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Second-Order FX Exposure in Foreign-Currency Basis Swaps

Article Quant Q&A · Author: Will Gu
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Summary

The note considers the foreign-exchange exposure of a basis swap denominated in a currency different from an investor’s reporting currency. It clarifies that the swap can carry second-order FX risk through changes in its mark-to-market, even when the initial delta to the exchange rate is zero. One answer characterizes this exposure as unlikely to require frequent hedging, though it gives no quantitative threshold or hedge schedule.

A second response proposes using an FX forward to lock the exchange rate on a future foreign-currency cash flow, illustrating a possible way to reduce spot-rate uncertainty. The discussion is brief and does not establish whether that hedge fully offsets the swap’s changing valuation or address forward points, changing cash flows, or other risks. Its practical lesson is to distinguish zero initial FX delta from the later FX sensitivity of mark-to-market and to assess the hedge against the actual cash flows.

Key ideas

  • A zero initial FX delta does not eliminate later FX sensitivity in the swap’s mark-to-market.
  • The exposure is described as second-order FX risk.
  • An FX forward is suggested as a way to lock the exchange rate on a future cash flow.
  • The discussion does not quantify hedge frequency or demonstrate that the proposed forward fully offsets valuation risk.

Tags

Fixed incomeForexRisk management
Full text
# FX risk of basis swap in foreign currencies


# FX risk of basis swap in foreign currencies












As an US investor, if I enter a basis swap in a foreign currency (say Euribor-Eonia basis in EUR), and book my trade using USD. I must have some sort of FX risk, right?

How do I hedge such risk? I'd imagine my delta to EURUSD is 0 at the time I enter this swap. But as market moves, my P&L either positive or negative. Does that mean I need to dynamically hedge this FX risk?

(please feel free to edit if my question isn't phrased clearly)

## Answer by Lliane (score 1)

https://quant.stackexchange.com/a/36212

Yes, you have a second order FX risk on the mark-to-market of your basis swap. However it is highly unlikely you will need to hedge it frequently.

## Answer by rupweb (score -1)

https://quant.stackexchange.com/a/36230

So near leg has an x EUR cost funded in USD and far leg returns y EUR. If the swap is even couldn't you use an FX forward to fix the price of the EURUSD cashflow at the far leg? Then you know the total cost of the basis swap no matter how the spot FX market moves.

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