Calculating Cross Currency basis swaps

Question

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 1

I do it very simply. First, figure out the swap rate for each currency. Let's do those for 1y EUR/USD:

1) y US swap is 1.8104 2) y EUR swap is -.5432 mid (yes, negative) 3) 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 .236075 EUR more at settlement, which is 2.136%

rate of 2.136 - [us rt] + [eur rt] = -.2236 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 2

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.