Funding-Based Discounting for Uncollateralized Cross-Currency Swaps
Summary
The document considers which discount curve to use for an uncollateralized cross-currency swap when valuation is expressed across two currencies. It weighs choosing a reporting currency and building a second curve with foreign-exchange forward or currency-basis adjustments, selecting a reference currency deal by deal, and discounting using funding costs in both currencies.
The answer favors discounting at the institution’s cost of funding because an uncollateralized derivative is not funded through a collateral agreement. This treatment can be represented as discounting from a chosen reference currency plus a separate funding valuation adjustment. The argument relies on treasury funding costs being consistent across currencies after accounting for FX forwards and cross-currency basis. The short discussion gives a conceptual consistency condition rather than a detailed valuation procedure, and it does not address xVAs beyond noting that they are excluded.
Key ideas
- An uncollateralized cross-currency swap is not funded through a collateral agreement.
- The response recommends discounting at the institution’s funding cost for uncollateralized derivatives.
- Funding-based discounting can be decomposed into reference-currency discounting and a funding valuation adjustment.
- Cross-currency funding costs should align after accounting for FX forwards and the currency basis.
- A consistent funding framework should make the selected reference currency immaterial to the final valuation.
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Full text
# What discount rate for uncollateralized cross currency swaps? # What discount rate for uncollateralized cross currency swaps? To expand on this question, what happens if the uncollateralized swap is of a cross currency variety? Ignoring any xVAs, it's unclear which currency would best determine the discount rate: a) we could choose our organization's functional/reporting currency as the "main" currency (justifying it for example by general funding considerations) and then proceed as in case of collateralized CIRS, ie. discount rate for cash flows in that currency would be OIS and discount rate for cash flows in the other currency would be a separate curve that incorporates appropriate FX forward / currency basis swap adjustment, b) we could choose a currency as "main" on a deal-by-deal basis (ex. based on hedging strategy considerations, say GBP if the uncollateralized client deal is going to be hedged with a bank with whom we have a GBP CSA) and then proceed as above - but it'd look very arbitrary and also allow two otherwise identical deals to have different valuations, c) discount at our cost of funding in both currencies (however our treasury defines it) instead of a risk-free rate - this is not desirable because I'd much rather deal with it as a separate FVA correction if necessary. Which of the above makes the most sense? Are there any other approaches used in practice? ## Answer by Antoine Conze (score 1, accepted) https://quant.stackexchange.com/a/37243 Discounting should not be different for CCS than for other derivatives: if the derivative is uncollateralized then it is not funded trough its CSA and thus should be discounted at its cost of funding, which would mean using c), which as you point out can always be decomposed into discounting as in a) plus an FVA. Also one would expect your cost of funding as defined by your treasury to be consistent across currencies: for instance your EUR cost of funding should be consistent with your USD cost of funding and the EURUSD forward / CCS basis, so that in the end it does not matter which currency you use as reference in c).
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