# Interpolating FX forward points

When computing an FX forward rate for an expiry that is not explicitly quoted, it seems to me that a reasonable way to do it is log-linear interpolation of the two nearest outright forward rates, which would correspond to assuming continuous compounding at a constant rate in both currencies. However, it seems that it is common to calculate this rate by linear interpolation (e.g., see this tutorial, page 12).

What is most commonly done in practice by FX traders?

Most common practise is to linearly interpolate. Log-linear would be wrong; forward points are commonly negative, and are merely a delta on the Spot. Closer would be log-linear on the outrights (Spot plus forward points), but even that is not worth bothering with.

If you have some idea of the shapes of the underlying yield curves, you can work out which are the more and less expensive days in the run and price accordingly.

If you don't know the relative yield curve shape, then there's no point in doing anything but linear interp since you're already approximating, and the convention is linear. I believe the phrase is 'you can't polish a ...'

The interesting question is really 'which underlying yield curves?'

• That comment at the end about yield curves really gets at the crux of the matter, particularly at the longer end of the forward curve when less liquid (or none at all) forwards are available.
– John
Sep 5, 2012 at 16:29
• As far as I know (and that's not much) forwards should compensate the arbitrage you could obtain if you exchange the money to a foreign currency and you get the interest rates of the other currency instead of the interests on your own currency. Interest rates are exponential (aren't they?). Therefore, I think that if we use linear interpolation to approximate an exponential function some (very small) arbitrage situations will be created, won't they? Feb 25, 2021 at 9:54
• @xavier: If the interest rate curves are flat in both currencies, and if the cash rates are correct and the spreads are narrow, and if there is no hidden cross currency demand bias change between the points, then sure. Feb 25, 2021 at 11:01

As Phil H mentioned, linearly interpolate them is what many traders will do.

Alternatively, if you look at deposit rates, you can try to imply either a spread on one leg or a rate on one leg and interpolate this rate. I did not do this since quite a long time but you should find that the results are not too different.

If I remember correctly usually the bid ask is fairly large for longer maturities, so you have not much chances to cross someone.

• The classic arb is to use depos on both currencies. Unfortunately that arb no longer holds and there is a basis involved. Also, depos are calendar dated, and FX fwds are calendar dated, so there is no extra definition of the cash curve between the FX dates as required. OIS rates, though, have meeting date definition. Sep 6, 2012 at 12:15
• Do you happen to really see arbs ? When I was working on a swap desk the b-o was so wide that I never even tried to look for one. Sep 6, 2012 at 13:45
• Well, not any more! It used to be the case that cash+fx was an arbitrage circuit. But the disappearance of cash (and thus wide prices) and the arrival of the basis has removed it. Perhaps the closest would be via Repos in both markets, but that does add collateral risk to the (reduced) counterparty risk and I assume additional costs to maintain and manage all the required collateral. Sep 11, 2012 at 13:29