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VIX and Expected Range

Continuing on trying to fight disinformation about VIX. Everyone knows that VIX index the square root of the expected 30-day variance, and if we drop mathematical precision - 30 day expected volatility of S&P index.  Scott Bauer, on CBO's website - " the VIX Index tells us the level of expected volatility of the S&P 500 Index for the next 30 days, with a 68% confidence level",  and you can find 100s of similar explanations around the web   The number 68% comes from expected frequency of 1 standard deviation of normal distribution, and is of course, grossly incorrect, and I will explain why.  While the Black-Scholes formula assumes normality of returns, this is not true of the VIX. Variance is variance but distribution is not assumed to be normal. And if you look at the returns, they are far far from normal.  I took 21 trading day returns of SPX index, and normalized them by monthly VIX ( VIX / 100 / sqrt(252/21)  )     These normalized returns have kurtosis over
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Volatility and Price of a Straddle, Are They The Same?

Yesterday I found another piece of ignorance on Medium: Stop Watching The VIX, Just Make Your Own tl;dr : Just use ATM straddles đŸ€Š This is of course not correct. As I have written before on this blog that (skipping mathematical rigor) the value of ATM straddle is or about 80% of the expected volatility. So if SPY = $400 and VIX = 20, the expected volatility is $400 * 20/100 = $80,  then 1 year ATM straddle would be about 80% of $80 ~ $64 Alternatively, if you see a straddle, you can approximate expected volatility dividing by 80%. For example SPY ATM straddle for 2022/11/18 expiration is about $25 . The expected volatility for November expiration is $25/0.8 ~ $31.25 Even animals are not spared from Russian violence. This dog was found with "V" burned on his snout Another dog had "Z" cut out on its snout ( video ) russian soldiers burned horses alive shot cattle for fun deliberately killed cattle and stole agricultural machinery in order to starve us. Most of the r

Volatility and Expected Range ( High - Low ), Are They The Same?

  This is not a post to correct some abstract mathematical technicality, or a semantic point. Rather I hope to shed some light on widespread mis-estimation of important risk metric that I often see on the internet. For example this double-decker of ignorance popped up on my twitter feed today. VIX as you know is an annualized measure and in order to calculate an expected daily move - that is from one trading day to another, one should use trading day count convention, and sqrt(1/252) - not 365 - as a factor.  sqrt(2/pi) ~ 0.8 is the multiplier to get the average absolute daily return, and here the author is correct. However the range of a random walk is double that amount, 2 * sqrt(2/pi) ~ 1.6 , and in our case over 3% Lower than 5% range we saw in S&P today, but the difference is far less dramatic than the tweet suggests. Traders, pay attention to numbers and formulas you use in your trading. Mistakes can costs you money!

Natural Clustering in VIX Futures Data

 If you take all available VIX futures data and create a scatterplot of daily settlement prices as a function of time to expiration you will see a curious pattern: Yes, there are clear clusters in prices. But what do these clusters mean? The simple explanation is that the VIX term structure passes from one regime to another and there is noise around these regimes. There is a low-volatility flat, regular volatility backwardation, and high volatility contango regimes.   To estimate a model like this from historical data one would need to run some sort of HMM - honestly I am not sure how to do this. But what I did instead is to create daily fits to a basic 3-parameter model, applied k-means to the fitted parameters (n_clusters = 3)      These 3 term-structures are pretty much what I expected. The fit would probably be better in log-space, but that is something I will work on for next time. For now I want to conclude that - completely unsurprisingly three regimes are correlated with S&