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Bear with me. Related (very good) question: How to calibrate a volatility surface using SVI

From this paper http://arxiv.org/pdf/1204.0646.pdf, page 21.

Why does the recipe suggest fitting to option prices rather than simply working with implied total variance?

Is there actually any (numerical?) point in working with option prices rather than impl vols or total implied variance?

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Different methods exists to compute implied vol from the same option prices, eventually it's prices that matters to calibration. But if you can reproduce same option prices accurate to the cent by fitting implied vol, I think it doesn't matter.

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