Asymptotic Single Risk Factor (ASRF) capital

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

`ɸ`

is the normal CDF.

`ɸ`

^{-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.

[1] Gordy, M.B. "A risk-factor model foundation for ratings-based bank capital
rule." *Journal of Financial Intermediation.* Vol. 12, pp.
199-232, 2003.