Catalog of 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 (or the equivalent Recovery Rate modelling). The list of references (academic / other publications).

Preference should be given to:

  • references with open source implementations
  • openly accessible references (e.g. a downloadable PDF file)
  • references that provide explicit and high quality documentation of the algorithms involved
  • reviews that provide pointers to further references

The focus of this catalog is on ex-ante loss-given default requirements / applications, not ex-post NPL valuation models for which there is a separate catalog.

Usual disclaimer apply:

  • Inclusion in the list does not imply any assurances about correctness, completeness or suitability
  • The list is not aimed to establish academic priority but to provide sufficient documentation for each listed model

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 at least the following segmentation:

Statistical Models

Models estimated directly on the basis of historical LGD data. Such models can further subdivided by approach:

  • Historical Averages. A simple approach, using possibly segmentation by various characteristics, but with no explicit modelling of underlying distribution
  • Parametric Distribution Models, which adopt an underlying model for LGD Risk is distributed. Those 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, which explore other available statistical tools

Non-Statistical Approaches

Models that are estimated primarily on the basis of non-statistical data (e.g. forward looking market data, or more or less complicated expert models)

  • Expert Based (subjective) Models: typically using scorecards and calibrated to internal or external evidence. Those tend to be used in the absence of sufficient empirical evidence
  • Simulation based LGD models: These are used in large bespoke transactions involving e.g., 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 compared 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 (which may be simply an assumption if there is no liquid market for the collateral)

List of Statistical Loss Given Default Models

This a live catalog of statistical loss given default models (algorithms)[2]

Model Name Simple / Composite Distribution Dynamic Factors Remarks
Linear Regression (OLS) Simple Normal Observed Covariates Does not enforce appropriate LGD bounds
Transformed Regression [3] Simple Inverse Gaussian Observed Covariates Suboptimal estimator [4]
Transformed Regression [5] Simple Inverse Beta Observed Covariates
Fractional Response Regression [6] Simple Logistic Observed Covariates Imposes a logistic link function
Censored Gamma Regression [7] Simple Truncated Gamma Observed Covariates
Two-Tiered Gamma Regression[8] Mixture Truncated Gamma Observed Covariates Two latent variables
Beta Regression [9] Simple Censored transformed beta Observed Covariates
Inflated Beta Regression [10] Mixture Bernoulli and Beta Observed Covariates
Mixed Effects Model [11] Simple Inverse Logit Observed Covariates and Latent Factor

Open Source Software

See Also


  1. C.Peter, Estimating LGD: Experience from Banking Practice, The Basel II Risk Parameters, 2nd Ed
  2. Models in the "Non-statistical category" are currently not represented but the scope and granularity of both model coverage and model characteristics may increase!
  3. Hu Perraudin, 2002, Qi Zhao, 2011
  4. Li, Qi, Zhang, and Zhao (2015)
  5. Gupton & Stein 2005
  6. Papke and Wooldridge (1996)
  7. Sigrist and Stahel (2011)
  8. Sigrist and Stahel (2011)
  9. Duan and Hwang, 2014
  10. Ospina and Ferrari, 2010, Pereira and Cribari-Neto 2010, Calabrese 2010, Yashkir and Yashkir 2013
  11. Hamerle et al (2006)