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Using Interest Rate Parity to Derive an FX Forward Curve

Article Quant Q&A · Author: new_fin_guy
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Summary

The document asks how to construct an FX forward curve from basic concepts such as interest rates and discounting, using EUR/USD as an example. It raises the roles of instruments such as IMM dates and overnight index swaps, but the response does not explain how to bootstrap a complete curve from those instruments.

The answer gives a brief relationship for deriving a short-dated implied local-currency rate from the spot rate, swap points, a USD curve, and the local day-count convention. This points to interest rate parity as the connection between forward pricing and the two currencies’ interest rates. The expression is only a sketch for a seven-day point; it does not address instrument selection, curve construction across maturities, collateral conventions, or practical calibration. Readers should treat it as an initial relationship rather than a complete recipe for building an FX curve.

Key ideas

  • FX forward prices can be related to the currencies’ interest rates through interest rate parity.
  • The response sketches a short-tenor implied-rate calculation using spot, swap points, and a USD curve.
  • Local day-count conventions affect the conversion of the implied rate.
  • The answer does not provide a full multi-tenor curve-building procedure or explain the roles of IMM and OIS instruments.

Tags

ForexFixed incomeDerivatives pricing
Full text
# How to build an FX curve?


# How to build an FX curve?












Apologies for the rather broad question! Essentially, I wanted to ask how to build an FX forward curve from scratch. I have some basic understanding of interest rates and discounting but I am lacking the theoretical and practical knowledge to figure out how it fits together to result in an EUR/USD SP to 2Y curve, for example. How roles do instruments like IMM, OIS, etc play in it?

Any links to/names of books, courses, tutorials, etc will be more than welcome. There is quite a lot of information out there but I am really struggling with where to start.

Thanks a lot in advance!

## Answer by Josh Chien (score 0)

https://quant.stackexchange.com/a/71212

I'm not sure whether below answer is you want. FX Curve, in general, means the curve is implied from based on USD by Interest Rate Parity (IRP). FX Curve(7D) = ((1+swap point/spot)*(1+USDCurve * 7/360)-1)*local currency convention(360or365) / 7

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.