hard · FRM Part 2 Credit Risk
A dealer computes unilateral CVA on an uncollateralized interest-rate swap with a corporate that has only out-of-the-money (negative) expected exposure to the dealer at every future date except a brief window. The desk then signs a CSA with zero threshold, zero minimum transfer amount, and instantaneous collateralization, eliminating residual exposure, and the trader concludes CVA falls to zero and the swap's fair fixed rate is unaffected.
Which critique is correct?
- The conclusion ignores that perfect collateralization converts counterparty credit risk into funding cost, so CVA is replaced by a funding valuation adjustment (FVA) on the collateral, which generally does not net to zero and shifts the fair rate
- The conclusion is correct: a zero-threshold, zero-MTA, continuously margined CSA eliminates residual exposure, so CVA, DVA, and FVA all vanish together and the fair fixed rate equals the risk-free swap rate exactly under this arrangement.
- The conclusion is wrong because CVA cannot simply be reduced by posting collateral; only the counterparty's default probability term, never the underlying exposure term, actually drives CVA, and signing a CSA does not change the counterparty's hazard rate.
- The conclusion is wrong because even perfect, instantaneous collateralization still leaves residual gap risk equal to the full expected positive exposure over the margin period, so CVA remains unchanged while a fresh FVA term is additionally introduced.
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