In the world of credit risk modeling and financial risk management, three key metrics help financial institutions assess and manage their credit risk exposure: Probability of Default (PD), Loss Given Default (LGD), and Exposure at Default (EAD). These metrics are fundamental in the calculation of expected credit loss (ECL) and regulatory capital requirements under frameworks such as Basel III. In this article, we explore the concepts, their theoretical foundations, and practical examples.

1. Probability of Default (PD)

Definition

Probability of Default (PD) is the likelihood that a borrower will default on their obligations within a specified time horizon, typically one year. It is expressed as a percentage and derived from historical default data, credit scores, and financial indicators.

Theoretical Basis

PD is often modeled using statistical techniques such as:

• Logistic Regression: Estimates the probability of default based on financial ratios and borrower characteristics.
• Machine Learning Models: Advanced techniques like random forests and gradient boosting improve prediction accuracy.
• Credit Scoring Models: Traditional models like the Altman Z-score predict corporate default risk.

Example

Consider a lending institution evaluating a personal loan applicant. If past data shows that 3% of similar borrowers default within a year, the PD = 3%. This means that out of 100 similar borrowers, approximately 3 are expected to default.

2. Loss Given Default (LGD)

Definition

Loss Given Default (LGD) represents the proportion of exposure that a lender expects to lose if a borrower defaults, after accounting for recoveries from collateral, guarantees, or legal proceedings. LGD is expressed as a percentage of the total exposure.

Theoretical Basis

LGD is typically estimated using:

• Historical Recovery Rates: Analyzing past recoveries from similar loans.
• Collateral Valuation: Assessing the market value of pledged assets.
• Scenario Analysis & Stress Testing: Evaluating potential changes in market conditions.

Example

Suppose an institution lends $100,000 to a borrower who defaults. After legal proceedings and collateral liquidation, the institution recovers $40,000. The LGD is calculated as:

$$ LGD = \frac{(\$100,000-\$40,000)}{\$100,000} = 60\%. $$

This means the institution incurs a loss of 60% of the original loan amount.

3. Exposure at Default (EAD)

Definition

Exposure at Default (EAD) is the total value a lender is exposed to when a borrower defaults. It includes the outstanding loan balance and any undrawn credit facilities that might be utilized before default.

Theoretical Basis

EAD is estimated using:

• Credit Utilization Models: Predicting how much of a credit line will be drawn before default.
• Loan Amortization Schedules: Estimating outstanding balances over time.
• Internal Risk Models: Incorporating borrower behavior and economic conditions.

Example

A company has a $500,000 revolving credit line with a bank. At the time of default, the company has already drawn $350,000 and is expected to utilize an additional $50,000 before default. The EAD is:

$$EAD=\$350,000+\$50,000=\$400,000.$$

This represents the bank’s total risk exposure at the time of default.

4. Bringing It All Together: Expected Credit Loss (ECL)

The three metrics (PD, LGD, and EAD) are used to calculate the Expected Credit Loss (ECL), a key measure in credit risk management:

$$ECL= PD \times LGD \times EAD. $$

For example, if:

• PD = 3%,
• LGD = 60%, and
• EAD = $400,000, then the expected credit loss is:

$$ECL = 0.03 \times 0.60 \times \$400,000 = \$7,200. $$

This means the lender expects to lose $7,200 on average due to this credit exposure.

Conclusion

Understanding PD, LGD, and EAD is essential for financial institutions to manage credit risk effectively. These metrics help in setting loan loss provisions, pricing credit products, and complying with regulatory frameworks like Basel III and IFRS 9. By leveraging statistical models and historical data, lenders can make informed credit decisions and mitigate financial risks effectively.

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