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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?

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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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