VIX

The concept of computing implied volatility or an implied volatility index dates to the publication of the Black and Scholes' 1973 paper, "The Pricing of Options and Corporate Liabilities", published in the Journal of Political Economy, which introduced the seminal Black–Scholes model for valuing options.{{Cite journal|last1=Black|first1=Fischer|last2=Scholes|first2=Myron|date=1973|title=The Pricing of Options and Corporate Liabilities|url=http://www.jstor.org/stable/1831029|journal=Journal of Political Economy|volume=81|issue=3|pages=637–654|doi=10.1086/260062|jstor=1831029|s2cid=154552078|issn=0022-3808|url-access=subscription}} Just as a bond's implied yield to maturity can be computed by equating a bond's market price to its valuation formula, an option-implied volatility of a financial or physical asset can be computed by equating the asset option's market price to its valuation formula.{{Cite web|last=Nickolas|first=Steven|title=Implied Volatility|url=https://www.investopedia.com/ask/answers/032515/what-options-implied-volatility-and-how-it-calculated.asp|access-date=2020-08-18|website=Investopedia|language=en}} In the case of VIX, the option prices used are the S&P 500 index option prices.{{Cite web|title=VIX Options|url=http://www.cboe.com/products/vix-index-volatility/vix-options-and-futures/vix-options|access-date=2020-08-18|website=www.cboe.com}}{{Cite web|title=Olymp Trade promo code|url=https://honestdigitalreview.com/2019/08/olymptrade-coupon-code-promo-code-bonus.html|access-date=2020-07-22|website=Honestdigitalreview.com|date=24 August 2019 }}

The VIX takes as inputs the market prices of the call and put options on the S&P 500 index for near-term options with more than 23 days until expiration, next-term options with less than 37 days until expiration, and risk-free U.S. treasury bill interest rates. Options are ignored if their bid prices are zero or where their strike prices are outside the level where two consecutive bid prices are zero.{{cite web | date = 2019 | title=Whitepaper: Cboe Volatility Index | work=CBOE.com | url=https://cdn.cboe.com/resources/vix/vixwhite.pdf |access-date=26 February 2020}}{{page needed|date=February 2020}}{{page needed|date=February 2020}} The goal is to estimate the implied volatility of S&P 500 index options at an average expiration of 30 days.{{Cite web|url=https://www.cboe.com/tradable_products/|title=Cboe Tradable Products|website=www.cboe.com}}

File:Vix historical 1990-2024.png

Given that it is possible to create a hedging position equivalent to a variance swap using only vanilla puts and calls (also called "static replication"),{{Cite web |date=May 2005 |title=Just what you need to know about Variance Swaps |url=http://spekulant.com.pl/article/Volatility%20products/JP%20Morgan%20Chase%20-%20Variance%20Swap%20introduction.pdf}} the VIX can also be seen as the square root of the implied volatility of a variance swap{{Cite journal |last=Kanas |first=Angelos |date=2013-06-01 |title=The risk-return relation and VIX: evidence from the S&P 500 |url=https://doi.org/10.1007/s00181-012-0639-4 |journal=Empirical Economics |language=en |volume=44 |issue=3 |pages=1291–1314 |doi=10.1007/s00181-012-0639-4 |issn=1435-8921|url-access=subscription }} – and not that of a volatility swap, volatility being the square root of variance, or standard deviation.

The VIX is the square root of the risk-neutral expectation of the S&P 500 variance over the next 30 calendar days and is quoted as an annualized standard deviation.{{Cite web |access-date=15 March 2024 |title=White Paper Cboe Volatility Index |url=https://www.sfu.ca/~poitras/419_VIX.pdf}}

The VIX is calculated and disseminated in real-time by the Chicago Board Options Exchange.{{citation needed|date=February 2020}} On March 26, 2004, trading in futures on the VIX began on CBOE Futures Exchange (CFE).{{cite journal |last1=Lin |first1=Yueh-Neng |title=VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation |journal=Journal of Banking & Finance |date=November 2013 |volume=37 |issue=11 |pages=4432–4446 |doi=10.1016/j.jbankfin.2013.03.006 |url=https://doi.org/10.1016/j.jbankfin.2013.03.006|url-access=subscription }}

