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I am trying to understand the difference between interpolating an FX volatility smile across deltas and log moneyness ( ln(K/F))

  1. Since Delta is dependant on the vol, it seems there is a difference between the interpolated moneyness and interpolated delta at a given strike due to the presence of a smile/skew. So which is the correct method and implications of using one over the other?

  2. Is it true that interpolating across delta space means calendar arbitrage is not guaranteed apriori while moneyness interpolation automatically takes care of it? Hence, can the interpolation be done across delta for a given maturity and the time interpolation is done along iso moneyness lines

  3. Finally, for volatilities of deep ITM/OTM options, which interpolation is better.

Thank you.

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