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Currently trying to model the IV Surface using the APPL options, to compare how different models of the underlying move the IV Surface. However, after getting the data, I've seen that some option contracts have $Volume=0$ but $Open\hspace{0.2cm} interest>0$. For a few of them, both metrics are zero. When plotting the IVs for a given time $t=T_n$, the volatility smile is discontinuous (large gaps) for some contracts.

Is there any filter to deal with this issue. I assume that absence of volume means no trading at all, and the last price might be very old to keep up with the other recently traded contracts.

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You can filter the options with no volume or too wide spread, it entirely depends what you are trying to do

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