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Does anyone know of any paper or research where they shift SABR’s skew and rebuild the surface?

In particular, I would like to prove theoretically whether the no arbitrage condition hold for the entire surface after shifting the “rho” parameter by a certain amount.

Shifting the “rho” parameter is commonly done in the industry to create stress scenarios for the vol skew, but after rebuilding the surface with this stressed parameters, I would like to see what happens with the no arb conditions and prove it theoretically. Thanks!

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