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When SABR LMM Adds Little for Vanilla Interest Rate Options

Article Quant Q&A · Author: Hasek
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Summary

The note considers whether a more complex SABR Libor Market Model offers an advantage over a simpler SABR model for pricing and hedging plain vanilla interest rate options. Its central point is that if the LMM is calibrated to the same volatility smile represented by SABR, and the calibration is exact, both models give the same vanilla price. In that setting, added model complexity does not itself provide a pricing benefit for a vanilla-only book.

The qualification is practical: the response says calibration is usually imperfect, so actual prices may differ. It does not quantify those differences, compare hedging performance, or explain how to choose between models for exotic products. Its conclusion is therefore narrow and conditional; it does not establish that the models are interchangeable in every use case or resolve whether a single model prevents cross-model arbitrage.

Key ideas

  • An exactly calibrated SABR LMM can reproduce vanilla prices from the SABR smile.
  • For a vanilla book, greater model complexity may add little pricing value under perfect calibration.
  • Real calibrations are described as imperfect, so practical prices may differ.
  • The note does not assess exotic pricing or compare hedging outcomes.

Tags

Fixed incomeOptionsDerivatives pricing
Full text
# Pricing & hedging vanilla interest rate options with SABR LMM


# Pricing & hedging vanilla interest rate options with SABR LMM












Are there any advantages of pricing and hedging plain vanilla interest rate options with more complex SABR LMM instead of simpler SABR model? Should one always go with the SABR LMM as a universal model when managing a book of vanillas and exotics in order to eliminate the possibility of cross-model arbitrage?

## Answer by jaehyukchoi49 (score 1, accepted)

https://quant.stackexchange.com/a/71186

I can hardly think of any advantage of using the SABR LMM for a vanilla book. The SABR LMM should be anyway calibrated to the smile (usually marked in the SABR model)? If the calibration is perfect (usually it is not), the price from the SABR LMM would be the same.

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