American Journal of Theoretical and Applied Statistics
Volume 8, Issue 2, March 2019, Pages: 39-46
Received: Apr. 1, 2019;
Accepted: May 15, 2019;
Published: Jun. 5, 2019
Views 224 Downloads 64
Sammy Mungasi, Institute of Mathematical Sciences, Strathmore University, Nairobi, Kenya
Collins Odhiambo, Institute of Mathematical Sciences, Strathmore University, Nairobi, Kenya
Credit risk is a critical area in finance and has drawn considerable research attention. As such, survival analysis has widely been used in credit risk, in particular to model debt’s time to default mechanisms. In this study, we revisit different survival analysis approaches as applied in credit risk defaulters’ data and assess their performance in light of the Kenyan context. In practice, inconsistency in validity of credit risk models used by many company when predicting and analysis of loan default is a common phenomenon that occurs unexpectedly. Loan defaults, often causes major loses to creditors’ and can be of great benefit if quantified correctly in advance by using correct models. Here, we address the unbiasedness, analysis and comparison of survival analysis approaches, particularly, the models of credit risk. We carry out data analysis using Cox proportional hazard model and it’s extensions as well as the mixture cure and non-cure model. We then compare the results systematically by investigating the most efficient and preferable model that produces best estimates in Kenyan real data setting. Results show, the Cox Proportional Hazard (CPH) model is more efficient in the analysis of Kenyan real data set compared to the frailty, the mixture cure and non-cure model.
Comparison of Survival Analysis Approaches to Modelling Credit Risks, American Journal of Theoretical and Applied Statistics.
Vol. 8, No. 2,
2019, pp. 39-46.
Allen, L., Delong, G., & Saunders, A. (2004). Issues in the credit risk modeling of retail markets. Journal of Banking & Finance, 28 (4), 727-752.
Gudmundsson, R., Ngoka-Kisinguh, K., & Odongo, M. T. (2013). The role of capital requirements on bank competition and stability: The case of the Kenyan banking industry. Kenya Bankers Association-KBA Centre for Research on Financial Markets and Policy Working Paper Series.
Wienke, A. (2010). Frailty models in survival analysis. Chapman and Hall/CRC.
Bellotti T. and Crook J. (2013). Forecasting and stress testing credit card default using dynamic models. International Journal of Forecasting 29 (4): 563 – 574.
Bellotti T and Crook J (2014). Retail credit stress testing using a discrete hazard model with macroeconomic factors. Journal of the Operational Research Society 65 (3): 340–350.
CBK. (2013a). Credit survey Report. Nairobi: Central Bank of Kenya.
CBK. (2013b). Risk Based Supervisory Framework. Nairobi: Central Bank of Kenya.
CBK. (2015). The Kenya financial sector stability report. Nairobi: Central Bank of Kenya.
CBK. (2016). Bank Supervision Annual Report. Nairobi: Central Bank of Kenya.
CBK. (2017). Bank Supervision Annual Report 2017. Nairobi: Central Bank of Kenya.
CBK. (2018). Credit Survey Report for the Quarter ended March 2018. Nairobi: Central Bank of Kenya.
Gupta, V. (2017). A survival approach to prediction of default drivers for India listed companies. Theoretical Economics Letters, 07 (02), 116-138.
Gaynor M. and Town R. (2011). Competition in Health Care Markets. Chapter for the Handbook of Health Economics, Volume 2. T. McGuire, M. V. Pauly, and P. Pita Barros, Editors 2011.
Jacobson, T., & Roszback, K. (2003). Bank lending policy, credit scoring and value at risk. Journal of Banking and Finance, 27 (4), 615-633.
J-K Im, DW Apley, C Qi and X Shan (2012). A time-dependent proportional hazards survival model for credit risk analysis. Journal of the Operational Research Society, 63 (3): 306-321.
Kagri, H. S. (2011). Credit risk and performance of Nigerian banks. Ahmadu Bello University, Zaria.
Kithinji, A. M. (2010). Credit risk management and profitability of commercial banks in Kenya.
Lore, D., Gerda, C., and Bart, B. (2017). Time to default in credit scoring using survival analysis. Journal of the Operational Research Society, 68, 652–665
Marimo, M. (2015). Survival analysis of bank loans and credit risk prognosis (Doctoral dissertation).
Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates. The Journal of finance, 29 (2), 449-470.
Narain B. (1992). Survival analysis and the credit granting decision. In: Thomas LC, Crook JN and Edelman DB, editors, Credit Scoring and Credit Control, pp. 109–121. Clarendon Press: Oxford.
Nevo A. (2001). Measuring Market Power in the Ready-to-Eat Cereal Industry. Econometrica 2001; 69 (2); 307-342.
Obuda, F. (2016). Analysis of credit risk on bank loans using cox proportional hazard model. (Unpublished master’s thesis). University of Nairobi.
Tong, E., Mues, C., & Thomas, L. (2012). Mixture cure models in credit scoring. European journal of operational research, 218 (1), 132-139.
Stepanova M. and Thomas L. (2002). Survival analysis methods for personal loan data. Operations Research Quarterly 50 (2): 277–289.
Cao, R., Vilar, J. M., & Devia, A. (2009). Modelling consumer credit risk via survival analysis. SORT: statistics and operations research transactions, 33 (1), 0003-30.
Anthony, W., & Othieno, F. (2016). Semi-Markovian credit risk modeling for consumer loans: Evidence from Kenya. Journal of Economics and International Finance, 8 (7), 93-105.
Zhang, A. (2009). Statistical Methods in Credit Risk Modeling.
Bellotti, T. & Crook J. (2009). Credit scoring with macroeconomic variables using survival analysis. The Journal of the Operational Research Society 60 (12): 1699–1707.
Cox, D. R. (1972). Regression models and life‐tables. Journal of the Royal Statistical Society: Series B (Methodological), 34 (2), 187-202.
Li, Y., & Ruppert, D. (2008). On the asymptotics of penalized splines. Biometrika, 95 (2), 415-436.
Duchateau, L., & Janssen, P. (2007). The frailty model. Springer Science & Business Media.
Goel, M. K., Khanna, P., & Kishore, J. (2010). Understanding survival analysis: Kaplan-Meier estimate. International journal of Ayurveda research, 1 (4), 274.