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Adapting SABR Calibration from Swaptions to Treasury Options

Article Quant Q&A · Author: Leos
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Summary

The document raises the problem of transferring a SABR volatility calibration setup from swaptions to options on Treasury securities. The existing spreadsheet relies in part on a swap rate as an input, which does not directly fit the Treasury option market. The model’s four parameters—rho, nu, alpha, and beta—must be calibrated to market observations, and the author asks what underlying rate or market inputs should replace the swaption-specific ones.

No solution, calibration recipe, or empirical evidence is included; the text is a question from an intern rather than a worked analysis. It highlights a practical modeling issue: adapting a pricing framework requires matching its underlying variable and market conventions to the instrument being priced. The document does not specify which Treasury option contract, quote convention, or SABR formulation is intended, so it cannot establish a particular mapping or recommended method.

Key ideas

  • SABR calibration requires estimating rho, nu, alpha, and beta from market data.
  • A swaption calibration spreadsheet may depend on swap-rate inputs that do not transfer directly to Treasury options.
  • Adapting the model requires identifying suitable underlying variables and market conventions for the Treasury option being priced.
  • The document poses the calibration question but does not provide a method or supporting evidence.

Tags

OptionsFixed incomeDerivatives pricingVolatility
Full text
# Adapt SABR Hagan/Obloj model from swaptions to treasuries options


# Adapt SABR Hagan/Obloj model from swaptions to treasuries options












I am a young intern in a brokerage company and I am currently working on developing a new pricer. I would like to encode a skew-visualisation tool and the best way that appeared to me is the SABR model. It is my first internship in finance plus I do not have a quant background, so pardon me in advance if my question seems simple. Here is my problem:

The hardest part of encoding SABR is the calibration of the 4 parameters (rho, nu alpha, beta). I hopefully found a spreadsheet on the the internet from which I started and now I have something that works fine on calibrating parameters. Problem is that this works for swaptions only: the inputs are among others the swaption's swap rate which does not.

I was then wondering: HOW TO ADAPT THIS TO TREASURIE'S OPTIONS ? If someone has any clue, I would be very very grateful :) . Have a good day

Regards from France,

Leos

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