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FRM Part II · FRM Exam Part II · Credit Value Adjustment

A bank hedges the credit-spread risk of its CVA on a 5-year interest rate swap book by buying CDS protection with a fixed notional equal to today's expected exposure. Over the next year, interest rates move so that the swap exposure rises sharply, while the counterparty's spread is unchanged. What is the most likely consequence for the hedge?

The fixed-notional CDS under-hedges, because higher swap exposure raises CVA and its sensitivity to the spread while the CDS notional stays fixed. The bank is left with residual credit-spread risk and must rebalance, which means a dynamic hedge with exposure-driven (market-risk) mismatch.

  1. AThe hedge is over-hedged because CVA falls when exposure rises
  2. BThe CDS notional now under-hedges the larger CVA, leaving residual spread riskCorrect
  3. CThe hedge fully adjusts automatically because CDS notional floats with exposure
  4. DThe hedge creates gamma-free protection against exposure changes

Explanation

CVA is roughly spread times expected exposure, so higher exposure raises CVA and its spread sensitivity. A fixed-notional CDS no longer covers it, leaving the bank under-hedged. This is a cross-gamma or exposure-driven mismatch, and the CDS notional does not adjust automatically.

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