VIX is derived from the implied vol of SPX options. I don't see the purpose of backing out SPX vols from the VIX.
Your not the first person by far to dive into this hole looking for value.... Emmanuel Derman derived a localized vol pricing model to account for the smile in options... Partial differential equations describe changing values across a surface..... I think honestly this is very important to model over time for yourself... Plus you will get experience in the skill of research . which is very important... There are mean reverting natures that are represented at extremes .. For example.. Spx options during a crash will lose the typical negative skew.. Meaning puts are more expensive then calls...and call skew can go up... I would recommend looking at these surfaces through times in which there are dislocations in the market...
OP, You only have access to VIX option data? Are you attempting this just as an exercise, or do you hope to implement this in practice? There are more straightforward ways to parametrize the vol curve. I would spend your energy on one of those.
He is not talking about the vix curve I don't believe... I think he is talking about the options skew, smile, and term structure considering all strikes graphed into a surface ..
Yes, Cave, I realize that. My point is that there are many other ways to derive the vol surface than whatever it is that he is asking re:Vix. I don't see the point of this exercise.
You know now that you say it doobs I'm not truely sure what the guy is trying to do... At first he mentioned the vix .. Then something about spx vol surface.. The odd thing is he thinks others haven't dug there...
He's trying to take the following info, say: A = 1 B = 1 C = 1 D = 1 Sum of ABCD = 4 He wants to take the Sum of ABCD = 4 (VIX value) and determine what A,B,C, and D are (SPX vol surface). The problem is ABCD could each equal 1 or A could = 4 and BCD could each equal 0. Presumably, he could build his own surface of what VIX represents (i.e. VIX of 4 means ABCD always each equal 1 so if A =2 and D = 0 then Sell A and Buy D) and back that surface out for comparison against market prices. Maybe, I don't really know.