Modelling LGD for unsecured personal loans

Transcription

1 Modelling LGD for unsecured personal loans Comparison of single and mixture distribution models Jie Zhang, Lyn C. Thomas School of Management University of Southampton 2628 August 29 Credit Scoring and Credit Control XI

2 Outline Loss Given Default and Recovery Rate Research Methods Data Single Distribution Models Mixture Distribution Models Model Comparison Conclusions and Further Research 2

3 Loss Given Default LGD is the final loss of an account as a percentage of the exposure, given that the account goes into default Recovery Rate = 1 LGD RR=Recovery Amount / Default Amount Recovery Amount = Default Amount Writeoff Amount OR Default Amount Last Outstanding Balance 3

4 Research Methods (1) Single distribution models Linear Regression Survival Analysis Models Censored data Fit various distributions Quantile 4

5 Survival Analysis models Usually use survival analysis in time but here use it in money or percentage of debt recovered. F(t)= Probability recovery rate is no greater than t% S(t) =1F(t) = Prob. Recovery rate above t Hazard function h(t) = F (t)/(1f(t))= density function recovery rate is t given it is at least t. For borrower with characteristics x life model, S(t) = S (e c.x t) Proportional Hazard model h(t) = e c.x h (t) 5

6 Research Methods (1) cont. Survival Analysis Models failure time models Logistic Regression first classify zero recoveries and nonzero recoveries Set distribution type in model building Cox proportional hazards models Both ways were tried Can fit any types of distribution 6

7 Research Methods (2) Mixture distribution models Different Recovery Rates in segments Debtors Views Different Distribution in segments Classification Tree model to segment the whole population then to build linear regression models and survival analysis models on each segment 7

8 Data The data is a default personal loan data set from a UK bank. The loans were issued from 1987 to 1999, and repayment patterns were recorded until the end of 23. Over 27, debts, 2% had been paid off, 14% were still being paid, 66% were written off. Key characteristics about debtors and debts includes: Residential status, Employment status, Marital status, Time at address, Time in occupation, Time at the bank, Second applicant status, Loan purpose, Age, Whether have mortgage, Loan term, Monthly income, Monthly expenditure, and so on 8

9 Data Distribution of Recovery Rate 35% 3% 25% P ercen t 2% 15% 1% 5% % 1% 15% 2% 25% 3% 35% 4% 45% 5% 55% 6% 65% 7% 75% 8% 85% 9% 95% 5% 5% 1% 15% 2% 25% 3% 35% 4% 45% 5% 55% 6% 65% 7% 75% 8% 85% 9% 95% 99.5% 99.5% 1% Recovery Rate 9

10 Results from single distribution models (Recovery Rate) The whole population was spilt to 2 parts: 7% as training sample for model building 3% as test sample for model test Results are based on test sample Linear regression Weibull Loglogistic Gamma Coxincluding Coxexcluding Optimal Quantile 34% 34% 36% 46% 3% R square Spearmen Rank

11 Results from single distribution models (Recovery Amount) Optimal Quantile R square Spearmen Rank Linear regression Weibull 34% Loglogistic 34% Coxincluding 46% Coxexcluding 3%

12 Another way to get predictions To get RR from Recovery Amount models Predicted Recovery Amount Predicted Default Amount R R To get Recovery Amount from RR models Predicted RR Default Amount Predicted Recovery Amount 12

13 Results from single distribution models (Two ways for Recovery Rate) from Recovery Amount model from Recovery Rate model Linear regression R square.292 Spearmen Rank R square.94 Spearmen Rank Weibull Loglogistic Gamma Coxincluding Coxexcluding

14 Results from single distribution models (Two ways for Recovery Amount) from Recovery Amount model from Recovery Rate model R square Spearmen Rank R square Spearmen Rank Linear regression Weibull Loglogistic Gamma Coxincluding Coxexcluding

15 Mixture distribution models Method 1: to maximise the distance of average RR between segments The classification tree is built on training sample and 4 segments are created. Linear regression and survival analysis models are built for each 4 segment. 4 test samples are combined to form the whole test sample the same as before. (1): Mortgage: Y Average:.4933 N: 4239 Loan: <6325 Average:.4331 N: 1682 (2): Residential Status: Tenets and others Average:.3647 N: 4418 Recovery Rate Average:.421 N: Mortgage: N Average:.4116 N: (4): Loan: >=6325 Average:.3538 N: 289 (3): Residential Status: Owners and With parents Average:.4395 N:

16 Mixture distribution models Method 2 : to split the whole population into 3 segments. Training sample (1) No recovery (RR<.5) (2) Partial recovery (.5<RR<.95) N: : 34.7% 2: 43.2% 3: 22.1% (3) Full recovery (RR>.95) (1): have mortgage, term=<12; OR have mortgage, time at address<78 months, have current account (2): others (1) 1 s N: 369 1: 45.8% 2: 35.3% 3: 18.9% (2) 2 s N: : 31.8% 2: 47.4% 3: 2.8% (3) 3 s N: : 33.3% 2: 37.5% 3: 29.2% (3): loan<432, insurance accepted 16

17 Results from mixture distribution models (Recovery Rate) Method 1 R square Spearmen Rank Method 2 R squar e Spearmen Rank Linear regression Linear regression Coxincluding Coxincluding Coxexcluding Coxexcluding 17

18 Results from mixture distribution models (Recovery Amount) Method 1 R squar e Spearmen Rank Method 2 R squar e Spearmen Rank Linear regression Linear regression Accelerate d Accelerate d Coxincluding Coxincluding Coxexcluding Coxexcluding 18

19 Model comparison (Recovery Rate) R square Spearmen Rank Single distribution model Linear regression Coxincluding Mixture distribution model Method 1 Linear regression Coxincluding Mixture distribution model Method 2 Linear regression Coxincluding

20 Model comparison (Recovery Amount) R square Spearmen Rank Single distribution model Linear regression Coxincluding Mixture distribution model Method 1 Linear regression Coxincluding Mixture distribution model Method 2 Linear regression Coxincluding

21 Conclusion and Further Research Linear regression is better than Survival analysis models for modelling LGD for unsecured consumer loans The prediction of recovery amount from RR model is better than that from recovery amount model Mixture distribution model does not improve prediction accuracy But linear regression is still poor, some magical variables are missing? How to segment the population? Cluster analysis? 21