On February 24, 2006, it became possible to trade options on the VIX. Several exchange-traded funds hold mixtures of VIX futures that attempt to enable stock-like trading in those futures. The correlation between these ETFs and the actual VIX index is very poor, especially when the VIX is moving.{{cite web|first=Brendan|last=Conway|date = 17 June 2014 | title=No, Your ETF Doesn't Track the VIX Volatility Index—and Here are the Numbers|work = Barrons.com | url=https://www.barrons.com/articles/no-your-etf-doesnt-track-the-vix-volatility-index-and-here-are-the-numbers-1403010972| access-date=26 February 2020}}

The VIX is the 30-day expected volatility of the SP500 index, more precisely the square root of a 30-day expected realized variance of the index. It is calculated as a weighted average of out-of-the-money call and put options on the S&P 500:

: $\backslash mathrm\{VIX\}=\; \backslash sqrt\{\backslash frac\{2e^\{r\; \backslash ,\backslash !\; \backslash tau\}\}\{\backslash tau\}\; \backslash left(\backslash int\_\{0\}^\{F\}\; \backslash frac\{P(K)\}\{K^2\}\; dK\; +\; \backslash int\_F^\{\backslash infty\}\; \backslash frac\{C(K)\}\{K^2\}\; dK\; \backslash right)\}$

where $\{\backslash tau\}$ is the number of average days in a month (30 days), $r$ is the risk-free rate, $F$ is the 30-day forward price on the S&P 500, and $P(K)$ and $C(K)$ are prices for puts and calls with strike $K$ and 30 days to maturity.{{cite web |last1=Papanicolaou |first1=Andrew |title=Identifying Links Between the S&P500 and VIX Derivatives |url=https://www.ipam.ucla.edu/research-articles/identifying-links-between-the-sp500-and-vix-derivatives/ |website=Institute for Pure & Applied Mathematics |date=5 April 2016 |publisher=UCLA |access-date=10 April 2020}}

The following is a timeline of key events in the history of the VIX Index:{{according to whom|date=February 2020}}

