Swap Payment Frequency and Comparability in Zero-Curve Bootstrapping

Summary

The document asks whether swap rates with different fixed-leg payment frequencies should be adjusted before bootstrapping zero curves intended for comparison. It contrasts annual fixed payments for euro swaps with semiannual fixed payments for US dollar swaps. The proposed adjustment converts a rate quoted at one payment frequency into an effective annual rate, then uses the adjusted rates in the bootstrap. The question is whether this conversion is necessary or whether each curve can be bootstrapped using its market-standard schedule.

No answer or calculation is provided, so the document does not establish whether annualizing the quoted rates produces comparable curves or what assumptions a valid comparison requires. It also does not discuss discounting conventions, day-count rules, floating-leg indices, or market quotation conventions, all of which may affect curve construction. The material is useful as a framing of a cross-currency methodology issue, but it should not be treated as a resolved procedure or a complete account of swap curve bootstrapping.

Key ideas

• The question compares euro swaps with annual fixed payments and US dollar swaps with semiannual fixed payments.
• It proposes converting semiannual swap rates into effective annual rates before bootstrapping.
• It asks whether curve comparison requires this conversion or can use each market's standard payment schedule.
• The document provides no answer or evidence resolving the methodological question.
• Other swap conventions that affect curve construction are not covered.

Tags

# Annualizing the pay frequency of underlying swaps when bootstrapping the zero curve?


# Annualizing the pay frequency of underlying swaps when bootstrapping the zero curve?












Say I'm looking to bootstrap two zero curves based on two swap curves with different underlying currencies and, consequently, two different pay structures in the swap contracts. For example, say I want to use vanilla EUR interest rate swaps that have an annual pay frequency for the fixed leg (e.g., EUSA1 ICPL, EUSA2 ICPL, etc). On the other hand, I want to use vanilla USD interest rate swaps that have a semiannual pay frequency (e.g., USSW1 CMPN, USSW2 CMPN, etc). If I want the resultant bootstrapped zero curves to be "comparable", is there any other way to do this other than annualizing the USD swap rates into effective rates? That is, convert the base USD swap rates into effective rates using:

s(t;n,1) = (1 + s(t;n,m)/m)^m) - 1

wehre s(t;n,m) is the n-year swap rate with coupon frequency m at time t

In this case, USD swap rates would have m=2 and then bootstrapping would be applied. Is there a huge issue with assuming different pay frequencies when constructing the zero curves? Can I just assume the semiannual pay frequency of the USD swaps?

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