Probability of Default Model

Definition

A Probability of Default Model (PD Model) is any formal quantification framework that enables the calculation of a Probability of Default risk measure on the basis of quantitative and qualitative information

Probability of Default Models have particular significance in the context of regulated financial firms as they are used for the calculation of own funds requirements under Basel III regulation

Structure of Probability of Default Models

Risk Drivers

Estimates must be based on the material drivers of the risk parameters. The relevant material risk drivers and rating criteria may be taken into consideration in several ways:

• when assigning exposures to different PD models;
• at a PD model level when assigning exposures to different ranking/scoring methods;
• as explanatory variables in ranking/scoring methods;
• as drivers in the process for the assignment of PDs to grades or pools (e.g. calibration segments).

When choosing the risk drivers for the models there is a risk that risk drivers that capture the characteristics of defaulted obligors could be inappropriately inferred as relevant risk drivers for the portfolio. To mitigate this risk, institutions should take appropriate measures against model misspecification with regard to overfitting. This is particularly relevant where default data for the development of the model are scarce.

Risk Segmentation

Rating systems must provide for a meaningful assessment of obligor and transaction characteristics, a meaningful differentiation of risk and accurate and consistent quantitative estimates of risk. To comply with this requirement, PD models should perform adequately on economically significant and material sub-ranges of application.

The sub-ranges are identified by splitting the full range of application of the PD model into different parts on the basis of potential drivers for risk differentiation, including the following drivers, where relevant:

1. For PD models covering exposures to small and medium-sized enterprises (SMEs): country, industry (e.g. statistical classification of economic activities in the European Community (abbreviated as NACE) code section classification A to U), size of obligor (e.g. different buckets in terms of total assets), past delinquency (e.g. obligors with delinquency events, i.e. days past due, in the last 12 months);
2. for PD models covering retail exposures: client type (e.g. high net worth/private banking, other individuals, self-employed, SMEs), product type (e.g. consumer credit, credit card, other), region (e.g. nomenclature of territorial units for statistics (NUTS) 1, 2 or 3 as defined by Eurostat), past delinquency (e.g. obligors with delinquency events, i.e. days past due, in the last 12 months), maturity (e.g. original or remaining maturity);
3. for PD models covering retail exposures secured by real estate: region (e.g. NUTS 1, 2 or 3 as defined by Eurostat), type of real estate (e.g. residential, commercial, other), past delinquency (e.g. obligors with delinquency events, i.e. days past due, in the last 12 months), maturity (e.g. original or remaining maturity);
4. for PD models covering exposures to financial institutions: business model (deposit-taking institutions, investment banking, insurance firms, other), jurisdiction (or global region as appropriate) and size (defined buckets of total assets);
5. for PD models covering exposures to Large Corporates: industry (e.g. NACE code section classification A to U), country (or global region as appropriate) and size (defined buckets of total turnover).

Risk Differentiation

Probability of default models should ensure a meaningful differentiation of risk which takes into account

• the distribution of obligors or facilities;
• the homogeneity of obligors or facilities assigned to the same grade or pool; and (
• the different levels of risk across obligors or facilities assigned to different grades or pools to which a different PD is applied.

To ensure that the PD model performs adequately in terms of risk differentiation, institutions should adopt the following approach:

• Define metrics (considering both their evolution over time and specific reference dates) with well-specified targets, taking into account tolerance levels that reflect the uncertainty of the metrics, and take action to rectify any deviations from these targets that exceed the tolerance levels. Separate targets and tolerances may be defined for initial development and ongoing performance.
• Ensure that the tools used to assess risk differentiation are sound and adequate considering the available data, and that they are also evidenced by records of the time series of realised default rates or loss rates for grades or pools under different economic conditions.

ECB TRIM Requirements

Where an institution uses multiple rating systems, the rationale for assigning an obligor or a transaction to a rating system must be documented and applied in a manner that appropriately reflects the level of risk. To comply with this requirement institutions should, in terms of the range of application of a PD model:

• Clearly describe its range of application (and sub-divisions into different ranking/scoring methods and calibration segments) and also include an explanation of the risk drivers which the institution has considered, but decided not to use;
• Ensure that there are no overlaps in the range of application of different PD models and that each obligor or facility to which the IRB approach should be applied can be clearly assigned to one particular PD model.