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Estimating Short-Dated Cross-Currency Basis from FX Forwards

Article Quant Q&A · Author: kfan
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Summary

The document explains how to estimate a short-dated EUR/USD cross-currency basis from spot and forward FX rates together with the relevant interest rates. It applies covered interest rate parity: the forward rate and the euro rate imply a dollar borrowing rate, whose difference from the observed dollar rate gives the basis spread. The relationship is rearranged to show the implied rate and resulting spread, using a day-count fraction for the tenor.

The explanation describes an approach used when reading Bloomberg’s ICVS page with FX forwards, and distinguishes that approach from using directly quoted basis spreads. It does not provide numerical inputs or a worked market example, and it points to separate material for an exact Bloomberg function replication. The formula shown assumes the stated simple-rate convention and day-count basis; conventions and curve construction may matter for matching a vendor quote precisely.

Key ideas

  • Covered interest rate parity links spot FX, forward FX, and the two currencies’ interest rates.
  • The forward rate and euro interest rate imply a dollar borrowing rate.
  • The cross-currency basis is calculated as the implied dollar rate minus the observed dollar rate.
  • Direct market basis quotes may be available, while FX forwards can also be used to infer the spread.

Tags

ForexFixed incomeArbitrage
Full text
# Bloomberg ICVS92 Cross Currency Basis


# Bloomberg ICVS92 Cross Currency Basis












Can someone help me understand how Bloomberg computes the Cross currency basis, for maturity < 1 year?

On the ICVS 92 (EUR vs. USD basis) page, we can see the CC basis mid (I don't have access to bloomberg at the moment and I am not able to provide a better picture):

The white paper on building bloomberg curves tells me that the basis is calculated by solving for CIP. But since it doesn't have a nice example, I failed to replicate the basis. Does someone know what data should I use and what would be the close formula for the CC basis swap? Or how to solve for it? Right now, I'm using zero rates provided in ICVS 92 and ICVS 490 (for the USD side), spot EUR-USD and FX Forward quoted on ICVS 92.

Thanks in advance.

## Answer by AKdemy (score 3)

https://quant.stackexchange.com/a/82431

It's worth noting that usually you have market quotes for cross currency basis spreads.

If you select to use FX forwards, as in the picture, it uses the same logic as FXFA, which is the function that the link in the comment mentions.

If you don't have access to Bloomberg, I am not sure what use this exercise has?

This approach uses the implied borrowing cost derived from covered interest rate parity (using spot, forward points, which can be found on FRD, and the other interest rate). The difference between the implied rate and the actual interest rate is the basis.

$${{S_{t}}}\frac {(1+i_{\ $}*\frac{k}{360})}{(1+i_{\ €}*\frac{k}{360})} = F_{t+k}$$, hence $$i_{\ $_{implied}} = \left(\frac {F_{t+k}*(1+i_{\ €}*\frac{k}{360})}{S_t} -1 \right)/\frac{k}{360}$$

rearranging a bit gives $$i_{\ $_{implied}} = \frac{360}{k} \left(\left(\frac{F_{t+k}}{S_t} \right) * \left(1+i{_\ €}*\frac{k}{360} \right) -1 \right)$$

and subtracting the yield provides the $$ Basis \ Spread = \left[\frac{360}{k} \left(\left(\frac{F_{t+k}}{S_t} \right) \left(1+i{_\ €}*\frac{k}{360} \right) -1 \right) \right] - i_{\ $}.$$

An exact replication of FXFA can be found on https://quant.stackexchange.com/a/76971/54838.

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.