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Choosing Black or Bachelier for Short-Term Interest Rate Options

Article Quant Q&A · Author: Harris Wallace
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Summary

The document raises a model-selection question for options on short-term interest rate futures, using SONIA as its example. It contrasts a normal model, motivated by the author's view of the underlying's distribution, with a lognormal Black model whose implied volatilities are used as an exchange quoting convention. The practical objective is to build a volatility surface from market prices and use it to value contracts at less liquid strikes.

No answers, calculations, market comparisons, or pricing results are included. The text therefore frames the modeling problem but does not establish which model is more suitable or explain how to calibrate either one. It leaves open how distributional assumptions, quoting conventions, strike coverage, and fit to observed prices should influence the choice. Readers should treat it as a question motivating further analysis rather than as a model recommendation or a demonstrated method for extrapolating prices to illiquid strikes.

Key ideas

  • The document compares normal and lognormal pricing frameworks for short-term interest rate options.
  • Exchange quoting conventions may differ from a trader's preferred distributional assumption.
  • The stated goal is to construct a volatility surface that supports pricing at less liquid strikes.
  • The document contains no response or evidence that resolves the model choice.

Tags

OptionsFixed incomeDerivatives pricingVolatility
Full text
# Appropriate Model for pricing STIR options - Black or Bachelier?


# Appropriate Model for pricing STIR options - Black or Bachelier?












I am interested in pricing some of the options on short term index future indices, namely the SONIA. I was wondering whether a Normal or Lognormal model would be better. On one hand the underlying does follow a normal distribution, but exchanges such as ICE quote lognormal implied volatilities (derived from Black) as a convention.

To be clear my aims are simply to construct a volatility surface from market prices which can be used to price contracts which lie on the more 'illiquid' strikes.

Thank you in advance, any advice is much appreciated!

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