# asrf

Asymptotic Single Risk Factor (ASRF) capital

## Description

`[`

computes regulatory capital and value-at-risk using an ASRF model.`capital`

,`VaR`

] = asrf(`PD`

,`LGD`

,`R`

)

The ASRF model is useful because the Basel II documents propose this model as the standard for certain types of capital requirements. ASRF is not a Monte-Carlo model, so you can quickly compute the capital requirements for large credit portfolios. You can use the ASRF model to perform a quick sensitivity analysis and exploring "what-if" scenarios more easily than rerunning large simulations.

`[`

adds optional name-value pair arguments. `capital`

,`VaR`

] = asrf(___,`Name,Value`

)

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

The capital requirement formula for exposures is defined as

$$\begin{array}{l}VaR=EAD*LGD*\Phi \left(\frac{{\Phi}^{-1}(PD)-\sqrt{R}{\Phi}^{-1}(1-VaRLevel)}{\sqrt{1-R}}\right)\\ capital=VaR-EAD*LGD*PD\end{array}$$

where

`ϕ`

is the normal CDF.

`ϕ`

^{-1} is the inverse normal
CDF.

`R`

is asset correlation.

`EAD`

is exposure at default.

`PD`

is probability of default.

`LGD`

is loss given default.

## References

[1] Basel Committee on Banking
Supervision. *"International Convergence of Capital Measurement and Capital
Standards."* June, 2006 (https://www.bis.org/publ/bcbs128.pdf).

[2] Basel Committee on Banking
Supervision. *"An Explanatory Note on the Basel II IRB Risk Weight
Functions."* July, 2005 (https://www.bis.org/bcbs/irbriskweight.pdf).

[3] Gordy, M.B. "A Risk-Factor Model Foundation for Ratings-Based Bank Capital
Rules." *Journal of Financial Intermediation.* Vol. 12, pp.
199-232, 2003.

## Version History

**Introduced in R2017b**