University of Science and Technology e-mail:firstname.lastname@example.org
Sheng-Jung Li, PhD
Dept. of Finance
National Kaohsiung First University of Science and Technology e-mail:email@example.com
Shifting probability of credit status of past due or non-performing loans across stage has always been the center of attention not only for banking institutions but also for academicians. Mortgage loans’ changing credit status has a major influence on bank’s required reserve for capital adequacy against possible default loss. If the probability of shifting credit for default loans can be understood, calculated, controlled, or even predicted, reserve cost for the banking institutions can be alleviated to achieve higher economic efficiency. Due to the practical need to study and forecast bad credit, this research tries to explore probability distribution of past-due loans and to estimate average survival time before transferring into next non-performing loan stages. This information may be useful for bank managers to understand how to deal with the problems of classification and average delinquency related with mortgage loans for the purpose of better managing and granting loans. Bank asset may be better protected by restricting the period of years in mortgage financing especially when loans become dangerously delinquent and collaterals fail to offer adequate protection. Banking institutions may even use life insurance to match the period of mortgage loans against potential default in the case of borrower accidents. Prediction of mortgage probability among credit stages may facilitate loan granting decision because of better quality in credit evaluation, which may, in turn, reduce a significant portion of mortgage risk. Mortgage Loan Default Stages may be commonly classified into 5 stages: normal, special mention, substandard, doubtful, and actual loss, with each stage having different probability of change either from good to bad or vice versa. This study use the Markov Chain to study the probability of shifting credit status and to estimate average survival delinquency of non-performing loans across stages, using the mortgage data collected from one of Taiwanese major banking institutions over a period of ten years (2001-2010). The study result shows that the probability distribution of mortgage loans can be classified in to the following five stages: 86.89% belong to normal, 2.12% need special mention, 0.56% turn out to be doubtful, 0.63% classify as substandard, and, finally, 9.8% become actual loss. The probabilities for past-due loans to return back to its previous stage are 5.64%, 3.86%, 2.3% and 0.05% respectively, showing that mortgage loans once become past-due out of its regular repayment will not be easy for them to return to its previous credit status. This study also estimates average delinquent period for credit stages to be 23.61, 7.38, 4.24, and 2.40 years respectively, showing that the downward spiraling nature of non-performing loans with an ever shorter of life-cycle for worse credit. keywords：Mortgage loan, default risk, absorbing Markov chain
Credit and loan and are the main business and a major source of earnings for banking institutions. The quality of credit and loan operations has a tremendous impact on the soundness of banking operations. One of the causes of the 2007 U.S. subprime mortgage crisis is the excessive credit expansion for financial institutions to ignore risk related to real estate loans, particularly when such loans are from high-risk populations suffering from unemployment or falling real estate prices. Bad loans did not occur instantly when credit is first...
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