I will attempt to explain. Typically, when you look for information on implied volatility surface you find reference to OTM and ATM options only, and this generally includes PUTs and CALLs, which when combined appear fairly simple and intuitive. However, if you instead observe all PUTs as a group separately from all CALLs as another group, the differences have me puzzled. To look at this, I pick some historic date (have looked at a number of dates), then use B&S to iterate on IV until I locate the IV that produced the observed price(since all other information is known, such as DTE, underlying price, interest rate (div=0 for SPX)). This is the method used to extract the IV for each option listed. Then I plot the IV on Z axis with moneyness on x axis and dte on y axis. I expected the plots to have fairly strong shape similarities, but find differences on the CALL IV that I do not understand. Some of these anomalies, may be unimportant, such as the downward curvature of deeper ITM CALL strikes (contribution to the option price is fairly negligible here, and probably low interest). However, I expected the IV with respect to DTE, to track closely with the IV with respect to DTE of PUT options, but often see a divergence. Also, the moneyness value of minimal IV for PUTs per expiration, seems to be nearly a constant for all DTE, but has a significant shift for CALL's, which I do not understand. There are other less bothersome differences, that may not be worth mentioning yet.
For moneyness I use the following formulas, which seem to be adequate:
CALL moneyness = log(price * exp(rt)/strike)/(t^.5)
PUT moneyness = log(strike * exp(rt)/strike)/(t^.5)
where r= interest rate
t= time to expiration
price = price of underlying
strike = strike price of the option
For reference I am attaching a graph of PUT IV, and then a graph of CALL IV for SPX on the same date.
It may be difficult to observe the IV with respect to DTE difference of the PUTs and CALLs -- The difference is slight, but still significant. I may poke around to find a better way to show the IV vs DTE difference.