• 1987 – The Sigma Index was introduced in an academic paper by Brenner and Galai, published in Financial Analysts Journal, July/August 1989.{{cite web|url=http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf |title=Volatility |publisher=people.stern.nyu.edu |access-date=2020-02-26}} Brenner and Galai wrote, "Our volatility index, to be named Sigma Index, would be updated frequently and used as the underlying asset for futures and options ... A volatility index would play the same role as the market index play for options and futures on the index."
• 1989 – Brenner and Galai's paper is published in Financial Analysts Journal. Brenner and Galai develop their research further in graduate symposia at The Hebrew University of Jerusalem{{citation needed|date=February 2020}} and at the Leonard M. Stern School of Business at New York University.{{citation needed|date=February 2020}}
• 1992 – The American Stock Exchange announced it is conducting a feasibility study on a volatility index, proposed as the "Sigma Index".{{cite web|url=http://people.stern.nyu.edu/mbrenner/research/IFR_report_on_Brenner-Galai_Sigma_Index.pdf |title=IFR report |publisher=people.stern.nyu.edu |date=1992 |access-date=2020-02-26}}
• 1993 – On January 19, 1993, the Chicago Board Options Exchange held a press conference to announce the launch of real-time reporting of the CBOE Market Volatility Index or VIX. The formula that determines the VIX is tailored to the CBOE S&P 100 Index (OEX) option prices, and was developed by Professor Robert E. Whaley of Duke University (now at Vanderbilt University), whom the CBOE had commissioned.{{cite web|url=http://rewconsulting.files.wordpress.com/2012/09/jd93.pdf |title=Derivatives on market volatility |publisher=rewconsulting.files.wordpress.com |date=2012 |access-date=2020-02-26}} This index, now known as the VXO, is a measure of implied volatility calculated using 30-day S&P 100 index at-the-money options.{{cite web| author = Mehta, Salil | date = July 2015 | title = Volatility in motion | work=Statistical Ideas | format = blog | url=http://statisticalideas.blogspot.com/2015/07/volatility-in-motion.html |via=Statisticalideas.blogspot.com |access-date=26 February 2020}}
• 1993 – Professors Brenner and Galai develop their 1989 proposal for a series of volatility index in their paper, "Hedging Volatility in Foreign Currencies", published in The Journal of Derivatives in the fall of 1993.{{full citation needed|date=February 2020}}
• 2003 – The CBOE introduces a new methodology for the VIX. Working with Goldman Sachs, the CBOE developed further computational methodologies, and changed the underlying index the CBOE S&P 100 Index (OEX) to the CBOE S&P 500 Index (SPX). The old methodology was renamed the VXO.{{verify source|date=February 2020}}
• 2004 – On March 26, 2004, the first-ever trading in futures on the VIX Index began on the CBOE Futures Exchange (CFE).{{Cite web|title=History|url=https://www.cboe.com/about/history/|access-date=2021-11-20|website=www.cboe.com}} VIX is now proposed{{clarify|date=February 2020}} on different trading platforms, like XTB.{{citation needed|date=February 2020}}
• 2006 – VIX options were launched in February of this year.
• 2008 – On October 24, 2008, the VIX reached an intraday high of 89.53.{{Cite news|date=2009-05-19|title=Update: 3-Volatility index below 30 for 1st time since Sept|language=en|work=Reuters|url=https://www.reuters.com/article/markets-stocks-vix-idUSN1945357120090519|access-date=2021-11-20}}
• 2008 – On November 21, 2008, the VIX closed at a record 80.74.{{cite news |author=Li |first=Yun |date=March 16, 2020 |title=Wall Street's fear gauge closes at highest level ever, surpassing even financial crisis peak |url=https://www.cnbc.com/2020/03/16/wall-streets-fear-gauge-hits-highest-level-ever.html |access-date=March 17, 2020 |publisher=MSNBC}}
• 2018 – On February 5, 2018, the VIX closed 37.32 (up 103.99% from previous close).{{cite web |title=CBOE Volatility Index |url=https://www.marketwatch.com/investing/index/VIX |website=MarketWatch |access-date=August 23, 2020 |archive-url=https://web.archive.org/web/20180207005155/https://www.marketwatch.com/investing/index/VIX |archive-date=February 7, 2018 |date=February 7, 2018}}
• 2020 – On March 9, 2020, the VIX hit 62.12, the highest level since the 2008 financial crisis due to a combination of the 2020 Russia–Saudi Arabia oil price war and the COVID-19 pandemic.{{cite news |author=Peterseil |first=Yakob |date=March 9, 2020 |title=VIX Spikes to Highest Since 2008 in Manic Monday Trading |url=https://www.bloomberg.com/news/articles/2020-03-09/vix-futures-spike-to-highest-since-2009-in-manic-monday-trading |access-date=March 9, 2020 |publisher=Bloomburg}}{{cite news |author=Evans |first=Pete |date=March 9, 2020 |title='This is basically panic selling': Stock markets plunge as coronavirus fear spreads |url=https://www.cbc.ca/news/business/markets-stocks-oil-1.5490697 |access-date=March 9, 2020 |publisher=CBC}}
• 2020 – During the COVID-19 pandemic, on March 12, 2020, the VIX hit and closed at 75.47, exceeding the previous Black Monday value, as a travel ban to the US from Europe was announced by President Trump.{{cite news |author=Jasinski |first=Nicholas |date=March 12, 2020 |title=The VIX Fear Gauge Is Soaring. It's Unlikely to Come Down Anytime Soon |url=https://www.barrons.com/articles/the-vix-fear-gauge-is-soaring-its-unlikely-to-come-down-anytime-soon-51584050364 |access-date=March 12, 2020 |publisher=Barron's}}
• 2020 – On March 16, the VIX closed at 82.69, the highest level since its inception in 1990.{{cite web|url=https://www.cnbc.com/2020/03/16/wall-streets-fear-gauge-hits-highest-level-ever.html|date=March 16, 2020|access-date=March 19, 2020|first=Yun|last=Li|website=cnbc.com|title=Wall Street's fear gauge closes at highest level ever, surpassing even financial crisis peak}}
• 2021 – The U.S. Securities and Exchange Commission fined the S&P Dow Jones Indices for halting data on February 5, 2018.Jonathan Stempel. (17 May 2021). "S&P Dow Jones Indices is fined by SEC over U.S. 'volatility' crash". [https://finance.yahoo.com/news/p-dow-jones-indices-fined-152400340.html Yahoo Finance website]. Retrieved 18 May 2021.

