I am seeking a better understanding of why SPX PUT IV surface seems logical with respect to moneyness and DTE, but SPX CALL IV seems very odd! (brothers from a different mother or something) If you are aware of some reading materials or white papers covering this anomaly, I'd like to hear. -- I am NOT looking for "trading" information regarding this. Am trying to better understand what I see. My focus is only on SPX.
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.
What is your conclusion based on your graphs? Are you saying that there is no put call parity or something else? I'm still not sure what specifically you are seeing is wrong and what would make it more correct? BTW, when you plug in the values, what are you using for the underlying price, the SPX cash or the ES future that is appropriate for that expiration?
Hm!!! Can you enlighten me regarding SPX options referencing ES future VS SPX? -- I recall you mentioning this before to someone, which went over my head! I think I need to understand this now! (I have been referencing the price of SPX for my SPX and SPXW options!)
June SPX options are hedged with the June ES future. Sep SPX options are hedged with the Sep ES future. If you look at the difference between each futures month, you will find the implied interest and dividend flows for that time period. For options in between futures, you have to adjust for the interest and dividend flows to get an underlying price, which I have never done and I don't know if it is linear. If you use today SPX cash, you are using the wrong price. That is only relevant at expiration for settlement price. http://www.cmegroup.com/trading/equity-index/us-index/e-mini-sandp500.html Look at the difference between the settlement values and the close of the SPX.