# ASRF model

## Definition

**ASFR Model** (asymptotic single factor risk model) is a simplified Credit Portfolio risk model that underpins the Basel II capital requirements

## Assumptions

The following is an indicative list of assumptions / design choices in constructing the ASFR model

- One year risk horizon
- Single factor model
- Normal distributions
- Homogeneous and large pool of exposures

## Formulae

Below are the explicit formulae for some banks’ major products:

- Corporate exposures,
- Small-medium enterprise (SME) exposures
- Residential mortgages and
- Qualifying revolving retail exposure. (S being Min(Max(Sales Turnover),5),50 )

In the formulas below:

- N(x) denotes the normal cumulative distribution function
- G(z) denotes the inverse cumulative distribution function
- PD is the probability of default as calculated by an approved internal risk model
- LGD is the loss given default as calculated by an approved internal risk model
- EAD is the Exposure At Default as calculated by an approved internal risk model
- M is the effective maturity as calculated by an approved internal risk model

### Corporate Exposures

The exposure for corporate loans is calculated as follows^{[1]}

#### Correlation Parameter

The correlation parameter offers a simple approach to capture an element of Default Correlation. The peculiar presence of exponentials is for normalization purposes

#### Maturity Adjustment

The maturity adjustment offers a simple approach to capture residual credit risks that may not materialise within the one-year risk horizon implied by the ASRF model.

#### Capital requirement

#### Risk-weighted assets

### Correlation adjustment for Large Financial Institutions

A multiplier of 1.25 is applied to the corporate correlation parameter of all exposures to financial institutions meeting the following criteria^{[2]}

- Regulated financial institutions whose total assets are greater than or equal to US $100 billion. Regulated financial institutions include, but are not limited to, prudentially regulated Insurance Companies, Broker/Dealers, Banks, Thrifts and Futures Commission Merchants
- Unregulated financial institutions, regardless of size.

#### Correlation Parameter

### Correlation adjustment for SME

For small and medium enterprises with annual Sales Turnover below 50 million euro, the correlation may be adjusted as follows:^{[3]}

#### SME Correlation

In the above formula, S is the enterprise's annual sales turnover in millions of euro.

### Residential mortgage exposures

The exposure related to residential mortgages can be calculated as this^{[4]}

#### Correlation

#### Capital Requirement

#### Risk-weighted assets

### Qualifying revolving retail exposures (credit card products)

The exposure related to unsecured retail credit products can be calculated as follows:^{[5]}

#### QRRE Correlation Assumption

#### Capital Requirement

#### Risk-weighted assets

## References

- ↑ Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework (BCBS) (November 2005 Revision), Paragraph 272
- ↑ Basel III: A global regulatory framework for more resilient banks and banking systems
- ↑ Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework (BCBS) (November 2005 Revision), Paragraph 273
- ↑ Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework (BCBS) (November 2005 Revision), Paragraph 328
- ↑ Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework (BCBS) (November 2005 Revision), Paragraph 329