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How Carry, Basis, and Collateral Affect Cross-Currency Swap CVA

Article Quant Q&A · Author: Alex
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Summary

The document discusses why a cross-currency swap paying euros and receiving dollars may have different credit valuation adjustment (CVA) from the reverse position. One explanation focuses on the final notional exchange: forward currency values, influenced by the interest-rate differential under covered interest rate parity, can make the bank’s position a net receivable. Receivables create counterparty exposure and can therefore contribute more to CVA than payables.

A second explanation points to a generally negative EUR/USD basis and the exposure associated with being short dollars on the notional exchange. The answers stress that the result is not universal: the swap’s cash-flow direction and the collateral agreement, including which currency may be posted, matter. The discussion offers qualitative mechanisms, not a numerical comparison or a complete CVA calculation, so the actual result depends on transaction terms and market conditions.

Key ideas

  • The final notional exchange can dominate a cross-currency swap’s exposure and CVA.
  • Forward currency values reflect interest-rate differentials under covered interest rate parity.
  • A negative EUR/USD basis may affect exposure on the dollar-short side of the notional exchange.
  • The collateral agreement, including eligible collateral currencies, can change the comparison.
  • The direction of the swap alone does not establish a universal CVA ranking.

Tags

Fixed incomeForexRisk managementDerivatives pricing
Full text
# Why might a cross currency swap from EUR into USD have higher CVA than a cross currency swap from USD into EUR?


# Why might a cross currency swap from EUR into USD have higher CVA than a cross currency swap from USD into EUR?












I was having a discussion with a colleague in the industry, who mentioned in passing that CVA on a cross currency swap from EUR into USD (pay EUR) is always higher than if paying USD and receiving EUR... why?

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/61684

The CVA on a cross currency swap comes mostly from the final exchange (being the biggest flow). If you as an end user are paying the EUR, then the bank is receiving the EUR a d paying the USD. They will see that this position is a net receivable, because EUR is more valuable on a forward basis than spot. Receivables attract a higher CVA than payables. (The reason EUR is valued more highly on forward dates is due to the interest rate differential between EUR and USD. See covered interest rate parity ).

## Answer by user35980 (score 0)

https://quant.stackexchange.com/a/61683

If by paying EUR you mean on the initial exchange you are short USD vs long EUR i.e. you're short USD forward, then a simple explanation might be the higher CVA is coming from the fact that the EUR/USD basis is generally negative (i.e. USD demand exceeds EUR demand). Hence the expected exposure is more material to the short USD position on notional exchange (offsetting any effect of the higher rate payer's position).

## Answer by Animesh Saxena (score 0)

https://quant.stackexchange.com/a/61700

It will also depend on the kind of CSA. For example if does it allow posting of collateral in EUR?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.