VIX definition

Did I miss anything here?

 

Too complicated. VIX is "market's expectation of 30-day forward-looking volatility", hence 30-day implied volatility. When there's an exact SPX option term for 30 days, it's the at-the-money implied vol on it, otherwise interpolate the ATM implied volatility between the two option terms before and after 30 days.

 

Too complicated for you perhaps . But that is a good concise description

 

Curious if there is a point to this post? If your intention is to understand how VIX is computed, why not observe the white paper that defines it. "https://cdn.cboe.com/resources/futures/vixwhite.pdf" Your formula missed two attributes of the actual form:
1) the algo for discarding zero BIDs (one is a simple bypass, and the other terminates the remaining strikes further OTM)
2) your equations need to be supplied to two expirations, then combined per the CBOE formula to determine the "30-day" value! (from VIN & VIF)

 

My point was just to see if I was missing some blindspot or something.. I am trying to understand a theoretical model and implement a monte-carlo estimator/calibration, etc. When I simulate I get results that look and feel correct (next step is to verify and test the generated samples against input parameters etc), So I really do just sum up the variance over the simulated sample paths then average the result to get the theoretical current value of VIX

 

Yes I've also read the whitepaper and almost finished working on a program to calculate VIX. Yes, I was following the CBOE whitepaper which is a little sloppy with notation.

 

IMHO, the implied volatility inferred by the ATM strikes is more precise at inferring the volatility of SPX. Using VIX adds artifacts to the value that I don't desire. The VIX value reflects an IIV in the range of a 20-30ish delta PUT which is impacted by SKEW, which I find undesirable. It may be simpler to use a more precise derivation of Implied Volatility of the INDEX than using VIX. (I did the VIX calc for my work previously, and abandoned that in favor of ATM IV, which I think is better for my purposes). As long as your approach is a good fit for your goal, that should be OK, but VIX was not a good choice for what I prefer.

 

Here is some R code to calculate the current VIX from Yahoo (using SPY since there is a bug in quantmod). I ported the same to Java with CBOE EOD data instead. For the most part, I found SPX ATM IV is close enough without going through the effort of calculating VIX from the options chain.

Code:

library(quantmod)

getSymbols("SPY", src = "yahoo")
S0 = as.vector(Ad(tail(SPY, n=1)))

#Today+30
SPY.OPTS <- getOptionChain("SPY", "2020-12-24", auto.assign = F)

Call <- as.data.frame(SPY.OPTS$calls)
Put <- as.data.frame(SPY.OPTS$puts)

K0 = max(Put[Put$Strike<S0,]$Strike, Call[Call$Strike<S0,]$Strike)
Call_OTM <- Call[Call$Strike>=K0,]
Call_OTM$dif = c(S0-K0, diff(Call_OTM$Strike))
Put_OTM <- Put[Put$Strike<=K0,]
Put_OTM$dif = c(diff(Put_OTM$Strike),S0-K0)

T = as.numeric(difftime(as.Date("2020-12-24"), Sys.Date()))/365
r=0.09/100
VIX_imp = 100*sqrt((2*exp(r*T)/T)*
  (sum(Call_OTM$Last/(Call_OTM$Strike^2)*Call_OTM$dif)+sum(Put_OTM$Last/ (Put_OTM$Strike^2) * Put_OTM$dif)))

print(VIX_imp)

 

This is bit complicated and out of my field, I hope someone can explain to me in short?

 

I think it can be summed up as: If you want to compute VIX yourself, you can. -- The CBOE published a step by step guide to do that (their VIX white paper).

The more important question to some of us is: Should we referencing VIX, or is our needs best served by a more direct and precise metric? (I prefer ATM IV when I want a measure of the IV of the underlying! This also allows reference with respect to the term (DTE)!