FRTB Basic Approach for CVA (BA-CVA, BCBS 325)

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Contribution of credit spread variability - 2 of 2

In the most general case, when both direct and indirect single-name CDS as well as index hedges are present, Kspread is calculated according to:

$K_{s p r e a d} = \sqrt{{(ρ \sum_{c} (S_{c} - \sum_{h \in c} r_{h c} S_{h}^{S N}) - \sum_{i} S_{i}^{i n d})}^{2} + (1 - ρ^{2}) {\sum_{c} (S_{c} - \sum_{h \in c} r_{h c} S_{h}^{S N})}^{2} + \sum_{c} \sum_{h \in c} (1 - r_{h c}^{2}) {(S_{h}^{S N})}^{2}}$
- $S_{h}^{S N} = R W_{b (h)} M_{h}^{S N} B_{h}^{S N}$ is the supervisory ES of price of single-name hedge $h$ .
- $S_{h}^{i n d} = R W_{b (i)} M_{i}^{i n d} B_{i}^{i n d}$ is the supervisory ES of price of index hedge $i$ .
- $b (e)$ is the supervisory risk bucket of entity $e$ (single-name or index).
- $B_{h}^{S N}$ is the discounted notional of single-name hedge $h$ .
- $M_{h}^{S N}$ is the remaining maturity of single-name hedge $h$ .
- $B_{i}^{i n d}$ is the discounted notional of index hedge $i$ .
- $M_{i}^{i n d}$ is the remaining maturity of index hedge $i$ .
- $r_{h c}$ is the correlation between the credit spread of counterparty $c$ and the credit spread of a single-name hedge $h$ of counterparty $c$ .