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Why FX Forward Bid and Ask Rates Use Twisted Conventions

Article Quant Q&A · Author: pqsn
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Summary

The document explains the economic reason bid and ask sides may appear reversed when deriving implied interest rates from an FX forward. A long AUD forward is described as a sequence: borrow USD, exchange USD for AUD at spot, and lend AUD. Each leg has its own bid-offer cost, so the forward quote reflects several transaction sides, while an interest-rate quote isolates a single borrowing or lending transaction. The bid and ask adjustments are intended to isolate the cost attributable to that rate input.

The answer also cautions that FX-forward-implied rates can differ from observed interest-rate swap rates, and points to cross-currency basis swaps as relevant context. It offers an economic explanation rather than a full derivation of the Bloomberg formulas: no equations, numerical example, or detailed convention treatment is included. The result depends on transaction direction and market quoting conventions, so the explanation should be mapped carefully to the specific currency pair and quote fields.

Key ideas

  • A long AUD forward can be decomposed into USD borrowing, a spot currency exchange, and AUD lending.
  • Each transaction leg contributes bid-offer costs to the forward quote.
  • An implied interest rate isolates one borrowing or lending component, which explains the bid-ask adjustments.
  • Forward-implied rates may differ from swap rates because of cross-currency basis effects.

Tags

ForexFixed incomeDerivatives pricingMarket microstructure
Full text
# Implied AUD Interest Rate from USDAUD FX Swap and USD Interest Rate


# Implied AUD Interest Rate from USDAUD FX Swap and USD Interest Rate












Can someone help me understand how to derive the implied interest rate or spot rate in BBG FXFA?

I actually get why the Forward rate, F_Ask and F_Bid are derived using the formula in the picture.

The problems are the other formula. I thought by rearranging the terms in the implied forward rate I can get the implied rate for AUD or USD or spot. But it appears the bid/ask need to be twisted as well.

Can someone help me with this? Probably using N_Bid formula as an illustration for its economic meaning.

Thanks in advance.

## Answer by Charles Fox (score 2, accepted)

https://quant.stackexchange.com/a/41806

The reason for the bid and ask twisting is that you can think of a long AUD forward as three transactions:

Borrow USD Sell USD, buy AUD spot Lend AUD

As a result, there are three sources of bid/offer cost for a forward. In contrast, for an interest rate, it's just one transaction (borrow or lend). This is why they twist those equations. They are trying to isolate the amount of the bid/offer attributable to that one source.

There will may be a gap between the implied interest rates and what you see for interest rate swaps. Reading about coss currency basis swaps may be of interest to you see here for example. I don't currently use a Bloomberg Terminal, but I think the command to see some of the cross currency basis levels is XCCY.

The above info is for educational purposes only, not investment advice.

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.