Loss Given Default Models

From Open Risk Manual

Catalog of Loss Given Default Models

This page aims to be a comprehensive collection of publicly documented models and algorithms used for loss given default modelling.

Scope

The loss given default model collection focuses on ex-ante LGD models applied to performing credit exposures. Out of scope for this page are the related Non-Performing Loan Valuation models.

LGD Model Classification

Loss given default models have been used globally for decades and in a variety of credit risk management contexts. This results in a large variety of possible quantification approaches, depending on the nature of the credit risk, the data and expertise available etc. A classification of typical LGD Model categories would include:

  • Statistical models
    • Historical averages, possibly segmented by characteristics, with no explicit modelling of underlying distribution
    • Parametric distribution models, which can be further classified according to:
      • Elementary (single distribution) models versus Composite (mixture models)
      • Static versus dynamic (including economic factors) models
    • Non-parametric or more complex statistical models
  • Non-statistical approaches
    • Expert based (subjective) models: typically using scorecards and roughly calibrated to internal or external evidence. Used in the absence of sufficient empirical evidence
    • Simulation based LGD models: These are typically used in large bespoke transactions involving Project Finance. Cashflow simulations based on various scenarios are used to estimate both likelihood of default and recover in case of default[1]. Despite the more quantitative nature compare to expert based models, the simulated scenarios may also involve a large degree of subjectivity
    • Market data based LGD models: For traded credit products (Corporate Bonds, Asset Backed Securities, Sovereign Bonds) market data (bond prices) can be used to estimate implied LGD / Recovery Rates. In general this is a joint estimate together with the implied probability of default. The models obtain point estimates at the time of observation. The underlying (risk-neutral) distribution may be derived from the bond pricing model used for fitting the market data.
    • Models based on the theory of corporate default: These models use option theoretic arguments and market data to fit a structural model. The underlying distribution is linked to the movement of asset markets

List of Statistical Loss Given Default Models

This a live catalog of statistical loss given default models (algorithms). Models in the "Non-statistical category" are currently not represented but the scope and granularity of both model coverage and model characteristics may increase!

Model Name Simple / Composite Distribution Dynamic Factors Remarks
Linear Regression (OLS) Simple Normal Observed Covariates Does not enforce appropriate LGD bounds
Transformed Regression [2] Simple Inverse Gaussian Observed Covariates Suboptimal estimator [3]
Transformed Regression [4] Simple Inverse Beta Observed Covariates
Fractional Response Regression [5] Simple Logistic Observed Covariates Imposes a logistic link function
Censored Gamma Regression [6] Simple Truncated Gamma Observed Covariates
Two-Tiered Gamma Regression[7] Mixture Truncated Gamma Observed Covariates Two latent variables
Beta Regression [8] Simple Censored transformed beta Observed Covariates
Inflated Beta Regression [9] Mixture Bernoulli and Beta Observed Covariates
Mixed Effects Model [10] Simple Inverse Logit Observed Covariates and Latent Factor

Usage

Collective (Portfolio-wide recovery rate) versus Individual facility models. For retail portfolios it may be the case that the LGD models are estimated and used always at a portfolio level, with the implicit assumption that all credit exposures within the portfolio are homogeneous with respect to LGD risk factors.

References

List of references (academic / other publications). Preference should be given to:

  • openly accessible references (e.g. a downloadable PDF file)
  • reviews that provide pointers to further references
  • references that provide explicit and high quality documentation of algorithms (no Word formulae)
  • focus on loss-given default requirements / applications, not NPL valuation

The list is not aimed to establish academic priority but to provide sufficient documentation for each listed model. Multiple references are ok if they complement each other.

Usual disclaimer applies: Inclusion in the list does not imply any assurances about correctness, completeness or suitability.

  1. C.Peter, Estimating LGD: Experience from Banking Practice, The Basel II Risk Parameters, 2nd Ed
  2. Hu Perraudin, 2002, Qi Zhao, 2011
  3. Li, Qi, Zhang, and Zhao (2015)
  4. Gupton & Stein 2005
  5. Papke and Wooldridge (1996)
  6. Sigrist and Stahel (2011)
  7. Sigrist and Stahel (2011)
  8. Duan and Hwang, 2014
  9. Ospina and Ferrari, 2010, Pereira and Cribari-Neto 2010, Calabrese 2010, Yashkir and Yashkir 2013
  10. Hamerle et al (2006)

See Also


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