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Choosing Calibration Instruments for a Hull–White Model of a Libor Note

Article Quant Q&A · Author: Samuel
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Summary

The document raises a practical calibration question for a one-factor Hull–White interest-rate model used to price a structured note. The example note pays annual coupons based on the positive part of three-month EUR Libor plus a spread, then returns principal at maturity. The author asks whether caps or swaptions are suitable instruments for calibrating the model’s two parameters and, if caps are used, how to select their dates and strikes.

A key market-data complication is that the available EUR cap quotes are described as referencing six-month Euribor, while the note’s coupon references three-month Libor. The document does not include replies or a proposed calibration method, so it provides no evidence for choosing particular instruments, strikes, or weights. It is useful as a statement of the instrument-matching problem, but leaves open how to handle tenor basis, model fit across maturities, and the structured note’s specific exposure.

Key ideas

  • The note concerns calibrating a one-factor Hull–White model for a Libor-linked structured coupon.
  • The example coupon depends on the positive part of three-month Libor plus a spread.
  • Caps and swaptions are proposed as candidate calibration instruments, but no choice is resolved.
  • The quoted cap market may reference a different Libor tenor from the note’s underlying rate.
  • Instrument tenor mismatch and the selection of dates and strikes remain unanswered.

Tags

Fixed incomeDerivatives pricingOptions
Full text
# Hull & White 1F - What is the appropriate calibration portfolio for Libor indexed structured note?


# Hull & White 1F - What is the appropriate calibration portfolio for Libor indexed structured note?












I'm wondering what is the best swaptions or caps portfolio I could use to calibrate the two parameters of H&W 1F model for a structured note with optionality on Libor underlying.

Let's suppose for example that the EUR trade I want to price is paying a coupon = Notional * max(Libor EUR 3M + spread, 0) each year, and consider as maturity 31/12/2030 where the Notional is paid.

My first thought would be to use a portfolio of Caps but then I would have to choose the appropriate dates and strikes (ATM?), and it's where it gets tricky. Furthermore, it seems that the EUR Caps vols/prices are quoted for EURIBOR 6M underlying, not 3M.

Need help!! Thanks! Samuel

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