Good point. Does this mean that kernel functions are not 'suitable' for data with no discernible underlying density? I need to think a bit more about this. It might be the wrong solution for the wrong problem.The data sample is not draws from a pdf, but option prices.
However you approach the problem, you have to tackle the issue of extrapolation (of the risk-neutral pdf) to non-marketed strikes.
This article does discuss a related problem it seems and authors are using slice kernel for interpolation and even a reference to extrapolation.
https://mathfinance.com/wp-content/uplo ... elling.pdf
Thanks for the link.
Re your question, with options there is a density via the Breeden-Litzenberger relation -- which can be applied in various forms once you've got a fitting algorithm. As to whether kernel functions are suitable, I noticed the authors said: "Normally the slice kernel produces reasonable output smiles based on a maximum of seven delta-volatility points". The "maximum of seven" gives me pause for my data -- but I haven't tried their method so don't know why they say that. What I am doing is somewhat related though.