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Why EURUSD Swaps Can Have EUR 3s6s Basis Sensitivity

Article Quant Q&A · Author: Always_Student
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Summary

The note explains why a EURUSD cross-currency swap can carry sensitivity to the EUR 6-month versus 3-month basis, in addition to USD LIBOR, EURIBOR, and the currency exchange rate. The explanation links the basis exposure to how the EUR leg is built: longer-dated EUR interest rate swaps commonly use 6-month Euribor, so a 3-month leg in the cross-currency basis swap may be represented using a 6-month swap plus EUR 3s6s basis.

It also mentions discounting effects from overnight indexed rates, such as EONIA or Fed Funds, which can introduce further basis sensitivities. Those discounting-related exposures are generally smaller than the forward-rate sensitivities. The discussion is a brief conceptual answer rather than a full valuation breakdown; actual sensitivities depend on the swap’s construction and market conventions.

Key ideas

  • EURUSD cross-currency swaps can be sensitive to EUR 3s6s basis as well as their main rate and FX factors.
  • A 3-month EUR leg may be represented using a 6-month Euribor swap plus a 3s6s basis component.
  • Overnight discounting can add EONIA or Fed Funds related basis exposure.
  • Discounting-related sensitivities are usually smaller than forward-rate sensitivities.

Tags

Fixed incomeForexDerivatives pricingRisk management
Full text
# Factor sensitivities for EURUSD swap


# Factor sensitivities for EURUSD swap












Trying to understand various risk factors for a EURUSD swap.

While I understand why a EURUSD swap would have USD LIBOR, EURIBOR, EURUSD currency as risk factors, why is it that it would also have EUR 6M3M sensitivity?

Thank you in advance!

## Answer by Phil H (score 0, accepted)

https://quant.stackexchange.com/a/26018

The dominant IRS float tenor at longer maturities for EUR is 6m Euribor. So we assume that the EUR 3m leg of the xccy basis swap is constructed from a 6m IRS and therefore also 3s6s EUR basis.

In the interbank world there will also be risk contributions from the EONIA or FedFund discounting, via OIS or again basis (3sOIS). These sensitivities are generally much smaller than the forward rate sensitivities.

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.