# VIX

CBOE Volatility Index (VIX) 2004–2020.

VIX is the ticker symbol and the popular name for the Chicago Board Options Exchange's CBOE Volatility Index, a popular measure of the stock market's expectation of volatility based on S&P 500 index options. It is calculated and disseminated on a real-time basis by the CBOE, and is often referred to as the fear index or fear gauge.

The VIX traces its origin to the financial economics research of Menachem Brenner and Dan Galai. In a series of papers beginning in 1989, Brenner and Galai proposed the creation of a series of volatility indices, beginning with an index on stock market volatility, and moving to interest rate and foreign exchange rate volatility.[1][2][full citation needed]

In their papers, Brenner and Galai proposed, "[the] 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."[This quote needs a citation] In 1992, the CBOE hired consultant Bob Whaley to calculate values for stock market volatility based on this theoretical work.[3] Whaley utilized data series in the index options market, and provided the CBOE with computations for daily VIX levels from January 1986 to May 1992.[not verified in body]

The resulting VIX index formulation provides a measure of market volatility on which expectations of further stock market volatility in the near future might be based. The current VIX index value quotes the expected annualized change in the S&P 500 index over the following 30 days, as computed from options-based theory and current options-market data.

To summarize, VIX is a volatility index derived from S&P 500 options for the 30 days following the measurement date,[4] with the price of each option representing the market's expectation of 30-day forward-looking volatility.[4][5] The resulting VIX index formulation provides a measure of expected market volatility on which expectations of further stock market volatility in the near future might be based.[5]

Like conventional indexes, the VIX Index calculation employs rules for selecting component options and a formula to calculate index values.[5][6] Unlike other market products, VIX cannot be bought or sold directly.[7] Instead, VIX is traded and exchanged via derivative contract, derived ETFs, and ETNs which most commonly track VIX futures indexes.[8]

In addition to VIX, CBOE uses the same methodology to compute the following related products:[5][6]

• Cboe ShortTerm Volatility Index (VIX9DSM), which reflects 9-day expected volatility of the S&P 500 Index,
• Cboe S&P 500® 3-Month Volatility Index (VIX3MSM),
• Cboe S&P 500® 6-Month Volatility Index (VIX6MSM)
• Cboe S&P 500 1-Year Volatility Index (VIX1YSM).

Cboe also calculates the Nasdaq-100® Volatility Index (VXNSM), Cboe DJIA® Volatility Index (VXDSM) and the Cboe Russell 2000® Volatility Index (RVXSM).[5] There is even a VIX on VIX (VVIX) which is a volatility of volatility measure in that it represents the expected volatility of the 30-day forward price of the CBOE Volatility Index (the VIX®).[9]

## Specifications

The concept of computing implied volatility or an implied volatility index dates back 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.[10] 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.[11] In the case of VIX, the option prices used are the S&P 500 index option prices.[12]

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.[5][page needed] The goal is to estimate the implied volatility of S&P 500 index options at an average expiration of 30 days.[13]

Monthly mean of VIX volatility index, 2004-2019

The VIX is the volatility of a variance swap and not that of a volatility swap, volatility being the square root of variance, or standard deviation.[citation needed] A variance swap can be perfectly statically replicated through vanilla puts and calls,[clarification needed] whereas a volatility swap requires dynamic hedging.[citation needed] 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.[citation needed]

The VIX is calculated and disseminated in real-time by the Chicago Board Options Exchange.[citation needed] On March 26, 2004, trading in futures on the VIX began on CBOE Futures Exchange (CFE).[citation needed]

On February 24, 2006, it became possible to trade options on the VIX.[citation needed] 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.[14]

## VIX Formula

The VIX is a 30-day expectation of volatility given by a weighted portfolio of out-of-the-money European options on the S&P 500:[5]

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

where ${\displaystyle {\tau }}$ is the number of average days in a month (30 days), ${\displaystyle r}$ is the risk-free rate, ${\displaystyle F}$ is the 30-day forward price on the S&P 500, and ${\displaystyle P(K)}$ and ${\displaystyle C(K)}$ are prices for puts and calls with strike ${\displaystyle K}$ and 30 days to maturity.[5][15]

## History

The following is a timeline of key events in the history of the VIX Index:[according to whom?]

• 1987 - The Sigma Index was introduced in an academic paper by Brenner and Galai, published in Financial Analysts Journal, July/August 1989.[16] 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."[This quote needs a citation]
• 1989 - Brenner and Galai's paper is published in Financial Analysts Journal.[full citation needed] Brenner and Galai develop their research further in graduate symposia at The Hebrew University of Jerusalem[citation needed] and at the Leonard M. Stern School of Business at New York University.[citation needed]
• 1992 - The American Stock Exchange announced it is conducting a feasibility study on a volatility index, proposed as the "Sigma Index."[17]
• 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.[18] 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.[19]
• 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]
• 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.[5][verification needed]
• 2004 - On March 26, 2004, the first-ever trading in futures on the VIX Index began on the CBOE Futures Exchange (CFE).[citation needed] VIX is now proposed[clarification needed] on different trading platforms, like XTB.[citation needed]
• 2006 - VIX options were launched in February of this year.[citation needed]
• 2008 - On October 24, 2008, the VIX reached an intraday high of 89.53.[citation needed]
• 2008 - On November 21, 2008, the VIX closed at a record 80.74.[20]
• 2018 - On February 5, 2018, the VIX closed 37.32 (up 103.99% from previous close).[21]
• 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.[22][23]
• 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.[24]
• 2020 - On March 16, the VIX closed at 82.69, the highest level since its inception in 1990.[25]

