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.
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.