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Inverting FX Forward Quotes and Understanding Bid-Ask Rates

Article Quant Q&A · Author: rupweb
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Summary

The document explains how to invert a two-way FX forward quote when changing the currency pair’s direction. Its example asks whether the reciprocal of the EURUSD bid and offer gives the corresponding USDEUR market. The answer confirms inversion, with the quote sides reversing because the trade direction changes. Deposit and loan rates underpin the bid and offer; all four relevant lending and deposit rates are already reflected in the original two-way FX prices.

It also distinguishes a single interest-rate differential from the inputs needed to calculate a bid-offer market. Given one rate per currency, the differential can support a single theoretical forward rate, but it cannot establish both sides of a quote without deposit and loan rates. The exchange illustrates the quote mechanics but does not develop the forward-pricing formula, specify conventions, or address market frictions beyond the rate spreads described.

Key ideas

  • To reverse an FX pair, take reciprocals of the original forward bid and offer and reverse their quote sides.
  • Deposit and loan rates contribute to the two-way FX forward spread.
  • A single interest rate for each currency provides a differential for a single forward rate.
  • Bid and offer pricing requires the separate deposit and loan rates for both currencies.
  • The explanation does not cover detailed pricing conventions or additional market frictions.

Tags

ForexDerivatives pricingArbitrage
Full text
# can an fx forward price simply be divided into 1 to quote the inverse?


# can an fx forward price simply be divided into 1 to quote the inverse?












Qu 1. Say I ask for EURUSD 1 week and get prices: 1.120986 / 1.120216

Does that mean to price USDEUR 1 week I can divide 1 / 1.120216 and 1 / 1.120986 and get rates: 0.8921 / 0.8927

Or is that result wrongly pitched according to the facts there's a bid/offer spread in the EUR interest rate to USD interest rate differential, and that the inverse of the EURUSD interest rate differential is not the same as the USDEUR interest rate differential? i.e. to get the inverse of the forward price the deposit and loan rates need to be swapped. The deposit and loan rates being the rates the FX forward rates correlate with to prevent arbitrage between FX markets and money markets.

Qu 2. If EUR 1 week LIBOR is -0.16286% and USD 1 week LIBOR is 0.15375% then what's the interest rate differential between them? (source http://www.global-rates.com/interest-rates/libor/european-euro/euro.aspx)

## Answer by RaveTheTadpole (score 2, accepted)

https://quant.stackexchange.com/a/20989

Yes, you can just invert (i.e. `1/x`) the EURUSD quotes to get the USDEUR bid and offer, as you did in your example.

Deposit and loan rates are really just bids and offers for deposits. The difference between them is what creates the bid-offer difference in the fx prices. All 4 rates (USD loan, USD deposit, EUR loan, EUR deposit) are used in the calculation of the bid and offer for EURUSD. All the information is already there. And inverting the fx rates reverses the direction of the trade, using all that same information.

Your second question is lacking the detail you need to create a bid and offer side. You quote a single rate for each currency, rather than their bids and offers (i.e. deposit and loan). So you can calculate a single forward fx rate, using the 0.3166% differential, but not a two-way market.

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.