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Constructing Synthetic FX Cross Rates with Bid and Ask Quotes

Article Quant Q&A · Author: xyzt
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Summary

The document explains how to construct EUR/USD from EUR/GBP and GBP/USD spot quotes. With the quoted currency legs aligned as EUR per GBP and GBP per USD, multiplying the rates cancels the intermediate GBP exposure and yields EUR per USD. It states that the ask cross is formed from the two ask quotes and the bid cross from the two bid quotes, and the response confirms this convention for a cross through a common currency.

This is a practical quote-construction rule for checking a synthetic currency pair against an observed market rate. Correct application depends on consistent quote orientation and units: if a leg is quoted in the inverse direction, the rate and bid/ask sides must be inverted appropriately. The source provides the formula and a brief confirmation, but no worked prices, execution example, or discussion of spreads, liquidity, or arbitrage costs. Those factors matter when comparing a calculated cross with a tradable market quote.

Key ideas

  • A cross rate can be built by multiplying two exchange rates that share an intermediate currency.
  • The intermediate currency cancels when the quote directions and units are aligned.
  • The cross ask uses the component ask quotes, and the cross bid uses the component bid quotes under the stated orientation.
  • Inverse quote conventions require reversing the rate and handling bid and ask sides consistently.
  • Market spreads and liquidity affect whether a calculated cross is executable.

Tags

ForexArbitrageExecution
Full text
# synthetic currency pair


# synthetic currency pair












I want to generate price of a synthetic currency pair. For example, I have EURGBP, GBPUSD prices and I want to generate EURUSD price. I preferred to use these already existing currency pairs to verify the calculation.

EURUSD(ask) = EURGBP(ask) * GBPUSD(ask)

EURUSD(bid) = EURGBP(bid) * GBPUSD(bid)

Is this correct?

Thanks in advence

## Answer by rupweb (score 1)

https://quant.stackexchange.com/a/37972

You can see how to calculate cross currency rates at FX and MM training

disclaimer I authored the page

## Answer by 0xFEE1DEAD (score 1)

https://quant.stackexchange.com/a/40549

Yes, that's correct:

> Formula 5.2 (FCa / FCb)ask = (FCa / DC)ask ×(DC/FCb)ask (FCa / FCb)bid = (FCa / DC)bid ×(DC/FCb)bid Where FCa and FCb are the two foreign currencies and DC is the domestic currency.

source: https://www.investopedia.com/exam-guide/cfa-level-1/global-economic-analysis/spot-market.asp

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.