Image:Vix.png r shown. Note that VIX has virtually the same predictive power as past volatility, insofar as the shown correlation coefficients are nearly identical.]]

VIX is sometimes criticized as a prediction of future volatility. Instead it is described as a measure of the current price of index options.{{according to whom|date=February 2020}}{{citation needed|date=February 2020}}

Critics claim that, despite a sophisticated formulation, the predictive power of most volatility forecasting models is similar to that of plain-vanilla measures, such as simple past volatility.{{cite journal |last1=Cumby |first1=R. |first2=S. |last2=Figlewski |first3=J. |last3=Hasbrouck |year=1993 |title=Forecasting Volatility and Correlations with EGARCH models |journal=Journal of Derivatives |volume=1 |issue=2 |pages=51–63 |doi=10.3905/jod.1993.407877 |s2cid=154028452 }}{{cite journal |last=Jorion |first=P. |year=1995 |title=Predicting Volatility in Foreign Exchange Market |journal=Journal of Finance |volume=50 |issue=2 |pages=507–528 |jstor=2329417 |doi=10.1111/j.1540-6261.1995.tb04793.x}}{{cite journal |last1=Adhikari |first1=B. |first2=J. |last2=Hilliard|year=2014|title= The VIX, VXO and realised volatility: a test of lagged and contemporaneous relationships|journal=International Journal of Financial Markets and Derivatives|volume=3 |issue=3|pages=222–240|doi=10.1504/IJFMD.2014.059637}} However, other works have countered that these critiques failed to correctly implement the more complicated models.{{cite journal |first1=Torben G. |last1=Andersen |first2=Tim |last2=Bollerslev |title=Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts |journal=International Economic Review |year=1998 |volume=39 |issue=4 |pages=885–905 |doi= 10.2307/2527343|jstor=2527343 }}

Some practitioners and portfolio managers have questioned the depth of our understanding of the fundamental concept of volatility, itself. For example, Daniel Goldstein and Nassim Taleb famously titled one of their research articles, We Don't Quite Know What We are Talking About When We Talk About Volatility.{{cite journal|first1=Daniel G.|last1=Goldstein|first2=Nassim Nicholas|last2=Taleb|date=28 March 2007|title = We Don't Quite Know What We are Talking About When We Talk About Volatility|journal = Journal of Portfolio Management | volume = 33 | issue = 4 | ssrn = 970480 |doi=10.3905/jpm.2007.690609|s2cid=153535794}} Relatedly,{{verify source|date = February 2020}} Emanuel Derman has expressed disillusion with empirical models that are unsupported by theory.{{clarify|date = February 2020}}{{citation needed|date = February 2020}}{{cite book | author = Derman, Emanuel | date = 2011 | title = Models Behaving Badly: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life | location = New York, NY | publisher = Simon and Schuster | isbn = 9781439165010 | url = https://www.google.com/search?tbm=bks&hl=en&q=9781439164983 | access-date = 25 February 2020 | pages = unknown page nos}}{{page needed|date = February 2020}} He argues that, while "theories are attempts to uncover the hidden principles underpinning the world around us ... [we should remember that] models are metaphors—analogies that describe one thing relative to another."{{page needed|date=February 2020}}

