# FX forward curve building

Can someone explain which curves are used to calculate FX forward rates? I have the idea that it involves using the local OIS curves for both currencies, but my calculation shows that it is not the case.

Thanks!

• Were you trying to match your calculation to observed values in the market? What currency pairs are we talking about here? There's a fundamental difference between G7 currencies and emerging market. Commented Dec 16, 2016 at 20:05
• Please check this post first and see if you have additional questions: quant.stackexchange.com/questions/18851/… Commented Dec 16, 2016 at 20:10
• even in OIS, ois in each currency is not enough either, to xcncy swap needs to be taken into account too.
– will
Commented Jan 16, 2017 at 16:09

Your method assumes you can borrow or lend at OIS in both currencies, but in practice you cannot. That's why there is a current basis swap market , where you lend at OIS in one currency versus borrowing at OIS + X in the other currency , where X is not zero. That is the missing piece of your calculation.

Why, you may ask , is X not zero , as many textbooks assume? Apparently because most institutions cannot actually borrow and lend at OIS in all currencies. For example , only certain banks in the US have access to the Federal Funds market.

• I do not think it is purely the difference in basis, otherwise it would match basis swaps. In reality the difference is much larger than the basis spread - there is also the considerations of which currency is favourable to hold, be it for credit reasons, or otherwise.
– will
Commented Dec 18, 2016 at 10:41
• FX forwards do match basis swaps. And, to answer your second point, basis swap markets take into account which currencies are favorable to hold. For example, the 1yr USD/JPY basis swap is around -70bp, reflecting the desire to borrow in USD.
– dm63
Commented Dec 18, 2016 at 14:08
• Your answer makes it seem like you're talking about the usd 3m libor vs usd 6m libor style basis swap that was zero before 2007, rather than the cross currency swap.
– will
Commented Dec 18, 2016 at 22:48
• Both types of basis swaps were close to zero before 2007, and widened out afterwards. They are both symptoms of the same need for long term usd funding.
– dm63
Commented Dec 19, 2016 at 2:43
• There has been a xcncy spread since long before 2007.
– will
Commented Dec 19, 2016 at 14:45

I agree with dm63 in that cross-currency swap (CCS) is essential for building FX forward curve. Let me add/correct two things:

1. FX curve < 1 year can be backed out by FX forward contract. CCS is typically longer than 1 year, so you need it for the long-end of the FX curve.

2. CCS swap is typically exchange of 3m USD LIBOR vs 3m FOREIGN LIBOR (or equivalent) + BASIS on top of the notional exchange at the start and end of the swap. (CCS against non-deliverable currencies are a bit different.) Anyway, CCS doesn't involve central bank rate like OIS. The BASIS is determined by market force depending on the need for the USD funding from the foreign counterpart (or vice versa). Given the BASIS, you solve the FX forward at the swap maturity which make the exchange of the two cashflows zero value. Starting from the shorter maturity CCS, you can boot-strap to the longer end.