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Cross-Currency Basis in FX Forward Curve Construction

Article Quant Q&A · Author: Quant.Geek
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Summary

The document explains why interest rate parity using two money market curves and spot FX may not reproduce traded FX forward prices. A cross-currency basis captures the difference between the parity-implied result and market pricing, reflecting funding conditions that can diverge from quoted reference rates. The answer argues that replacing LIBOR curves with overnight reference rates does not remove this basis and may make the discrepancy more visible, especially when dollar funding liquidity is limited.

The basis is described as variable rather than fixed, with reporting cycles, credit spreads, and institutional currency funding needs among its drivers. The practical suggestion is to calculate the basis implied by overnight curves and compare its effect on forward prices with market spreads and client needs. The discussion is qualitative: it gives no calibration procedure, data sample, or quantified impact, and notes that implementation may depend on proprietary analysis or software.

Key ideas

  • Interest rate parity alone may not match observed FX forward prices because funding costs differ from reference rates.
  • Cross-currency basis swaps provide a market measure of that pricing difference.
  • The basis can vary with liquidity, credit spreads, and institutional reporting and funding cycles.
  • Assess the basis using overnight curves and determine whether its impact matters for the client’s pricing context.

Tags

ForexFixed incomeArbitrageRisk management
Full text
# Constructing an FX forward curve


# Constructing an FX forward curve












A lot of our clients are currently using interest rate parity as a means of constructing an FX forward curve. For instance, to construct the USD-GBP FX Forward curve, they are using the USD LIBOR, GBP LIBOR and the spot FX rates to determine the forward FX rate. Since the LIBOR curves are going away and are going to be replaced with overnight rates (SOFR and SONIA), are there any thought on how this is going to impact them? How are FX Forward curves going to be built after the conversion in 2021..

Thanks for the responses...

## Answer by Phil H (score 4)

https://quant.stackexchange.com/a/46409

## Interest rate parity is not sufficient now

There is a cross currency basis between the IRP result and observed market prices, because essentially Libor does not represent the cost of funding; in particular the implied USD funding rate deviates significantly from the USD Libor.

Cross currency basis (as a swap) is a traded quantity which covers that difference.

## Yes, it will change, and the difference will be more apparent

Using the overnight rates (whether the current ones or the new reference rates like SOFR) the basis is even more apparent, particularly when there is a lack of liquidity in the USD market. Attempting to use IRP to price FX is even worse in this scenario.

The rates are already available, so you can try the experiment now; calculate the implied rates and compare to market rates. Again USD is the most indicative.

## The basis is not straightforward, not static, and varies over the reporting cycle

Many such kinds of basis are largely static, but the cross currency basis is blown by many winds, including reporting cycles, credit spreads, and so on. The FX forward market is used extensively by institutions to fund their need for currencies for reporting, which is particularly apparent with USD where they do not have access to overnight rates. As a result, the no-arbitrage conditions on which interest rate parity is based do not apply, and the effective funding rates deviate from the overnight rates strongly.

## Decide whether it matters to your client

Perhaps they will not mind a gap between their implied FX and the market prices; evidently they do not mind at present. I would suggest analysing the basis from the overnight rates and looking at how much such a basis would move the actual calculated prices. If they do not move them by enough for the client to care (e.g. if the spreads on prices are wide and the maturities are short), then they may be able to avoid making any significant changes (beyond repointing at different swaps) for now.

It may not surprise you to know that getting the calculation right is the subject of a lot of proprietary analysis and 3rd party software :)

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.