Michael Harris, the trader, programmer, price pattern theorist, and author, has argued that VIX just tracks the inverse of price and has no predictive power.{{cite web|

author = Harris, Michael | date = 21 August 2012 | title = On the Zero Predictive Capacity of VIX—Price Action Lab Blog | work = PriceActionLab.com | format = self-published blog |

url=http://www.priceactionlab.com/Blog/2012/08/on-the-zero-predictive-capacity-of-vix/| access-date = 25 February 2020 }}{{cite web| author = Harris, Michael | date = 25 August 2012 | title = Further Analytical Evidence that VIX Just Tracks the Inverse of Price | work = PriceActionLab.com | format = self-published blog | url=http://www.priceactionlab.com/Blog/2012/08/further-analytical-evidence-that-vix-just-tracks-the-inverse-of-price/ | access-date = 25 February 2020 }}{{better source needed|date=February 2020}}

According to some,{{who|date=February 2020}} VIX should have predictive power as long as the prices computed by the Black–Scholes equation are valid assumptions about the volatility predicted for the future lead time (the remaining time to maturity).{{citation needed|date=February 2020}} Robert J. Shiller has argued that it would be circular reasoning to consider VIX to be proof of Black–Scholes, because they both express the same implied volatility, and has found that calculating VIX retrospectively in 1929 did not predict the surpassing volatility of the Great Depression—suggesting that in the case of anomalous conditions, VIX cannot even weakly predict future severe events.{{cite web |author= Shiller, Robert |author-link= Robert J. Shiller |date= 30 March 2011 |title=Econ 252-11: Financial Markets [Lecture 17—Options Markets] |location= New Haven, CT |publisher= Yale University |format= college course content |url= http://oyc.yale.edu/transcript/1086/econ-252-11 |access-date= 26 February 2020 | url-status= dead |archive-url= https://web.archive.org/web/20160922071546/http://oyc.yale.edu/transcript/1086/econ-252-11 |archive-date= 22 September 2016 |via= OYC.Yale.edu }}

An academic study from the University of Texas at Austin and The Ohio State University examined potential methods of VIX manipulation.{{cite journal | author1=Griffin, John M.|author2=Shams, Amin|date=May 23, 2017|title=Manipulation in the VIX?|website = SSRN.com | url = https://ssrn.com/abstract=2972979 | ssrn = 2972979 | doi = 10.2139/ssrn.2972979 |s2cid=157586475| access-date = 25 February 2020|url-access=subscription}} On February 12, 2018, a letter was sent to the Commodity Futures Trading Commission and Securities and Exchange Commission by a law firm representing an anonymous whistleblower alleging manipulation of the VIX.{{cite journal | author= Cornish, Chloe |date= 13 February 2018 |title=Anonymous 'Whistleblower' Claims 'Rampant Manipulation' of Vix Index |journal= Financial Times |url= https://www.ft.com/content/a89eba68-10b4-11e8-940e-08320fc2a277 |access-date= 26 February 2020 |url-access= subscription |via= FT.com }}

{{anchor|VVIX}}In 2012, the CBOE introduced the "VVIX index" (also referred to as "vol of vol"), a measure of the VIX's expected volatility.{{cite web|date=March 13, 2012 | title=Double the Fun with CBOE's VVIX Index|work = CBOE.com | url=http://www.cboe.com/micro/vvix/documents/vvix-termstructure.pdf|access-date=November 19, 2019}} VVIX is calculated using the same methodology as VIX, except the inputs are market prices for VIX options instead of stock market options.

