**ICOM R 223 Sujoy 2**

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Hosted by: Conference partners: NOVEL WAY OF RETAIL CREDIT GRANTING DECISION Sujoy Roychowdhury### NOVEL WAY OF RETAIL CREDIT GRANTING DECISION:

Sujoy Roychowdhury Alumnus- IIM, Bangalore NOVEL WAY OF RETAIL CREDIT GRANTING DECISION### BACKGROUND:

BACKGROUND Credit scoring techniques available since 1960’s Objective is to identify “good” customers from “bad” and extend credit based on that Currently most techniques focus on entire Credit Risk Management Lifecycle (CRMC) Credit scoring in most cases have focussed on different classification algorithms However, thresholds used in the classification algorithms is often arbitrary### Financial Model of Loan:

Financial Model of Loan A delay in loan payment may not be loss-making if sufficient interest is charged for delayed days A defaulted loan may also not be loss-making if loan can be sold off to collecting agency at a discount if sufficient number of payments have been made Cash flow and NPV model of loans need to be considered to find when is a loan actually loss-making This analysis is based on Booth, P., & Walsh, D. E. (1998). Acturial Techniques in Risk Pricing and Cash Flow Analysis for U.K. Bank Loans. Journal of Acturial Practice , 63-111### HOW IS LOAN GRANTED:

HOW IS LOAN GRANTED Automotive Finance Equity Debt Treasury Loan Application Credit Rating Unit Credit rating Equity backing Tier II Capital Loan from Treasury Borrowing from external market Loan Granted### CASH FLOW MODEL (DIAGRAMATIC):

CASH FLOW MODEL (DIAGRAMATIC) LOAN DEPARTMENT (BANK) Repayments to treasury – includes initial costs repayment EMI (from customer) Equity capital returned Interest on equity capital Running expenses Net interest paid out on debt capital Objective: Cash flows discounted at hurdle rate (required internal rate of return) by bank must give positive NPV### Math formulation – no default …(1/2):

Math formulation – no default …(1/2) Net monthly income at month t EMI Monthly rate of cost of funds Loan outstanding at month t Initial costs Equity returned at end of mont t Interest earned on equity capital Net interest paid out on debt Monthly costs### Math formulation – no default …(2/2):

Math formulation – no default …(2/2) This is the NPV of the loan discounted at the hurdle rate - the rate of return required by the firm Initial equity capital put in the loan This is the discounting formula### IN CASE OF RISK OF DEFAULT:

IN CASE OF RISK OF DEFAULT LOAN DEPARTMENT (BANK) Repayments to treasury – includes initial costs repayment EMI (from customer) Equity capital returned Interest on equity capital Running expenses Net interest paid out on debt capital Objective: Cash flows discounted at hurdle rate (required internal rate of return) by bank must give positive NPV Need to convert each of the quantities to expected value per month based on probability of default in that month### Formulation – with prob. of default:

Formulation – with prob. o f default = Probability of default in month t = Probability loan will remain in force in month t = = Expected ratio of loss during month t to### Literature Review ….. (1/2):

Literature Review ….. (1/2) Author Article Source Relevant Obs. Booth P. , Walsh D.E. Actuarial Techniques in Risk Pricing and Cash Flow Analysis for U.K. Bank Loans Journal of Actuarial Techniques 1998 pp. 63-111 This paper discussed the loan model discussed above but no discussion of how to estimate probabilities nor any citation Pazdera J., Rychnovsky M., Zahradnik P. Survival Analysis in Credit Scoring http://artax.karlin.mff.cuni.cz/~rychm5am/Project.pdf Use survival probabilities in scoring### Literature Review ….. (2/2):

Literature Review ….. (2/2) Author Article Source Relevant Obs. Stepanova M. , Thomas L.C. Proportional Hazards Analysis Behavioural Scores Journal of Operational Research Society 2001 pp. 1007-1016 Proportional hazards model based on behavioural data about monthly balance and delinquency Zhao Y., Zhao Y., Song I. Predicting New Customers’ Risk Type in the Credit Card Market Journal of Marketing Research 2009 pp 506-517 Willingness of pay and ability to pay separated using microeconomic perspective ( latent variable approach)### Prediction of default probability:

Prediction of default probability In the model of (Booth & Walsh, 1998) discussed above we need to estimate default probability at month t In this study, I follow a survival modeling approach Survival models estimate the probability at time t of an individual being alive beyond a time t i.e. The density function is given by Hazard function is given by### Delay & Default events:

Delay & Default events Delay:- When a customer delays a payment but pays when followed-up He/she needs to pay a hefty simple interest per day on delay not only to cover additional cost of funds, operational costs in follow-up but also create a strong dis-incentive to delay A delay event can be assumed not to be loss-making Default:- If customer does not pay within 120 days then there is no further follow-up Outstanding loan amount sold to a collecting agency at a hefty discount who would then collect the collateral from the customer### Using delay and default events:

Using delay and default events Thus if we have a delay event and a default event we should use this to estimate the probability of survival This is based on the assumption that a customer who delays often is having a higher probability to default than one who does not Joint modeling of a recurrent event and a terminating event. Also a semi-competing risks model as one event is censoring the other event and not vice-versa### Joint Frailty Models:

Joint Frailty Models Frailty is used to account for individual variations in a heterogeneous population Joint frailty models estimate the hazard function for recurrent events and the hazard function for terminating event Death (in medical studies where survival models are commonly used) or default (in this study) is an informative censoring The effect of explanatory variables are assumed to be different for recurrent and terminating events U se a time-to-event model as number of payments till default is the question of interest### Joint Frailty Model Definition:

Joint Frailty Model Definition### Dataset … (1/3):

Dataset … (1/3) Dataset is of an automotive finance company Data for 72 months (6 years) Loans extended for 2-wheelers Loans period :- 10 , 12. 18. 24 months One row per loan, one column per month If month is not within loan period then NULL If no delay on loan then entry =0 If delay then entry = no. of days of delay If entry > 120 , identify as default Some non-defaulting loans do not have information for as many months as the tenure. Considered as censored observations### Dataset … (2/3):

Dataset … (2/3)### Dataset … (3/3):

Dataset … (3/3)### Dataset transformed … (1/3):

Dataset transformed … (1/3) Data transformed to an event structure for survival analysis If there is a delayed payment we create one row with delay =1 and default_flag=0. We populate the month into the loan in the stop column. In the start column we populate 0 if this is the first event for the contract in question or the stop time of the previous event for the contract. If there is a default event we create one row with default=1 and delay=0. We populate the month into the loan in the stop column. In the start column we populate 0 if this is the first event for the contract in question or the stop time of the previous event for the contract. If the loan has defaulted we do not create further entries for that loan. There exist some contracts where there is data beyond the first default period but these are data issues. If there has not been any default and the total number of payments is less than the number of months a new row is created with delay=0, default=0 and event=0 (censoring flag) If there has not been any delay or default at all on a contract, we create one row with default=0 and delay=0. We populate the start time with zero and the stop time with the TENOR period of the loan.### Dataset transformed … (2/3):

Dataset transformed … (2/3)### Dataset transformed … (3/3):

Dataset transformed … (3/3)### Model, estimation and use:

Model, estimation and use A joint frailty model was estimated using the dataset and coefficients for the covariates estimated These used in hazard function and survival probabilities for every month calculated Expected NPV calculated in financial model for a small sample of loans For most defaulted loans expected NPV was negative , however some did have positive expected NPV### Further work:

Further work Use the expected NPVs for the entire population of results and then rank-order them to create a scoring model Replication in other datasets and validation of this approach### Q&A:

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