OK, I pulled up my TOS, which will never use proper interest and dividend flows. SPX closed today at 2049.58. The Sep call and put market are wide but the Implied vol on TOS for the 2050 call is 13.51 and the put is 17.89. The reason those are that way is because they are using the wrong dividend and interest too. If TOS used the correct one, the Ivol on both would be very close or you could arb them. Their assumptions are wrong.
From 2011 to 2014 we had a team building a risk platform with a focus on portfolio margin in a live environment and stress testing. I was the beta tester on that team. We found that our SPX and VIX options always had bad values when we used the cash. My boss met with a large MM group on the CBOE that told us we need to either use the correct future or simulate the interest and div flows using the future to get the correct underlying. Once we adapted to the correct future for each option, it lined up properly.
BTW, the OCC, when it calculates PM, does the puts and calls separately. The OCC has no put call parity when they do their risk shocks. 100 point box spreads can can be worth more than 100 one day and way under the next.
I hope this helps.
Bob