The VIX can be thought of as the velocity of investor fear. The VVIX measures how much the VIX changes and hence can be thought of as the acceleration of investor fear.{{Cite web |title=What is the VVIX (Cboe VVIX Index)? |url=https://www.vixfaq.com/what-is-the-cboe-vvix-index/ |access-date=2024-04-29 |website=VIXFAQ.com |language=en-US}}

{{Portal|Business and economics}}

{{div col|colwidth=15em|small=yes}}

• Economic Policy Uncertainty Index
• Greed and fear
• Hindenburg Omen
• IVX
• Market trend
• Option on realized variance
• Probability of default
• S&P/ASX 200 VIX
• SKEW
• Volfefe index

{{div col end}}

{{reflist}}

• Black, Fischer and Myron Scholes. "The Pricing of Options and Corporate Liabilities". Journal of Political Economy (May/June 1973), pp. 637–659.
• {{cite journal |last1=Brenner |first1=Menachem |last2=Galai |first2=Dan |date=July–August 1989 |title=New Financial Instruments for Hedging Changes in Volatility |journal=Financial Analysts Journal |volume=45 |issue=4 |pages=61–65 |doi=10.2469/faj.v45.n4.61 | url=http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf }}
• {{cite journal |last1=Brenner |first1=Menachem |last2=Galai |first2=Dan |date=Fall 1993 |title=Hedging Volatility in Foreign Currencies |journal=The Journal of Derivatives |volume=1 |number=1 |pages=53–58 |doi=10.3905/jod.1993.407870 |url=http://people.stern.nyu.edu/mbrenner/research/JOD_article_of_Vol_Index_Computation.pdf }}
• "Amex Explores Volatility Options", [http://people.stern.nyu.edu/mbrenner/research/IFR_report_on_Brenner-Galai_Sigma_Index.pdf International Financing Review], August 8, 1992.
• Black, Keith H. "Improving Hedge Fund Risk Exposures by Hedging Equity Market Volatility, or How the VIX Ate My Kurtosis". The Journal of Trading. (Spring 2006).
• Connors, Larry. "A Volatile Idea", Futures (July 1999): pp. 36–37.
• Connors, Larry. "Timing Your S&P Trades with the VIX". Futures (June 2002): pp. 46–47.
• Copeland, Maggie. "Market Timing: Style and Size Rotation Using the VIX". Financial Analysts Journal, (Mar/Apr 1999); pp. 73–82.
• Daigler, Robert T., and Laura Rossi. "A Portfolio of Stocks and Volatility". The Journal of Investing. (Summer 2006).
• Fleming, Jeff, Barbara Ostdiek, and Robert E. Whaley, "Predicting Stock Market Volatility: A New Measure", The Journal of Futures Markets 15 (May 1995), pp. 265–302.
• Hulbert, Mark, [http://online.barrons.com/article/SB50001424052748703464104576616983309689062.html "The Misuse of the Stock Market's Fear Index"], Barron's, October 7, 2011.
• Mele, Antonio and Yoshiki Obayashi. "The Price of Fixed Income Market Volatility". Springer Verlag: Springer Finance Series, New York (2015).
• Moran, Matthew T., "Review of the VIX Index and VIX Futures", Journal of Indexes, (October/November 2004). pp. 16–19.
• Moran, Matthew T. and Srikant Dash. "VIX Futures and Options: Pricing and Using Volatility Products to Manage Downside Risk and Improve Efficiency in Equity Portfolios". The Journal of Trading. (Summer 2007).
• Szado, Ed. "VIX Futures and Options—A Case Study of Portfolio Diversification During the 2008 Financial Crisis". (June 2009).
• Tan, Kopin. "The ABCs of VIX". Barron's (Mar 15, 2004): p. MW16.
• Tracy, Tennille. "Trading Soars on Financials As Volatility Index Hits Record". Wall Street Journal. (Sept. 30, 2008) p. C6.
• Whaley, Robert E., [http://rewconsulting.files.wordpress.com/2012/09/jd93.pdf "Derivatives on Market Volatility: Hedging Tools Long Overdue"], The Journal of Derivatives 1 (Fall 1993), pp. 71–84.
• Whaley, Robert E., "The Investor Fear Gauge", The Journal of Portfolio Management 26 (Spring 2000), pp. 12–17.
• Whaley, Robert E., "Understanding the VIX", The Journal of Portfolio Management 35 (Spring 2009), pp. 98–105.

• [https://www.cboe.com/tradable_products/vix/ Official website] at CBOE

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