Prudential Regulation Authority Rulebook

1.

The variance of the loss distribution of type 1 exposures as referred to in 3E13.4 must be equal to the sum of V_inter and V_intra.

2.

A firm must calculate V_inter in accordance with the following formula:

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

where:

1. (a) the sum covers all possible combinations (j,k) of probabilities of default on single name exposures in accordance with 3E12; and
2. (b) TLGD_j and TLGD_k denote the sum of loss-given-default on type 1 exposures from counterparties bearing a probability of default PD_j and PD_k respectively.

3.

A firm must calculate V_intra in accordance with the following formula:

$$V_{intra}=\sum _j\frac{1.5\cdot {PD}_j\cdot (1-{PD}_j)}{2.5-{PD}_j}\cdot \sum _{{PD}_j}{LGD}_i^2$$

where:

1. (a) the first sum covers all different probabilities of default on single name exposures in accordance with 3E12;
2. (b) the second sum covers all single name exposures that have a probability of default equal to PD_j; and
3. (c) LGD_i denotes the loss-given-default on the single name exposure i.