Objective

To validate the Probability of Default (PD) and Loss Given Default (LGD) models for a fixed-rate mortgage portfolio for the client.

CRISIL's Solution

• Project Parameters
  
  • Validation based on logistic regression for PD model and Zero-One Inflated Beta Regression for LGD model. This includes the following steps:
    
    • Quantitative validation of the Logistic regression and Beta regression models
      
    • Development of the challenger model using alternate approach/information
      
  • The Logistic Regression and Beta Regression model to estimate the PD and LGD respectively for Mortgage portfolio are:
    
    • logit(p) = β0+ β1 * fico + β2 * mi_pct + β3 * cltv + β4 *dti + β5* Unemployement Rate; PD =(1/(1+𝑒^(−𝑙𝑜𝑔𝑖𝑡(𝑝))))
      
    • LGD = β0+ β1 * ltv + β2 * dti + β3 * House.Price.Index.Level
• Data Quality & Audit
  
  • Replicated development dataset from raw files available in the general ledgers
    
  • Validation of data cleansing and preparation steps (e.g., validating imputation and transformation of data)
    
  • Routine checks in verifying the inclusion of data corresponding to full economic cycle, data relevancy
    
  • Validated the macroeconomic variables data from the internal repository which gets updated frequently
    
• Validation of Key Aspects
  
  • Alternative approaches like contractual term, weighted average method using default/prepayment used to estimate the life of loan
    
  • Current default definition tested against the regulatory definition, underlying assumptions and role of senior management
    
  • Forecast horizon and macro-economic model forecast of reasonable and supportable forecast validated
    
• Selection of Initial Pool of Variables
  
  • Variable selection process used in model development document and multi-collinearity validated
    
  • Assigned different significance levels for different variables and options to filter models with user-specified signs for different variables
    
• Model Replication & Challenger Models
  
  • Replicated the entire variable selection process using information provided in the model development document
    
  • Verified the model coefficients along with the significance of the variables and verified the economic intuition of the sign of the variables chosen
    
  • Developed the challenger model using alternative approach/different variable
    
• Independent Testing
  
  • Performed Model Fitting Tests, Coefficient Stability Analysis, Assumption Testing, Seasonality Check, Accuracy Tests of Model, Sensitivity and Scenario Analysis
    
  • Performed back-testing analysis between actual and predicted PDs and LGDs
    
    

Client Impact

Validation project completed on time and on budget. 

Questions

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