Cross-Currency Basis Exposure with Third-Currency Collateral

Summary

The document examines the basis risks in a SEK–USD cross-currency swap collateralized in euros. It reasons from the collateral currency: discounting the SEK cash flows may involve a SEK–EUR basis, while discounting the USD cash flows may involve a USD–EUR basis. It then asks whether the swap also carries SEK–USD basis exposure and whether the sensitivities to the different basis moves are equal.

The text is an initial hypothesis, not a resolved explanation. It proposes that the combined currency relationships imply SEK–USD exposure and expects unequal sensitivity because the legs’ cash flows have different basis deltas. However, it provides no pricing equations, market data, or expert confirmation to establish that decomposition or quantify the risks. The discussion is useful as a framing of collateral-dependent discounting and basis risk, but the conclusions should be checked against the swap’s valuation framework and conventions.

Key ideas

• The collateral currency affects how each currency leg is discounted.
• With euro collateral, the author expects SEK–EUR and USD–EUR basis components to matter.
• The document hypothesizes an additional relationship to SEK–USD basis risk.
• It suggests sensitivities may differ across basis shocks, but does not demonstrate or quantify this claim.

Tags

# What is a CCS exposed to when collateral is in a 3rd currency?


# What is a CCS exposed to when collateral is in a 3rd currency?












Say I enter a SEK USD xCCY swap, however collateral is posted in EUR.

Does this have exposure to SEKUSD basis or SEKEUR basis or both?

If the answer is 'both', is the risk symmetric?

My attempt at an answer:

If collateral was in USD, then there's be risk to the SEKUSD basis (and this risk would enter via the discounting of the SEK cashflows that must contain a basis to USD).

However, if collateral is in EUR, then the discounting of the SEK cashflows must contain a basis to EUR instead. Likewise the USD cashflows will contain a basis to EUR.

So it seems we are exposed to the SEKEUR basis on the SEK leg and on the USDEUR basis on the USD leg, and therefore we must also be exposed to the SEKUSD basis.

Furthermore, the risks are NOT symmetric (100bps shock to SEKEUR basis does not affect me as much as a 100bps shock to USDEUR basis), since a shock to SEKEUR basis affects my SEK cashflows and a shock to the SEKUSD basis affects my EUR cashflows, and since the cashflows have different deltas to the basis (presumably?), the risk are not symmetric.

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.