ASRF model

From Open Risk Manual

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:

Corporate Exposures

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

Correlation Parameter

R = 0.12  \frac{1 - e^{-50  PD}}{1 - e^{-50}} + 0.24 \left(1- \frac{1 - e^{-50  PD}}{1 - e^{-50}}\right)

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

b= (0.11852 - 0.05478  \ln(PD))^2

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

K= \left[\mbox{LGD} \, N\left(\sqrt{\frac{1}{1-R}}  G(\mbox{PD}) +\sqrt{\frac{R}{1-R}} G(0.999)\right) -  (\mbox{LGD} \, \mbox{PD})\right]  \frac{1+(M-2.5) b}{1-1.5 b}

Risk-weighted assets

RWA = K  12.5  EAD


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

R = 1.25 * [0.12  \frac{1 - e^{-50  PD}}{1 - e^{-50}} + 0.24 \left(1- \frac{1 - e^{-50  PD}}{1 - e^{-50}}\right) ]

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

R = 0.12  \frac{1 - e^{-50 * PD}}{1 - e^{-50}} + 0.24 \left(1- \frac{1 - e^{-50  PD}}{1 - e^{-50}}\right)  - 0.04  (1-\frac{\max(S-5,0)}{45})

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

R = 0.15

Capital Requirement

K=LGD  \left[N\left(\sqrt{\frac{1}{1-R}}  G(PD) +\sqrt{\frac{R}{1-R}} G(0.999)\right) -  PD\right]

Risk-weighted assets

RWA = K  12.5  EAD

Qualifying revolving retail exposures (credit card products)

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

QRRE Correlation Assumption

R = 0.04

Capital Requirement

K=LGD  \left[N\left(\sqrt{\frac{1}{1-R}}  G(PD) +\sqrt{\frac{R}{1-R}} G(0.999)\right) -  PD\right]

Risk-weighted assets

RWA = K  12.5  EAD

References

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