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Currency Basis Swaps Adjust FX Forward Rates Beyond Interest Parity

Article Quant Q&A · Author: gordon613
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Summary

The explanation connects currency basis swap (CBS) rates to FX forward pricing in the Garman–Kohlhagen currency option model. A forward rate can be taken directly from the FX forward market or derived from spot and the two currencies’ interest rates using covered interest parity (CIP). When the parity calculation differs from traded forward prices, applying the relevant currency basis adjusts the interest-rate inputs so the implied forward better reflects market pricing.

The document characterizes the CBS rate as a market-quoted measure of the gap between the CIP-implied relationship and observed FX market conditions. Its example of adding the non-USD currency’s basis to the USD rate describes one convention for correcting the inputs. It does not derive that sign convention, define quote or collateral conventions, or explain the economic causes of the CIP deviation. Those details matter in implementation, so the adjustment should be matched to the currency pair, market convention, and model setup rather than treated as universal.

Key ideas

  • FX forwards can be sourced from market quotes or calculated from spot and interest rates using covered interest parity.
  • Currency basis adjustments help align parity-based forward calculations with observed market pricing.
  • A basis quote reflects the gap between the theoretical parity relationship and market conditions.
  • The sign and placement of a basis adjustment depend on the quoting and modeling conventions.
  • The document notes that causes of deviations from covered interest parity require separate analysis.

Tags

ForexOptionsDerivatives pricingFixed incomeArbitrage
Full text
# Why is CBS (Currency Basis Swaps) added to Interest Rates?


# Why is CBS (Currency Basis Swaps) added to Interest Rates?












We are trying to analyze an algorithm (internal to our company) to calculate currency option pricing using the Garman and Kohlhagen model.

Our internal algorithm calls for CBS (Currency Basis Swaps) rates to be added to interest rates in the following manner.

> Add to the USD interest rate the CBS rate for the non-USD currency.

Can anyone explain the logic for taking the CBS rate in the model? There is unfortunately no documentation in our code.

## Answer by nbbo2 (score 2, accepted)

https://quant.stackexchange.com/a/53948

This is an issue that arises in the calculation of currency forward rates:

- You could simply take the Forward Rate from the FX Forward market, as "the market is always right" ;)

- You could calculate the Forward Rate from the Spot Rate and the Interest Rates in the 2 countries. This relies on the CIP Formula (Covered Interest Parity) which until 2008 was believed to be highly accurate... However you would get a Forward Rate different from the actual rate in the market and hence not accurate. The solution is as you indicated: by adding the CBS in this manner you correct for the malfunction in the CIP relation and recover the correct forward rate. The CBS is quoted in the market and measures the discrepancy between the CIP theory and the current state of the FX market.

There are many posts here and elsewhere as to the causes of the discrepancy between the CIP and real life. Which is a separate and more complicated subject.

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.