Estimating Cross Currency Basis from Swap Curves and FX Forwards
Summary
The document addresses how to estimate a cross currency basis for EUR/USD and explains why comparing forward-rate differentials directly can produce implausible results at some tenors. One answer gives an illustrative one-year calculation: infer a yield from the spot and forward exchange rates, then compare that yield with the relevant currency swap rates. The resulting difference is presented as an approximation to the basis, with a small discrepancy attributed to market conventions.
A second answer outlines the more general curve-based method. Observed market spreads across tenors are used to calibrate a discount curve so that the foreign-currency leg, including its spread, matches the local-currency leg discounted at OIS; the calibrated curves can then be used to derive a spread for another tenor. The numerical example is explicitly simplified and convention-sensitive. The document does not spell out day-count, payment, collateral, or curve construction details, so it is an introduction rather than a complete pricing recipe.
Key ideas
- A spot-to-forward FX yield can be compared with currency swap rates to approximate a cross currency basis.
- Observed swap spreads across tenors can calibrate a discount curve for basis calculations.
- The calibrated curves allow estimation of basis spreads at tenors without direct quoted observations.
- Results depend on market conventions and discounting assumptions.
- A simple forward-differential calculation may fail, especially when applied inconsistently across tenors.
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# Calculating Cross Currency basis swaps # Calculating Cross Currency basis swaps I am trying to calculate cross currency basis swaps for personal use. I generally understand what they are (essentially swapping one currency for another currency on a floating interest rate basis) but not how to calculate the basis. I have read quite a bit on them and understand the basis exists because the forward rate is higher/lower than justified by the interest rate differential according to CIP. I have done the following for a 1 year EUR/USD cross currency basis swap Take 3m libor and 3m euribor forward rate spreads, (2.03+.475)=2.505, (1.95+.55)=2.5, (1.605+.59)=2.195, (1.49+.62)=2.11. Then using the current EUR/USD 1YR forward of 2.89 bps subtract this from the IR differential which leaves a basis of -.385. Is this the correct way to calculate the 1 year cross currency basis swap? If so how do you do this for a 3 month basis and a 5 year basis? When I use the same process for calculating a 3 month basis swap I get a figure in excess of 150bps which I know is not correct. Thanks ## Answer by JoshK (score 6) https://quant.stackexchange.com/a/47591 I do it very simply. First, figure out the swap rate for each currency. Let's do those for 1y EUR/USD: - y US swap is 1.8104 - y EUR swap is -.5432 mid (yes, negative) - look at the implied yield for the FX spot vs the 1y fwd. Spot is 1.1052 and 1y is 1.1341275. That gives you .028928 EUR more at settlement, which is 2.6174% rate of 2.6174 - [us rt] + [eur rt] = 0.2638 And that is the xccy basis. It should be 0 if the world was fair. I'm off a little from bb b/c of convention, but this should give you the idea. Here's the screen on BB. It has too many rows so I'm capturing the top, where you can see spot, and the bottom, where you can see 1y XCCY: ## Answer by Math (score 4) https://quant.stackexchange.com/a/47068 The general way to do this is first take observed market spreads for various tenors, then calibrate a discount curve such that the foreign leg plus the spread at each tenor discounted at the calibrated curve is equal to the local currency leg discounted at OIS. Then you can calculate a spread from the curve for any given tenor using the two discount curves.
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