Discount Curves for Cross-Currency Collateral and Uncollateralized Cash Flows

Summary

The document discusses discounting choices for cash flows under different collateral arrangements. For a trade with EUR cash collateral that accrues at the relevant overnight rate, the response explains that valuing a USD cash flow involves considering the currency swap needed to transform the collateral into USD. The resulting USD funding rate, described as typically Fed Funds plus a spread, is presented as the appropriate discount rate for present value in that setup.

For uncollateralized cash flows, the response describes practice as variable and suggests a risk-free reference rate plus a counterparty-specific credit spread. Some institutions may also include a funding reserve reflecting their expected funding cost. These points are market-practice guidance rather than a universal rule: the applicable collateral terms, currency conversion, counterparty credit, and institution methodology matter. The document does not provide a numerical valuation example or a detailed framework for deriving the spreads and reserves.

Key ideas

• The collateral remuneration terms influence the discount curve used for a collateralized trade.
• For USD cash flows backed by EUR cash collateral, a currency swap can inform the USD rate used for discounting.
• Uncollateralized cash flows may be discounted using a risk-free rate plus a counterparty credit spread.
• Some practices add a funding reserve to reflect the institution’s expected funding cost.
• Discounting conventions vary with contractual terms and institutional methodology.

Tags

# Discounting (collateralized / uncollateralized / other ccy)


# Discounting (collateralized / uncollateralized / other ccy)












I have been out of the market for quite some time and I see that nowadays discounting is a more complicated discipline.

For collateralized trades I do understand the standard method is to use discounting based on curve associated with the collateral index rate. So if we have EUR cash-flow and collateral in EUR, we would use some EUR OIS curve for the discounting.

However, I'm not sure what's the current market practice for:

- discounting USD cash flow in a pool collateralized in EUR. What curve should be used for this discounting?

- discounting uncollateralized cash flow. Now that xBOR rates are being phased out, what rate to use for uncollateralized cash flow?

## Answer by dm63 (score 0, accepted)

https://quant.stackexchange.com/a/71371

- If collateral is provided in EUR cash, with interest paid at Ester ( the successor to Eonia which has been abolished), then you need to perform a currency swap to change the collateral into USD. This would result in a USD rate of typically Fed Funds+ 10bp , which becomes the appropriate discount rate to calculate the PV.

- Practices vary, but typically one would use a risk free rate (Fed funds or Eonia ) plus a credit spread appropriate for that counterparty. Some may also add a ‘funding reserve’ reflecting the expected cost of funding the position at the bank’s cost of funds.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.