An FX-implied curve is backed out from a discount curve and forward points

Parity runs in both directions. A discount curve in one currency, spot and the outrights give an FX-implied curve in the other currency.

With \(s\) the spot date:

\[\frac{D_q(T)}{D_q(s)} = \frac{S}{F(T)} \times \frac{D_b(T)}{D_b(s)}\]

This curve holds the cross-currency basis, so it is not the same as the other currency's own OIS curve. QuantLib bootstraps such a curve with FxSwapRateHelper, and ORE builds SEK-IN-USD from FX forward and basis quotes.

• FX forwards — the structure note.
• The US dollar is the natural hub for FX forward curves — completes: the usual starting curve.
• Covered Interest Parity and FX Forward Pricing — completes: the relation in reverse.
• Multi-Curve Construction — completes: where such a curve fits.

• DiscountingFxForwardEngine and FxSwapRateHelper in QuantLib
• DiscountingFxForwardEngine and the SEK-IN-USD example in ORE
• Market view enhancements, Riskval
• CIP, FX swaps, cross-currency swaps and the factors that move the basis, BIS Quarterly Review, September 2016