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Collateral Currency Effects in Cross-Currency Curve Stripping

Article Quant Q&A · Author: BlueTrin
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Summary

The document asks whether deriving interest rate curves under a Credit Support Annex (CSA) creates convexity effects when moving between fixing dates. Its example concerns a US dollar trade collateralised in euros, and asks whether correlation between foreign exchange rates used to convert forward cash flows and euro discount factors affects valuation, and how such an effect could be incorporated.

The reply states that the arrangement is equivalent to an implicit currency swap, indicating that collateral currency can introduce cross-currency effects. It points to an external discussion and an article on collateral currency choice, but does not explain a calculation method or quantify the effect. The short exchange gives a useful conceptual pointer rather than a complete modelling treatment.

Key ideas

  • Collateralising a trade in a currency different from its payment currency can affect curve valuation.
  • The reply characterises the setup as an implicit currency swap.
  • The question raises possible dependence between FX conversion rates and collateral discount factors.
  • The exchange provides references but no detailed method for calculating convexity.

Tags

Fixed incomeDerivatives pricingForexRisk management
Full text
# Do taking in account the CSA create convexity effects in your stripping?


# Do taking in account the CSA create convexity effects in your stripping?












When you strip your rate curves using CSA, what kind of convexity effects might appear as a result when computing the CSAed curve from one fixing to another ?

For example if you are valuing an USD trade collateralised in EUR LIBOR 3M, is there an effect caused by the correlation between the FX rates you use to convert the forward cashflows and the discount factors in the EUR fixings used for collateral ?

If there is, how can you take it in account ?

## Answer by quant_dev (score 2)

https://quant.stackexchange.com/a/4473

Yes, because you're entering into an implicit currency swap.

There was an article in "Risk" some time ago on this topic: http://www.risk.net/risk-magazine/technical-paper/1935412/choice-collateral-currency

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.