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Why do options traders usually model and trade the IV surface? I appreciate that the IV surface is more standard across assets, but why do we go to so much trouble with the IV surface?

To me it seems that the call price surface is just simpler, for example the no-arb conditions are simply convexity in strike and monotonicity in tenor.

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    $\begingroup$ The call price surface of today is not comparable to the call price surface of yesterday, due to the passage of time. $\endgroup$
    – nbbo2
    Aug 14 at 14:38

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