# Talk:VIX

## Example

I think a better example would be in order. It's confusing where the calculations came from. I'm going to try to figure it out myself and then change it. KevinPuj 00:46, 17 August 2006 (UTC)

By all means, if there is something that can be better explained, please do so. Ronnotel 01:46, 17 August 2006 (UTC)
No actually, it's fine, it just didn't have the unit "months". I fixed it. KevinPuj 22:22, 17 August 2006 (UTC)

An updated graph would be nice: An illustration of the development after Q3/2008 would be interesting, as we just see the start of the "financial crisis / recession". —Preceding unsigned comment added by 79.160.222.90 (talk) 17:15, 2 September 2010 (UTC)

## Equation

Would someone like to add the equation for how the VIX is calculated/defined? —The preceding unsigned comment was added by 82.211.86.2 (talk) 15:29, 17 January 2007 (UTC).

The exact calculation is a kernel-smoothed estimator and it's not easy to provide a meaningful summary without going into excessive detail. I considered adding it some time ago, but concluded that it would not enhance the article to do so. Please note that there is a reference to the exact methodology, which is available at the CBOE web site in pdf format. If there is a consensus view that the formula should be included, then I would recommend to be as sparing as possible (the derivation runs to multiple pages in the PDF). Ronnotel 15:45, 17 January 2007 (UTC)
Any chance you could point us in the direction of this multiple page derivation? I've had a look at the CBOE pdf cited, but can only find one showing the equation of the new VIX and this has no derivation at all, just an example and explanation of how to plug the numbers is. I'd be very interested in a more mathematical reference for where the equation comes from and why it takes that exact form (which has rather counter intuitive behaviour IMHO). Cpdo 17:31, 29 January 2007 (UTC)
As with most anything of substance to do with volatility, it comes from Derman and his clique at Goldman. Take a look here. Free registration is required. Ronnotel 18:59, 29 January 2007 (UTC)
Why does the example on this (i.e. VIX) page scale from +10 to +40%, but the same graph on Yahoo Finance scale from -60 to +120%? 08:04, 21 October 2007 (UTC) —Preceding unsigned comment added by BomberJoe (talkcontribs)

## Validation of the VIX....???

If the VIX is too simplified as described in the section of Criticism, then validation of the method should be conducted. One needs to bear in mind that financial market is a complex stage. If a single VIX is not enough to measure the volatility, generate another or others to complement it with the implementation of validation process simultaneously

I would have liked to see something like "performance", i.e. VIX compared to real life volatility over a period, compared, schematically at least, to one or more other volatility measures — Preceding unsigned comment added by 78.141.129.116 (talk) 08:44, 23 January 2012 (UTC)

The Belvoir package (http://hobbes.nmsu.edu/h-search.php?key=belvoir&pushbutton=Search) contains the VIX (close) since 1990 upto and including july/august 2012, and contains a Moving Average of (high/low*100-100)*8 of the S&P 500 index (5 days). Source: http://finance.yahoo.com (the MA-5 is multiplied by 8 because of the scale of the graph). The application itself creates a graph with a width equal to the number of trading days (5691 or 5702), but you'ld be able to create any graph with the data, because the data files are plain pc text files (VIX.TXT and SP500MA5.TXT).
The unoptimized graph (I won't upload it) clearly shows the correlation, i.e. the VIX doesn't predict anything and it's roughly identical to an intraday volatility.
In general the critism is more right than expressed here, and the graphs are as meaningless as a future-predicting VIX. Essentially the VIX is an overinterpreted way to calculate a historical volatility, the correlation in the graph is remarkable, to say the least. — Preceding unsigned comment added by 84.53.88.202 (talk) 04:12, 16 August 2012 (UTC)

## Revert edits by User:84.68.104.223

I reverted two edits:

1. The math asserted in the example is incorrect. The original answer of 4.3% change in 30 days is correct. Please see Volatility (finance).
2. There is already a reference to the CBOE specification in the article.

Ronnotel 00:31, 27 August 2007 (UTC)

## Expected return

The example on the VIX article states that if the VIX is at 15, the S&P has a 68% chance of moving up or down 4.33%. That assumes the expected return is 0%, correct? If the expected return were mu, then the S&P would have a 68% chance of ending at mu + / - 4.33% in one month, correct?

