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Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition by Jon Gregory

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16.4 Credit Hedges

We will now discuss the hedging of the credit component of CVA. Initially, the focus will be on single-name hedging assuming liquidity of CDS, referencing the counterparty. After this we discuss hedging with indices, which is more practical given the lack of depth in the single-name CDS market.

16.4.1 Credit Delta

Unlike a bullet structure, the credit spread hedging of the 5-year swap cannot be closely replicated with a 5-year CDS instrument. We first consider the sensitivity to the CDS spread, as shown in Figure 16.10. There is a significant impact across the CDS tenor. An increase in the 1-year CDS premium, for example, causes the 1-year default probability to increase and the 1-year to 2-year default probability to decrease. This means that the overall CVA will decrease since the EE is smaller in the first year compared with the second year – there is, therefore, a negative sensitivity at 1 year. An increase in the 3-year CDS will move default probability to the 2- to 3-year region from the 3- to 4-year region, where the EE is higher, and therefore creates a positive sensitivity. The impact of changes to the shape of the CDS curve (flat curve versus upwards-sloping curve) has little impact on the CDS risk. This emphasises that the term structure impact arises almost entirely from the EE profile of the swap.

Figure 16.10 Sensitivity of the interest rate swap CVA to changes in CDS premiums of various maturities (represented in terms of CDS notional). The 5-year ...

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