Evaluating Credit Risk Models Using Loss Density Forecasts: A Synopsis

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Evaluating Credit Risk Models Using Loss
Density ForecastsA Synopsis

• Amanda K. Geck
• Undergraduate Student
• Department of Computational and Applied
  Mathematics
• Rice University
• November 12, 2003

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Outline

• Background information/motivation
• Frerichs-Löffler evaluation framework, Berkowitz
  procedure
• Two-state model, Multi-state model
• Applications
• Conclusions

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• Background information/motivation
• Frerichs-Löffler evaluation framework, Berkowitz
  procedure
• Two-state model, Multi-state model
• Applications
• Conclusions

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What is credit risk?

• Credit risk is the chance that a borrower will
  default on a loan
• Firm defaults when asset value drops below
  critical value determined by liabilities (Merton
  1974)

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Who uses credit risk models?

• Banks
• Bank regulators
• Risk managers

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What is a portfolio credit risk model?

• Quantifies potential losses/gains from holding
  portfolio of risky debt
• Produces probability distribution for value
  effects of credit-related events

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Characteristics of portfolio credit risk models

• Some restrict analysis to losses from defaults
• Some include effects of credit quality changes
• Many capture credit event correlations through
  correlated latent variables

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Limitations

• Scarcity of credit events
• Long forecast horizons
• Data limitations
• Evaluation procedure concerns

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Research Scarce

• Only empirical paper Nickell, Perraudin,
  Varotto (2001)
• Only theoretical paper Lopez, Saidenberg (2001)

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• Background information/motivation
• Frerichs-Löffler evaluation framework, Berkowitz
  procedure
• Two-state model, Multi-state model
• Applications
• Conclusions

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Frerichs-Löffler Framework

• Monte Carlo study
• H0 is correct, rejection frequency should be
  equal to chosen significance level
• H0 wrong, rejection frequency (power of test)
  should be as high as possible

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Berkowitz Test Procedure

• Observed credit losses transformed into iid
  standard normal random variables
• H0 model is correct
• Standard likelihood ratio tests

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• Background information/motivation
• Frerichs-Löffler evaluation framework, Berkowitz
  procedure
• Two-state model, Multi-state model
• Applications
• Conclusions

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Two-state model

• Neglects migration risk and recovery rate
• Describes full loss distribution by distribution
  of number of defaults in portfolio

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Why a two-state model?

• Little data requirements
• Consistent data not available for recovery rates
• Data available for number of recent defaults

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Base Case Setup

• No recovery in case of default
• 10,000 borrowers in portfolio
• 1 unconditional default probability
• Uniform asset correlation in true data-generating
  model w2 5
• Asset value distribution N(0,1)
• 10 year credit loss history

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Base Case
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Different Sample Sizes
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Different Histories
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Issues with two-state model

• Choosing an appropriate asset correlation value
• Detecting misspecifications in asset correlation
  when default probability estimates noisy

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Heterogeneous portfolio

• Split portfolio into seven rating classes
• Add noise
• Overestimate by 50 default probabilities for
  half of borrowers in each rating class
• Underestimate by 50 for other half

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Heterogeneous Portfolio(contd)

• w2 20
• With properly specified heterogeneous default
  probabilities, power 93
• With noise, power 90
• Results of evaluation robust to noise

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Heterogeneous Default Probabilities
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Multi-state Model

• Accounts for
• Risk of default
• Risk of migration
• Systematic/unsystematic recovery risk
• Neglects
• General interest rate risk
• Specific spread risk

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Two-state vs. Multi-state

• H0 when w2 0
• multi-state power 100
• two-state power 100
• H0 when w2 20
• multi-state power 68
• two-state power 97.1

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Why is two-state power higher?

• Compare unexpected losses
• Multi-state w2 20 leads to unexpected loss
  1.7 times higher than with w2 5
• Two-state same ratio is 3 times higher

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• Background information/motivation
• Frerichs-Löffler evaluation framework, Berkowitz
  procedure
• Two-state model, Multi-state model
• Applications
• Conclusions

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Applications for Banks

• Use evaluation method to
• Confirm or improve chosen model specifications
• Assess powers of models applied to banks data
• Decide weight given to results in specification
  process

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Applications for Regulators

• Validate underlying assumptions of new capital
  adequacy framework (Basel Committee, 2001)
• Encourage banks with enough records of past
  losses to check consistency with Basel
  assumptions
• Check if assumptions sufficient on average

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• Background information/motivation
• Frerichs-Löffler evaluation framework, Berkowitz
  procedure
• Two-state model, Multi-state model
• Applications
• Conclusions

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Conclusions

• Tests good for identifying misspecifications of
  asset value distribution
• Results robust to variations in portfolio size
  and composition
• Power significantly better for two-state model
  than for multi-state

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Reference

• Frerichs and Löffler, Evaluating Credit Risk
  Models Using Loss Density Forecasts, Journal of
  Risk, Summer 2003