If you look at the "What is VIX?" section of http://www.cboe.com/micro/vix/VIXoptionsQRG.pdf it would appear that you are correct. --MichaelTurley (talk) 20:16, 21 March 2008 (UTC)

If the expected return were nonzero, arbitrage would adjust the price until the expected return became zero. --Doradus (talk) 15:43, 3 December 2008 (UTC)
Sorry, my bad. Clearly the expected return for the stock market must be higher than zero, or nobody would invest. Not sure what I was thinking there. --Doradus (talk) 07:17, 8 December 2008 (UTC)

Why 12 was squarerooted in the calculation? — Preceding unsigned comment added by 199.198.251.108 (talk) 17:15, 11 July 2012 (UTC)

I don't understand how 15% annual change can imply 4.33% monthly change. 1.0433*1.0433*...etc. 12 times = 1.0433^12 = 1.66306984, which is not a 15% gain. It seems like it should be 1.15^(1/12)=1.0117, or a 1.17% monthly change. Superm401 - Talk 06:54, 7 October 2008 (UTC)
Please remember that it's variance that scales linearly with time. Since volatility is the square root of variance, it scales with the square root of time. Here's an old option traders' trick. If the implied volatility of an option is 32% (per annum), then the market is expecting the underlier to move by 32/sqrt(252) = 32/16 = 2% per day (assuming 252 trading days per year) Ronnotel (talk) 11:36, 7 October 2008 (UTC)
16*16 is 256, not 252. Never mind that, it's close enough. I don't want to deny a math trick in use, but in reality it'll be reversed. The recent intraday volatility was about 2% on average in the past, so the implied volatility will be about 32%. There's no such thing as an implied volatility which predicts the future. Implied volatility is a complicated way to try to describe the past. — Preceding unsigned comment added by 84.53.88.202 (talk) 04:30, 16 August 2012 (UTC)

15% should be used the similar way? 15/16=1% per day? — Preceding unsigned comment added by 199.198.251.108 (talk) 17:18, 11 July 2012 (UTC)

## History

Should we add history of the VIX? Specifically, should we mention the VXO, which is the "old VIX"? We could list differences between VIX and VXO, and the underlying formulae for each. I don't know enough about it myself to write the content, though. —Preceding unsigned comment added by Kreline (talkcontribs) 04:23, 30 September 2008 (UTC)

## Update the graphic on the page?

(Thursday, October 9, 2008) Just saw a "Breaking News" headline on CNN.com saying that "Dow falls more than 600 points. Gauge of investor fear -- an index known as the Vix , hits an all-time high." Perhaps someone could take this as an opportunity to update and re-plot the Vix history graph on the page? Dave (talk) 20:08, 9 October 2008 (UTC)

## Professor Robert E. Whaley has been quoted as writing that he "back figured" the VIX to see a level of around 180 just before the 1987 crash.

Professor Robert E. Whaley has been quoted online as writing that he "back figured" the VIX to see a level of around 180 just before the 1987 crash.

If true, that suggests the 2008 levels seen to date are relatively less threatening than currently believed —Preceding unsigned comment added by 66.167.61.107 (talk) 20:07, 16 October 2008 (UTC)

## Chart of 5 indicators, including VIX -- good external link

• An excellent chart of five credit-availability and risk indicators, including the VIX, is available at htt ETC w3 ETC .nytimes.com/interactive/2008/10/08/business/economy/20081008-credit-chart-graphic.html —Preceding unsigned comment added by Ocdcntx (talkcontribs) 13:43, 17 October 2008 (UTC)

## Chart of 5 indicators, including VIX -- good external link

• An excellent chart of five credit-availability and risk indicators, including the VIX, is available at htt ETC w3 ETC .nytimes.com/interactive/2008/10/08/business/economy/20081008-credit-chart-graphic.html Ocdcntx (talk) 13:48, 17 October 2008 (UTC)
```totally agree  —Preceding unsigned comment added by 192.234.99.1 (talk) 19:04, 24 October 2008 (UTC)
```

