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Choosing Cross-Currency Swaps for USD CSA Discount Curves

Article Quant Q&A · Author: Ajk
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Summary

The document asks how to build a non-USD discount curve for EUR/USD and GBP/USD mark-to-market basis swaps collateralized in USD. The proposed construction uses forward rates for the short end and cross-currency basis swaps at longer maturities. The central choice is whether to calibrate the longer end with constant-notional cross-currency swaps or mark-to-market basis swaps, which the author says are more liquid.

The author notes that the instrument choice materially affects interest-rate delta, but provides no calibration comparison, market data, or recommendation. The discussion therefore frames a curve-construction decision rather than resolving it. A practical analysis would need to account for each instrument’s cash flows and collateral terms, as well as the consistency of the resulting curve with the instruments being valued; those details are not supplied here.

Key ideas

  • The curve construction described uses forwards at short maturities and cross-currency basis swaps further out.
  • The question is whether to use constant-notional swaps or mark-to-market basis swaps for calibration.
  • The author considers mark-to-market basis swaps because they are more liquid.
  • The choice of calibration instruments can materially change interest-rate delta.
  • The document gives no answer or supporting quantitative comparison.

Tags

Fixed incomeMulti-assetDerivatives pricingRisk management
Full text
# Multi-currency CSA discounting curve construction


# Multi-currency CSA discounting curve construction












I have a number of eur/usd and gbp/usd MtM Basis swaps that are collaterized in USD. For the non-usd legs I'm constructing the muti-ccy csa discounting curve. Im using forwards for the short end of the curve and cross-currency basis swaps further out on the curve. Question is, should i be using constant notional cross currency swaps or MtM Basis swaps for this. MtM basis swaps are more liquid, so think they would be better, but not certain.The choice has a significant impact on my IR delta.

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