VIX true value - Market Analysis for Jan 2nd, 2017

I got a very interesting question in one of the threads so I'm going to post the answer here. The question is why even though VIX closed at 14.04 on Friday I claim that the true value is in fact 14.90 (I computed that when VIX was around 14.13)

We know that VIX closed at 14.04 but the real value is 14.80 because of the way options are priced. The reason is that to avoid weekend arbitrage opportunities option dealers start discounting prices for all of the options to take into account the 3 non trading days that follow. Imagine for a second that they didn't do that, you could sell an option on Friday, hedge the exposure, and on Monday you could repurchase it substantially cheaper because of the 2 day time decay (on a normal weekend), basically free money because there was no risk involved and the time decay has to happen in any case. So what happens in reality is that the software used by Market Makers and option dealers starts pricing options with less time to expiration: the total time minus the 3 days of the long weekend, this process usually starts one day early, and by Friday afternoon it accelerates. The end result is that by 4:00PM on Friday the price quoted roughly matches the price that the options should have on the opening tick on Tuesday (or whenever the opening  tick occurs), so as you can see the prices of options on Friday are actually prices for several days later (the time decay of 3 days is already included).

Now, VIX is computed from option prices and the way that CBOE computes VIX is very general and it only cares about total time to expiration, the formula doesn't care about weekends, long weekends, holidays, nothing at all. So because of that, because options are cheaper, VIX is also cheaper than it should be, this is an instance where the VIX computation is using a different time to expiration than the options themselves. This same effect also happens with retail software like ToS, or IB or any other retail platform, the retail software is not taking into account the weekend effect and as a result the implied volatility displayed for options comes back very low. After the weekend everything goes back in sync again (because the time to expiration is in sync again).

So now you see my friends, that 14.04 for VIX is actually 14.80, in other words if the market is unchanged (it opens at exactly the same level that it closed on Friday), VIX would automatically go to 14.80 on Tuesday open. For those of you curious about how I compute that number here is the explanation. The adjustment factor by the close on Friday is:

AF = sqrt(T/T-3)  Where T is the time to expiration in days for a particular option, and 3 is the number of non trading days of a long weekend (it would be 2 for normal weekends).

Because VIX is always the 30 day rolling implied volatility, then the adjustment factor for VIX is:

AF = sqrt(30/27) = 1.054

So in that case:

Real VIX = VIX *1.054 = 14.04*1.054= 14.80