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Valuing Third-Currency-Collateralized Cross-Currency Basis Swaps

Article Quant Q&A · Author: bf52020
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Summary

The document addresses valuation of a cross-currency basis swap whose two currency legs are collateralized in a third currency. Its example uses Indian rupee and South African rand cash flows with US dollar collateral. The stated procedure is to convert each leg’s forward-valued cash flow into the collateral currency using the corresponding forward foreign-exchange rate, then discount the resulting value using the collateral currency’s overnight indexed swap curve.

This is a concise valuation rule rather than a full derivation or worked example. It does not discuss curve construction, basis adjustments, collateral mechanics, or market availability, and it provides no empirical evidence or validation. Applying the rule therefore depends on having consistent forward FX and collateral discounting inputs for each leg.

Key ideas

  • Value each foreign-currency leg’s cash flows forward before converting them into the collateral currency.
  • Use the relevant forward FX rate to convert each leg’s forward value.
  • Discount the converted values using the overnight indexed swap curve for the collateral currency.
  • The explanation gives a valuation rule but does not detail curve construction or collateral adjustments.

Tags

Fixed incomeForexDerivatives pricing
Full text
# Valuing a cross currency basis swap using a third currency as a collateral


# Valuing a cross currency basis swap using a third currency as a collateral












Suppose India and South Africa goes into a cross currency basis swap. But the collateral is specified upon USD. How does one value this type of swaps? Or is it even available directly on the markets?

## Answer by Antoine Conze (score 2)

https://quant.stackexchange.com/a/39015

Multiply each INR (resp. ZAR) leg flow forward value by the corresponding INRUSD (resp. ZARUSD) forward FX, then discount at USD OIS.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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