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I have a EUR-GBP cross currency swap, collateralised in GBP, each leg is paying 3m EURIBOR/LIBOR respectively. I know GBP leg can be modelled with 3m LIBOR forward curve and GBP OIS discount curve. How about the EUR leg?

I heard there are two approaches: 1. 3m EURIBOR as forward curve, and the discount curve should be EUR IOS adjusted with EUR vs GBP spread. 2. 3m EURIBOR adjusted with EUR vs GBP spread as the forward curve, and the discount curve should be GBP OIS

I am not sure if both above are accurately described, as I am not familiar with such trades. Can anyone share some insights and explain if any/both of them are correct? Many thanks.

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The EUR leg should be valued in EUR but in a manner consistent with GBP collateral:

This means:

  • a 3m EURIBOR forward curve consistent with GBP collateral
  • a EUR discount curve consistent with GBP collateral

In theory both curves should be jointly bootstrapped to fixed vs EURIBOR swaps collateralized in GBP and EURGBP FX swaps and cross currency swaps collateralized in GBP.

In practice if market data for fixed vs EURIBOR swaps collateralized in GBP is unavailable, you should use fixed vs EURIBOR swaps collateralized in EUR. The theoretical difference between the 3m EURIBOR forward curve under GBP collateral and the 3m EURIBOR forward curve under EUR collateral is a covariance term between EURIBOR and the EUR/GBP basis spread, so assuming that the two curves are the same is equivalent to neglecting the EURIBOR, EUR/GBP basis correlation.

As for the EUR discount curve it should be the EUR OIS adjusted with EUR/GBP OIS basis spread. Beware that the OIS basis spread needs to be bootstrapped: the spread in a zero PV cross currency swap cannot be used directly as it is (roughly) equal to the EUR/GBP OIS basis spread plus the difference between the OIS-Libor spreads in both currencies.

As an alternative if you already have the forward EURGBP FX curve available, you can obtain the adjusted EUR OIS curve as GBP OIS discount x spot EURGBP / forward EURGBP.

Hope this helps.

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  • $\begingroup$ I think the last part of your answer is definitely the easiest route! $\endgroup$ – will Apr 26 '17 at 6:49

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