## Good faith edit by User:Elgas

I have temporarily reverted a series of edits by User:Elgas pending discussion. I'm afraid I don't understand the proposed edits, particularly the meaning of the phrase:

The expected (mean) movement in the Gaussian world is 0,8 times the VIX

Can you please point a source with this information? I believe the correct description of the VIX comes from the CBOE as it was in text before your edit. Thanks. Ronnotel (talk) 20:53, 30 December 2008 (UTC)

## Pricing model for VIX Options

Who can compare the existing pricing model for VIX options? —Preceding unsigned comment added by 64.94.157.1 (talk) 18:52, 20 March 2009 (UTC)

## graph mid 2009 update

can someone please update the graph, thanks —Preceding unsigned comment added by 170.170.59.138 (talk) 22:46, 17 May 2009 (UTC)

## VIX usually inversely correlated with S&P

This article, at the end, seems to argue that bullish sentiment is as bullish for the VIX as bearish sentiment, only the volaitlity matters. That clearly isn't true. On sharp upward movement, the VIX almost always declines. 67.168.203.186 (talk) 02:15, 25 October 2009 (UTC)

## Criticism section for deletion

The section seems to be a rant by some particular individual, and the subject of the rant is not very relevant to the article anyway. No sources are cited. There had been a tag on the section for almost a year, asking for sources. Since there has been no improvement, I am deleting the section. —Preceding unsigned comment added by Kotika98 (talkcontribs) 14:51, 18 November 2009 (UTC) The part commencing with "In a similar note, Emanuel Derman ..." seems much to generic here? — Preceding unsigned comment added by 78.141.129.116 (talk) 08:41, 23 January 2012 (UTC)

Agree criticism should be deleted, but because criticism irrelevant to VIX. VIX is not designed as a forecasting model, but as the rest of the article makes clear, as an index of a market price of "volatility". It is a bit like criticising the concept of a bond yield because it does not forecast future interest rates. — Preceding unsigned comment added by Sv507 (talkcontribs) 13:13, 30 March 2012 (UTC)

I agree it should be deleted but not more for the neutriality reason. Since VIX is by definition the volatility of S&P over the next 30 days, it is fair enough to say is it used as a forecasting model.

I also think this section should be deleted since it is irrelevant, the criticism talks about the forecast performance of statistical models such as GARCH. The VIX index is not based on any statistical time series model. — Preceding unsigned comment added by 78.69.31.29 (talk) 10:15, 21 September 2012 (UTC)

Referring to the Shiller qoutation (end of paragrapf Criticism):

This is circular reasoning: When comparing the standard deviation ex post related to time “t” for the period “t til t+30" the prediction intended) and not with the “actual (historical) volatility” for the period “t-30 til t) one will find that the VIX is a little bit “behind” (some 30 days!) and not at all a proof for B&S.

Gaschroeder (talk) 06:01, 19 September 2016 (UTC)

## Wrong explanation in the article

I can read in the article: "Higher (or lower) volatility of the underlying security makes an option more (or less) valuable, since there is a greater (or smaller) probability that the option will expire in the money (i.e. with a market value above zero). So a higher option price implies greater volatility, other things being equal."

This is not true in general. ATM options are more expensive when volatility is high, but their probability to be in the money is the same, no matter what the vol is. In fact when volatility is high, the expected payoff of the options is higher, not necessarily their probability to be in the money.

A possible explanation for the article could be: options can be seen as an insurance against a rise (call) or a fall (put) of their underlying. High volatility increases the probability of wide market moves, making such insurance more expensive to buy. As a consequence, options are more expensive when the implied volatility of their underlying is high.

But english is not my mother tongue...I would like someone to check the spelling first.

Wrong, the probability is higher because implied volatility is based on the past. If the historical volatility is 2% a day instead of 0%, it's more likely that the option will be ITM.

If the strike is 12, exactly ATM, a neutral variation of the underlying value is about 11.76-12.24. If the volatility would be 0%, it'll always remain 12. The higher the volatility, the more likely it is that an option will be ITM, at least for a short while. But making money is less sure, because you'll be paying the seller of the option a premium of about 0.24.

