Article 201 - Variance of the loss distribution of type 1 exposures

1.The variance of the loss distribution of type 1 exposures as referred to in paragraph 4 of Article 200 shall be equal to the sum ofVinterandVintra.

2.V_inter shall be equal to the following:

$$V_{\mathrm{inter}} = \sum_{(j,k)} \frac{\mathrm{PD}_{\mathrm{k}}\frac{\mathrm{PD}_{k} \cdot (1 - \mathrm{PD}_{\mathrm{k}})\mathrm{PD}_{k}) \cdot \mathrm{PD}_{\mathrm{j}}\mathrm{PD}_{j} \cdot (1 - \mathrm{PD}_{\mathrm{j}})}{1.25\mathrm{PD}_{j})}{1.25 \cdot (\mathrm{PD}_{\mathrm{k}}(_{\mathrm{PD}_{k}} + \mathrm{PD}_{\mathrm{j}})\mathrm{PD}_{j}) - \mathrm{PD}_{\mathrm{k}}\mathrm{PD}_{k} \cdot \mathrm{PD}_{\mathrm{j}}}\mathrm{PD}_{j}} \cdot \mathrm{TLGD}_{\mathrm{j}}\mathrm{TLGD}_{j} \cdot \mathrm{TLGD}_{\mathrm{k}}$$\mathrm{TLGD}_{k}$$

where:

(a)the sum covers all possible combinations (j,k) of probabilities of default on single name exposures in accordance with Article 199;

(b)TLGD_j and TLGD_k denote the sum of losses -given- default on type 1 exposures from counterparties bearing a probability of default PDj and PDk respectively.

3.V_intra shall be equal to the following:

V_{\mathrm{intra}} = \sum_{\mathrm{j}} \frac{1.5 \cdot \mathrm{PD}_{\mathrm{j}} \cdot (1 - \mathrm{PD}_{\mathrm{j}})}{2.5 - \mathrm{PD}_{\mathrm{j}}} \cdot \sum_{\mathrm{PD}_{\mathrm{j}}} \mathrm{LGD}_{\mathrm{i}}^2

where:

(a)the first sum covers all different probabilities of default on single name exposures in accordance with Article 199;

(b)the second sum covers all single name exposures that have a probability of default equal to PD_j;

(c)LGD_i denotes the loss-given-default on the single name exposure i.