User:Frühstücksdirektor/sandbox

In the formulas below, ,
 * N(x) denotes the normal cumulative distribution function
 * G(z) denotes the inverse cummulative distribution function
 * PD is the probability of default
 * LGD is the loss given default
 * EAD is the exposure at default
 * M is the effective maturity

Corporate Exposure
The exposure for corporate loans is calculated as follows

Correlation

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

Maturity adjustment

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

Capital requirement

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

Risk-weigthed assets

 * $$RWA = K * 12.5 * EAD

$$

Corporate exposure adjustment for SME
For Small and Medium Enterprises with Sales between 5 and 50 Million Euros, the correlation needs to be adjusted as follows:

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{S-5}{45})

$$ In the above formular, S is the Enterprise's Sales in Million Euros.

Residential mortgage exposure
The exposure related to residential mortgages can be calculated as this

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 exposure (credit card product)
The exposure related to unsecured retail credit products can be calculated as follows:

Correlation

 * $$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

$$