rmorse: I am unable to find support for your statement. It could be true, but as a test, I looked at the following as a near ATM monthly SPX option was expiring, to correlate what the options were referenced to. I observed the price of SPX on TOS, and the price of ESU5 on TOS. All prices being captured at same time point. This seems to imply the SPX is indeed what the option prices are reference to. What am I missing? I'll continue and observe a few more expiring contracts. -- I may add that I know nothing about futures, so pardon my ignorance!
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
The oddity in the graphs is just an illusion, the problem is that SPX ITM calls and puts are very illiquid and the quoted bid and asks are either stale, very wide, or plainly wrong. All of the research papers that deal with IV surfaces first "sanitize" the quotes for ITM options (calls and puts) and then perform computations. Once you do something like that there should not be any discrepancies with the IV surfaces.
One more observation and then I'm done. Sep VZ future is around 20.70. The same 2050 puts and calls have almost the same mid point on the ES options vs the SPX options on TOS and TOS says those Ivols are 22.13 for the call and 18.46 for the put. None of this makes sense since you can trade the ES option vs the SPX option as a hedge, at the right ratio. You can't assume any retail platform or broker neutral platform will have the correct inputs for dividends and interest.
Robert, only VIX options require a forward price adjustment when computing IV or greeks (what you call using the right futures). SPX options only need the current level of the index and they are fine. I reiterate that the problem of the OP is that quotes for SPX in-the-money options are usually wrong, sometimes for huge ranges. Just do a simple put-call parity on them and you will notice violations after 10 points ITM.
This is wrong. Options are priced off the forward which is calculated with future dividends. If you use the right firward put call parity is not violated. If put call parity is violated, the most basic options related arbitrage is presented.
Blue, I'm not sure where you get that from. If I'm wrong, I'd like to know more. SPX closed at 2,049.58 Friday and the September ES contract settled at 2029.25. The difference is 20.33 points. SPX and ES option mirror each other. I think we can agree that any trading in ES will hedge with the future. I also think we can agree that hedging with the basket of 500 stocks is not efficient. What would you hedge an option position in Jul, Aug or September with? That hedge is the input price for the underlying in any model.
That is correct conceptually newurldmn, however when you use something like BSM to price the options it takes care of this for you as all the formulas are already in forward price mode. The input to the equations *should* be the current underlying spot price as most of the closed form solutions for BSM already take into account that. No need to do it twice (you will get wrong results). As for the put call parity of course it needs to be adjusted by forward Strike C-P = S-D*K But even with that adjustment you will find that ITM options for SPX consistently violate put call parity. My whole point of the comment is that the quotes for those options are stale most of the time and therefore wrong.