—Preceding unsigned comment added by 194.98.239.11 (talk) 09:57, 4 August 2010 (UTC)

## Can a variance swap really be perfectly statistically replicated using options?

Is this actually true? A reference would be nice. I know that a result like this holds for models with where the price is a continuous semimartingales, but we are not talking a model here. I guess its also not entirely clear what statistically means here. Is there really a static hedge that perfectly replicates a variance swap in all situations? I also doubt that the VIX can be replicated via dynamic hedging. This seems like another theoretical result that holds under specific model assumptions. Update, I just went over the vix page on cboe, and the formula they present under "mathematical derivation" uses Ito's Lemma. This means it depends upon the forward price being continuous. As for as I can tell, this statement is clearly false without further assumptions.

—Preceding unsigned comment added by 72.179.49.120 (talk) 21:04, 15 October 2010 (UTC) agree with above - the assumption fails for jumps ...also the "model independent" price assumes you statically replicate with an infite array of options ( same maturity, infinte strike range) — Preceding unsigned comment added by Sv507 (talkcontribs) 13:21, 30 March 2012 (UTC)

## Omission of a contribution by two Israeli scholars?

I have added an external link to a site where the development of the index is co-attributed to two Israeli scholars.[1] Seems to need future clarification in the body of the article, as done in the Hebrew version.RomanB2011 (talk) 23:32, 2 April 2011 (UTC)

## Annualisation calculation

I don't think the "15%/sqrt(12) - 1.17%" calculation in the "Interpretation" section is correct - shouldn't it be the twelfth root of 1.15?

Also, am I correct in understanding that a VIX of 40 does not actually imply an expected 40% change in the SP500 index over the next year? Is there an equivalent index that measures something like that? 205.228.82.139 (talk) 11:40, 26 August 2011 (UTC)

the correct calculation of inter period volatility comes up frequently. Please see footnote #3 in the references. Ronnotel (talk) 12:00, 26 August 2011 (UTC)
0.15 / sqrt(12) = 0.0433012702
1.15 / sqrt(12) = 0.331976405
15 / sqrt(12) = 4.33012702
I don't see how any of these equal 1.17%
205.228.82.139 (talk) 12:55, 26 August 2011 (UTC)
Someone who edited the article has apparently confused scaling volatility with annualizing returns. He or she obtained 1.17% by taking the twelfth root of 1.15 (i.e. 1.15^(1/12) = 1.0117), which would be correct in the case of compounding returns. However, that is incorrect here because that's not the way volatility is scaled. Volatility is scaled by multiplying by the square root of the number of time periods. Thus, 4.33% is correctly obtained by dividing 15% by the square root of 12. Strictly speaking, this only holds true for i.i.d. random variables, but the square root rule is used in practice and usually works well enough for small numbers of time periods. Fw9322 (talk) 04:17, 2 September 2011 (UTC)

### Both issues exist

IMHO, the issues of

• scaling volatility

and

• converting between annualized returns and a change over 30 days

both exist in the Interpretation section. I am basing this upon this version, which was the current version when this ["Both issues exist"] subsection was added.

OK, as for scaling volatility, I defer to the comment above (from Fw9322 and dated "04:17, 2 September 2011 (UTC)") about that topic. I probably do not know enough about scaling volatility, but I think several of the commenters above, like me, do know a thing or two about "converting between annualized returns and a change over 30 days", and IMHO that issue is not handled (explained) well, in the Interpretation section.

See, the Interpretation section says, in part, [quote]

For example, if the VIX is 15, this represents an expected annualized change of 15% over the next 30 days; thus one can infer that the index option markets expect the S&P 500 to move up or down 15%/√12 = 4.33% over the next 30-day period.

It appears to me, that the "calculation" shown, contains only the math for

• scaling volatility

not for

• converting between annualized returns and a change over 30 days

Maybe the author or editor assumed that everyone "knows" that where it says "15%" in the quoted sentence above, that it really means [something more like]

(the twelfth root of 1.15) minus one

. But, such an "assumption" (about what everyone "knows") should not be relied upon. IMHO the "15%" there, should be replaced by something more correct, or at least accompanied -- if appropriate -- by an explanation (in parentheses) like this:

(where the "15%" there, means -- in this context -- the percentage that corresponds to moving up or down at a 15% annual rate, but only doing so for 30 days).

