Implied distributions

[the learner]

Hi, I have read the article below and trying to replicate the calculation of the implied distribution. Any suggestion about the interpolation and how to derive all the prices we need?
The original article at https://tradingmatex.com/volatility-smiles-and-implied-distributions/

 

[newwurldmn]

It can be approximated by pricing butterflies or call/put spreads. You can also use N(d2) as a CDF

 

[the learner]

Thank you, yes that's what they are suggesting here. But to calculate these butterflies with extremely small strike distance we should interpolate and I am not sure about 2 things: what interpolation to use (not sure it really makes a difference on such small grid) and, more importantly, how close we need to choose the strikes. 0.01 USD on QQQ would be a good choice or still too large to make a sensible approximation?

 

[LM3886]

This R package (RND) can calculate the implied distribution for you.

 

[newwurldmn]

Thank you, yes that's what they are suggesting here. But to calculate these butterflies with extremely small strike distance we should interpolate and I am not sure about 2 things: what interpolation to use (not sure it really makes a difference on such small grid) and, more importantly, how close we need to choose the strikes. 0.01 USD on QQQ would be a good choice or still too large to make a sensible approximation?

If you are using listed butterflies then you are limited to the strikes that exist.

if you are using fictitious butterflies, you might as well use N(d2)