CS01 is also called credit DV01 (CDV01)1. The value depends on which spread is moved. The set of values from moving each maturity's spread by 1bp one at a time is the bucketed CS01, and the value from moving all of them together is the parallel CS01. The sum of the bucketed values does not exactly equal the parallel value because the bump is finite.
Consider a hypothetical example in which a holder has a CDS with a CS01 of 20,000 yen per 1bp. The holder gains 200,000 yen if the spread rises 10bp and loses 200,000 yen if it falls 10bp. This is an estimate for small moves, and the value changes for large moves.
DV01 is the change in value for a 1bp rise in interest rates, and CS01 is the change for a 1bp rise in the credit spread. The same idea is applied to CVA as the change when the counterparty's spread moves by 1bp. The Basel Committee's standardized approach for CVA calculates required capital from the change in CVA when a risk factor moves by a set amount (the sensitivity).
Notes
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OpenGamma Quantitative Research, "The Pricing and Risk Management of Credit Default Swaps, with a Focus on the ISDA Model". ↩