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I'm new to quant finance and currently working on my first project.I'm trying to construct the Implied volatility surface for cryptocurrencies from deribit ( as options from deribit are the most liquid ones ). I applied splines techniques to interpolate/extrapolate the surface and I got satisfying results according to my superiors but I still have some doubts.

  1. why do we need to filter illiquid options and work with only liquid options to construct the surface? I'm asking this question because I found the majority of options are illiquid (ask_iv - bid_iv <0 and open_interest =0 also the bid_iv is 0 for some options)

  2. After some researches I found that the surface should satisfy some conditions one of them is no arbitrage opportunities: Is it the case for crypto markets ? How can I verify it ?

  3. Does having a surface with no peaks and tweaks is sufficient to say that we have no overfitting? how can I verify if there's overfitting otherwise ?

Thank you

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