So I’ve been tracking this in OV for some time, and I’ve come to believe that any differences in IV between the calls and the puts can be tied back to the Dividend Yield that is used to measure the IV.
As far as I can tell, OV uses a single dividend yield to measure the IV’s and model the position regardless of expiration. In reality though, the dividend yield on indices is not static across different tenors, as the Index constituents go ex-dividend at different times throughout each quarter. This can lead to notable differences between the implied forward price that is calculated using the current spot, dividend yield, and risk free interest, and the implied forward price measured from the option chain. I’m inclined to believe the implied forward that is measured from the option chain is more accurate because there the differences between strikes is usually in the cents, while the difference between the implied forward based on a single dividend yield and the implied forward measured from the option chain can be in the dollars.
I believe OV is using the IV’s that are calculated based on this single dividend yield to model out the position in the Analyze graph. This can lead to discrepencies in the analyze graph between Call/Put/Iron butterflies, especially for expiration months where this single dividend yield is not an accurate measure of the forward price of the index for that month. This is the reason I personally prefer to use Combined Put/Call skews in all circumstances.