How to construct a GBP FVA curve from a USD FVA curve

Question

Our business funds itself in 2 currencies, USD and ZAR. As a consequence we have a USD funding curve. I need to price a GBPZAR cross-currency swap (XIRS) against a counterparty with which we have no CSA agreement. I would like to get clarity on 2 points:

1. My approach to price the swap would be to use a GBP funding curve. However, how do I construct it given we only have USD and ZAR funding curves? Do I use the GBPUSD basis curve as a discount curve to convert the USD funding rates into equivalent implied GBP "funding" rates and use that to price the GBPZAR XIRS?
2. Alternatively, can I not just price 2 cross-currency swaps: GBPUSD and then USDZAR, using the business' USD funding curve? What would the assumptions be that would make this alternative viable?

I have scoured the internet to try and find a book that will give clarity on such nuances but I have not found any. Please recommend one if you know of it! :)

Thanks in advance

Answer 1

There are two aspects to consider here. Aspect 1 is funding the notional of the Xccy swap and the coupons (strictly speaking this is not FVA). Aspect 2 is funding the MtM of the swap throughout the life of the trade if you hedge the non-CSA trade with an offsetting transaction against a CSA counterparty (usually the "street") (this would classify as an FVA)..

I assume your question is about 1, not 2.

In a GBP/ZAR Xccy swap, there are two possible directions.

Case (i): we pay GBP rates and receive ZAR rates: here we receive GBP notional at inception and we post ZAR notional at inception against it. We therefore need to fund the ZAR notional for the duration of the trade. I assume that here, you would "price" the floating coupons on the ZAR leg that you will be receiving throughout the duration of the swap, and these should be priced using your ZAR funding curve (+ spread). I assume the GBP floating coupons would be GBP Libor flat (standard convention).

Case (ii): we pay ZAR rates and receive GBP rates: here we receive ZAR notional at inception and we need to post GBP notional at inception against it. We therefore need to fund the GBP notional for the duration of the trade. If your institution funds itself via USD or ZAR, there are two ways to fund the GBP notional: either via USD or via ZAR.

If it's funded via USD, you could indeed use your USD funding curve to price a GBP/USD Xccy break-even swap. GBP/USD Xccy basis swaps are very liquid with quotes available on Bloomberg. The GBP/USD xccy swap would be quoted as quarterly USD Libor flat vs. quarterly GBP Libor + spread (call it "spread 1").

I assume your USD funding curve is expressed as USD Libor + spread (call it "spread 2"). So add this "spread 2" from your USD funding curve to the quoted "spread 1" on the USD/GBP Xccy swap, and that should reflect your real funding cost of raising GBP via USD. Then use this GBP curve (GBP Libor + "spread 1" + "spread 2") as the floating rate that the counterparty needs to pay on the GBP notional for "break-even" (add another spread if you want to make profit).

If you fund the GBP notional via ZAR, rather than USD, then I assume the same approach could be used: although I am not sure how liquid GBP / ZAR swaps are.

In any case, if you need to post GBP notional at inception and you need to fund it, then I suppose it should be funded via whatever is cheaper for your institution to fund it with: whether that is ZAR or USD.