Objective

To validate the Probability of Default (PD) and Loss Given Default (LGD) models for wholesale CRE and C&I portfolios for the client.

CRISIL's Solution

• Project Parameters: Wholesale CRE Portfolio
  
  • Validation based on M-factor approach (historical transition matrix) using linear regression for PD model, and linear regression for LGD model. This includes the following steps:
    
    • Quantitative validation of the OLS regression model
      
    • Development of the challenger model using alternate approach/information
      
  • The OLS model to estimate the PD and LGD  for CRE portfolio is:
    
    • M-factor = β0+ β1 * Mfactor_1Lag + β2 *Real_GDP_Growth+ + β3 * BBB_Corporate_yield + β4 *Japan_Inflation; PD =∅((𝜙^(−1) (𝑃𝑇)  + 𝑀𝑓𝑎𝑐𝑡𝑜𝑟∗(−√𝜌))/(√(1−𝜌)))
      
    • LGD = β0+ β1 * Real_GDP_Growth_2Lag + β2 * BBB_Corporate_yield_4Lag
      
• Project Parameters: Wholesale C&I Portfolio
  
  • Validation based on M-factor approach (historical transition matrix) using linear regression for PD model, and linear regression for LGD model. This includes the following steps:
    
    • Quantitative validation of the OLS regression model
      
    • Development of the challenger model using alternate approach/information
      
  • The OLS model to estimate the PD and LGD for C&I portfolio is:
    
    • M-factor = β0+ β1 * Mfactor_1Lag + β2 *Unemployment_rate_2Lag; PD =∅((𝜙^(−1) (𝑃𝑇)  + 𝑀𝑓𝑎𝑐𝑡𝑜𝑟∗(−√𝜌))/(√(1−𝜌)))
      
    • LGD = β0+ β1 * UK_Bilateral_dollar_ExchangeRate_1Diff + β2 *Developing_Asia_Bilateral_dollar_ExchangeRate_1Diff
      
• 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 for both portfolios.

Questions

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