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Cross-Currency Basis and Three-Month FX Forward Points

Article Quant Q&A · Author: mateusk
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Summary

The document explains why a simple interest-rate-differential formula may fail to match observed three-month FX forward points. It identifies cross-currency basis as the key market adjustment that emerged prominently after the global financial crisis. The underlying issue is that market participants cannot necessarily borrow or lend unlimited amounts at the quoted three-month rates, and their funding costs can differ by currency.

The answer outlines a valuation approach that chooses a funding currency and a discount curve in that currency. Cash flows in the funding currency are discounted on that curve; cash flows in another currency are converted through a cross-currency swap before discounting. This offers a conceptual explanation for the discrepancy, but the document does not provide the rates, quote conventions, curve-building steps, or a worked numerical calculation needed to compute specific forward points. Actual results depend on the selected curves and market basis.

Key ideas

  • The simple spot and interest-rate differential formula may not match market FX forward points.
  • Cross-currency basis reflects differences in funding access and costs across currencies.
  • A valuation can select one currency as the funding currency and use its curve for discounting.
  • Other-currency cash flows can be swapped into the funding currency before discounting.
  • The document explains the adjustment conceptually but does not give a numerical pricing example.

Tags

ForexDerivatives pricingFixed income
Full text
# How to calculate the Fx Forward Points for 3M


# How to calculate the Fx Forward Points for 3M












I'm trying to find the FX Forward Points for 3M, the same as in the table. However, in the conventional way (Forward points = Spot x (USD Rate - EUR Rate) x 90/360) I get a different result.

Can anyone help me with this?

## Answer by Lliane (score 1, accepted)

https://quant.stackexchange.com/a/53365

That conventional way of pricing forwards doesn't work since the great financial crisis, there is something called the cross currency basis. Basically market participants cannot borrow or lend unlimited amounts at the 3m interest rates.

It's realtively well explained on Wikipedia https://en.wikipedia.org/wiki/Currency_swap

> It is well recognized[4][5] that traditional "textbook" theory does not price cross currency (basis) swaps correctly, because it assumes the funding cost in each currency to be equal to its floating rate, thus always giving a zero cross currency spread. This is clearly contrary to what is observed in the market. In reality, market participants have different levels of access to funds in different currencies and therefore their funding costs are not always equal to LIBOR. An approach to work around this is to select one currency as the funding currency (e.g. USD), and select one curve in this currency as the discount curve (e.g. USD interest rate swap curve against 3M LIBOR). Cashflows in the funding currency are discounted on this curve. Cashflows in any other currency are first swapped into the funding currency via a cross currency swap and then discounted.[5] See Interest rate swap § Valuation and pricing for further discussion, as well as a description of the related curve build.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.