I am not sure that such an explanation (in parentheses) is the best solution. Maybe it would be better, to update the math, so that it correctly handles (takes care of) both the issues, of

• scaling volatility

and

• converting between annualized returns and a change over 30 days

Any advice or other comments? (Thanks for reading this)! --Mike Schwartz (talk) 09:54, 25 May 2014 (UTC)

Scaling is risky

The practice: "Volatility is scaled by multiplying by the square root of the number of time periods." is correct only as long as the volatility is "stationary". However, stationary volatility doesn't happen to be observed regarding all existing volatilities being volatile themselves. The VIX in particular is to a reasonable degree scale invariant. Mr. Diebold is warning us since Dec, 1996! [1] Gaschroeder (talk) 08:05, 21 September 2016 (UTC)

References

1. ^ Diebold, Francis X., et al „Converting 1-Day Volatility to h-Day Volatility: Scaling by is Worse than You Think“ (Francis X. Diebold University of Pennsylvania, fdiebold@mail.sas.upenn.edu) December 1996

## Interpretation

There seems to be a general misunderstanding of what the volatility means in the interpretation section. VIX by itself says very little about how much S&P 500 Index is likely to change over any period expressed in days or longer. Vix measures prices of options and therefore measures expected instantaneous volatility (micro) of S&P 500 averaged over the next 30 days. To clarify: take minute by minute volatility of S&P and average that over 30 days. The 30-day volatility as mentioned in the article does not care what happens throughout 30 days and only looks at the first and last level and it measures cumulative (macro) 30-day volatility. The change in S&P 500 through 30-day period (macro) has something to do with VIX (micro) and they are somewhat correlated, but they are simply not the same thing. In general, if volatility is constant and process is not mean reverting then 30 day average of instantaneous volatility is the same as 30 days volatility. Aside from theoretical Gaussian process there are no real world financial variables, especially S&P 500 Index, satisfying those conditions. — Preceding unsigned comment added by 146.127.253.13 (talk) 15:38, 25 October 2011 (UTC)

As a footnote to [#Wrong_explanation_in_the_article], the statement:

"Higher (or lower) volatility of the underlying security makes an option more (or less) valuable, since there is a greater (or smaller) probability that the option will expire in the money (i.e. with a market value above zero). "

is also misleading for a different reason. The cited comment correctly points out that volatility is independent of the probability of ITM expiration. However, the antecedent clause is false. It should read:

"Higher (or lower) volatility of the underlying security makes an option more (or less) expensive"

Higher volatility increases the option risk premium, which increases the option price. 'valuable' is an imprecise term in this context and should be replaced by 'expensive'. — Preceding unsigned comment added by FredLoney (talkcontribs) 18:01, 30 January 2012 (UTC)

## Fear & Greed? Or, just fear?

The article says,

Although the VIX is often called the "fear index", a high VIX is not necessarily bearish for stocks.[7] Instead, the VIX is a measure of market perceived volatility in either direction, including to the upside. In practical terms, when investors anticipate large upside volatility, they are unwilling to sell upside call stock options unless they receive a large premium.

It seems clear enough that if lots of put option contracts are bought for high prices, the VIX will reflect expectations of a big move down. Hence "fear."

But what if lots of call option contracts are bought for high prices? Does the formula lower the VIX because the option buys mean there is less fear of a drop in stock prices? Or, does the formula raise the VIX (as the article currently says) because the option buys reflect expectations of a sharp move up?

## Implied volatility vs VIX-measured volatility

Implied volatility is derived using the reverced option pricing formula specific to the certain model (in 99% time it's Black-Scholes). VIX is calculating an estimate of annualized expected intrgrated quadratic variation which is fundamentaly different approach.

The links to "Implied Volatility" article in the beggining of the VIX article are misleading, giving reader an impression that VIX is measuring BS implied volatility. — Preceding unsigned comment added by 176.14.140.34 (talk) 07:07, 7 October 2015 (UTC)