I have read similar posts regarding this topic lately. But I am still not very clear what caused the big difference of some option implied vol for the same stock, from different sources. For example, the option IV for FCX has a huge difference btw TOS and IB. Here is the picture from TOS.
It could be the way the diff vendors calculate it ... for example in balck-schooles one may use the interest rate from the otr tsy 10yr, other may use the 30yr ...
Does interest rate play such an important role? No matter what method they use, I am still expecting the pictures of stock's option IV from two sources should at least have the similar shape. Apparently their shapes are almost totally different??
They both look similar when it comes to current value. Could just be that the history of the TOS chart was not reset after the adjustment in January while the IB chart was. Kind of like a stock chart being adjusted after a split. (Not sure what caused the adjustment. Probably just a recalculation of sorts) I've noticed this on a few IV charts on TOS but not too many.
Also I noticed you're using the Prophet Chart for your IV. I tried FCX on the TOS Charts and it gave a different picture for the IV. You'll have to add an avg, but at least it doesn't have the weird sudden drop off in IV. Hope this helps.