The EBA Guidelines on PD and LGD estimation is due to apply from 1 January 2021, in which the banks are expected to have a framework in place as part of the risk rating and reporting process to adjust and correct the uncertainties identified from deficiencies in data, system and methodology. The ECB Guide on the TRIM in the meantime state that the requirement of Margin of Conservatism (MoC) also applies for the CCF estimation. In this paper, we develop and present a consistent framework to quantify the identified uncertainties for the purpose of IRB risk parameter estimation.
Table of Contents
1. Category and Triggers of Identified Deficiencies
2. Design Concepts: a post-publication update
Part I. PD Estimation
3. Math Expression of PD Related Parameters
4. Appropriate Adjustment and Best Estimate for Default Rates
5. Category C Deficiencies: the General Estimation Error
Part II. LGD Estimation
6. Mathematical Definition of LGD Related Parameters
7. Notation Update and Application for LGD Estimation
Part III. CCF Estimation
8. Math Expression of CCF
9. Notation Update and Application for CCF Estimation
Part IV. Margin of Conservatism Framework
10. Genral Form Results for PD, LGD and CCF Estimation
11. Final Margin of Conservatism
12. Conclusions
Objectives & Core Topics
This paper develops a consistent quantitative framework to identify, measure, and adjust for uncertainties in IRB risk parameter estimation (PD, LGD, CCF) in compliance with EBA guidelines, specifically addressing data, methodological, and general estimation errors.
- Categorization of deficiency triggers (Category A, B, and C).
- Methodology for "Appropriate Adjustment" and "Best Estimate" calculation.
- Mathematical quantification of Margin of Conservatism (MoC).
- Integration of the MoC framework into existing model development processes.
- Numerical examples for PD, LGD, and CCF parameter estimation.
Excerpt from the Book
Appropriate Adjustment
The Appropriate Adjustment is an important term for the quantification of the MoC. Paragraph 38 of the Guideline states that: 38. In order to overcome biases in risk parameter estimates stemming from the identified deficiencies referred to in paragraphs 36 and 37, institutions should apply adequate methodologies to correct the identified deficiencies to the extent possible. The impact of these methodologies on the risk parameter (‘appropriate adjustment’), which should result in a more accurate estimate of the risk parameter (‘best estimate’), represents either an increase or a decrease in the value of the risk parameter. Institutions should ensure and provide evidence that the application of an appropriate adjustment results in a best estimate.
Highlighted that, an adequate methodology is required to correct the identified deficiency; post-correction, the impact of this methodology on the risk parameter, is defined as ‘appropriate adjustment’. This is an important concept because it is observed that even professionals in the industry could have misunderstood the methodology of correction as the appropriate adjustment itself.
For example, in case of missing value in the data records, practitioners may choose to replace the missing value with mean or median of the actual observed data. This is a methodology to correct the deficiency, however, the appropriate adjustment in this case, is the impact of this methodology on the risk parameter. The post-adjustment expectation of this impact is that the practitioner obtains a more accurate estimate of the risk parameter, the ‘best estimate’, by correcting the missing data deficiency.
Summary of Chapters
1. Category and Triggers of Identified Deficiencies: Categorizes potential sources of uncertainty into data/methodological deficiencies (A) and internal/external factors (B) based on EBA guidelines.
2. Design Concepts: a post-publication update: Outlines the modular design of the quantification framework, emphasizing that it relies on simple counting and observed ratios rather than complex distributional assumptions.
3. Math Expression of PD Related Parameters: Provides the formal mathematical definitions for calculating 1-year and long-run average default rates as required by regulatory standards.
4. Appropriate Adjustment and Best Estimate for Default Rates: Introduces propositions for calculating relative uncertainty and adjusting raw default rate estimates to arrive at a "best estimate."
5. Category C Deficiencies: the General Estimation Error: Details the quantification of rank ordering errors and calibration errors as the primary components of general estimation uncertainty.
6. Mathematical Definition of LGD Related Parameters: Establishes the formal definitions for economic loss, realized LGD, and long-run average LGD calculations.
7. Notation Update and Application for LGD Estimation: Adapts the general adjustment framework to LGD-specific parameters, incorporating LGD-related deficiency triggers.
8. Math Expression of CCF: Defines realized CCF and long-run average CCF approaches, including fixed horizon and cohort methods.
9. Notation Update and Application for CCF Estimation: Applies the uniform MoC adjustment notation to CCF calculations, maintaining consistency across all risk parameters.
10. Genral Form Results for PD, LGD and CCF Estimation: Generalizes the adjustment and estimation formulas (AA and RP) to be applicable across all three risk parameter types.
11. Final Margin of Conservatism: Derives the final MoC values by combining the impacts of Category A, B, and C deficiencies, ensuring alignment with regulatory sum-of-parts requirements.
12. Conclusions: Summarizes the benefits of the proposed modular, transparent, and regulatory-compliant framework for risk parameter monitoring.
Keywords
Advanced IRB, Long-run Default Rate, Long-run LGD, Central Default Tendency, Risk Weighted Assets, Margin of Conservatism, Probability of Default, Loss Given Default, Credit Conversion Factor, Exposure at Default, Appropriate Adjustment, Best Estimate, EBA Guidelines, Deficiency Trigger, Model Calibration.
Frequently Asked Questions
What is the core objective of this paper?
The paper develops a consistent, modular framework to quantify and monitor uncertainties in IRB risk parameter estimation, ensuring compliance with EBA guidelines effective from January 2021.
What are the primary categories of deficiency defined?
Deficiencies are classified into Category A (data and methodological issues), Category B (underwriting, risk appetite, and external environment changes), and Category C (general estimation errors).
What is the primary goal of the MoC framework?
The goal is to quantify the uncertainty not fully captured by raw estimation, providing a transparent, reversible methodology that integrates with existing monitoring processes without requiring model re-estimation.
Which scientific methodology is used for the adjustment?
The framework utilizes a modular "Appropriate Adjustment" approach based on relative uncertainty parameters (alpha and beta) derived from identifying and counting deficiencies at the individual record level.
What does the main body of the work cover?
It covers the mathematical definitions of PD, LGD, and CCF, the development of general adjustment formulas, the quantification of Category C estimation errors, and the final derivation of the Margin of Conservatism.
Which keywords best describe this research?
Key terms include Advanced IRB, Margin of Conservatism (MoC), Probability of Default (PD), Loss Given Default (LGD), Credit Conversion Factor (CCF), and Best Estimate.
How does the framework handle zero-default portfolios?
The framework addresses the division-by-zero problem in no-default situations through re-based calculations and logical substitution, allowing for consistent impact monitoring in low-default environments.
How does the framework ensure it avoids double counting?
The framework avoids double counting by construction, as the modular design allows for independent assessment of triggers, ensuring each deficiency's impact is captured separately before aggregation.
Why is the "Appropriate Adjustment" distinction important?
It is vital because industry professionals often incorrectly equate the methodology used to correct a deficiency (e.g., mean imputation) with the "appropriate adjustment" (the resulting impact on the risk parameter).
- Quote paper
- Yang Liu (Author), 2019, Margin of Conservatism Framework for IRB PD, LGD and CCF, Munich, GRIN Verlag, https://www.grin.com/document/923170