## Criticism

Performance of VIX (left) compared to past volatility (right) as 30-day volatility predictors, for the period of Jan 1990-Sep 2009. Volatility is measured as the standard deviation of S&P500 one-day returns over a month's period. The blue lines indicate linear regressions, resulting in the correlation coefficients 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?][citation needed]

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.[26][27][28] However, other works have countered that these critiques failed to correctly implement the more complicated models.[29]

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.[30] Relatedly,[verification needed] Emanuel Derman has expressed disillusion with empirical models that are unsupported by theory.[clarification needed][citation needed][31][page needed] 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]

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.[32][33][better source needed]

According to some,[who?] 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] 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.[34]

An academic study from the University of Texas at Austin and Ohio State University examined potential methods of VIX manipulation.[35] 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.[36]

## Volatility of Volatility

In 2012, the CBOE introduced the "VVIX index" (also referred to as "vol of vol"), a measure of the VIX's expected volatility.[37] VVIX is calculated the same as VIX, except the inputs are market prices for VIX options, instead of stock market options.[38]

## References

1. ^ Brenner, Menachem; Galai, Dan (July–August 1989). "New Financial Instruments for Hedging Changes in Volatility" (PDF). Financial Analysts Journal. 45 (4): 61–65. doi:10.2469/faj.v45.n4.61.[full citation needed]
2. ^ Brenner, Menachem; Galai, Dan (Fall 1993). "Hedging Volatility in Foreign Currencies" (PDF). The Journal of Derivatives. Unknown volume (unknown issue): unknown page nos.[full citation needed]
3. ^ Bob Pisani (29 March 2020). "Father of Wall Street's 'fear gauge' sees wild volatility continuing until coronavirus cases peak". Retrieved 29 March 2020.
4. ^ a b Kuepper, Justin. "CBOE Volatility Index (VIX) Definition". Investopedia. Retrieved 2020-04-10.
5. CBOE Staff (2019). "Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. Retrieved 26 February 2020.[page needed]
6. ^ a b "How Does the Cboe's VIX® Index Work? | Six Figure Investing". sixfigureinvesting.com. Retrieved 2020-04-10.
7. ^ Iachini, Michael. "VIX ETFs: The Facts and Risks". Schwab Brokerage. Retrieved 2020-04-10.
8. ^ Reiff, Nathan. "How to Use a VIX ETF in Your Portfolio". Investopedia. Retrieved 2020-04-10.
9. ^ "Cboe Index Dashboard". www.cboe.com. Retrieved 2020-09-02.
10. ^ Black, Fischer; Scholes, Myron (1973). "The Pricing of Options and Corporate Liabilities". Journal of Political Economy. 81 (3): 637–654. doi:10.1086/260062. ISSN 0022-3808. JSTOR 1831029. S2CID 154552078.
11. ^ Nickolas, Steven. "Implied Volatility". Investopedia. Retrieved 2020-08-18.
12. ^ "VIX Options". www.cboe.com. Retrieved 2020-08-18.
13. ^ "Cboe Tradable Products". www.cboe.com.
14. ^ Conway, Brendan (17 June 2014). "No, Your ETF Doesn't Track the VIX Volatility Index—and Here are the Numbers". Barrons.com. Retrieved 26 February 2020.
15. ^ Papanicolaou, Andrew. "Identifying Links Between the S&P500 and VIX Derivatives". Institute for Pure & Applied Mathematics. UCLA. Retrieved 10 April 2020.
16. ^ "Volatility" (PDF). people.stern.nyu.edu. Retrieved 2020-02-26.
17. ^ "IFR report" (PDF). people.stern.nyu.edu. 1992. Retrieved 2020-02-26.
18. ^ "Derivatives on market volatility" (PDF). rewconsulting.files.wordpress.com. 2012. Retrieved 2020-02-26.
19. ^ Mehta, Salil (July 2015). "Volatility in motion" (blog). Statistical Ideas. Retrieved 26 February 2020 – via Statisticalideas.blogspot.com.
20. ^ Yun Li (March 16, 2020). "Wall Street's fear gauge closes at highest level ever, surpassing even financial crisis peak". MSNBC. Retrieved March 17, 2020.
21. ^ "CBOE Volatility Index". MarketWatch. February 7, 2018. Archived from the original on February 7, 2018. Retrieved August 23, 2020.
22. ^ Yakob Peterseil (March 9, 2020). "VIX Spikes to Highest Since 2008 in Manic Monday Trading". Bloomburg. Retrieved March 9, 2020.
23. ^ Pete Evans (March 9, 2020). "'This is basically panic selling': Stock markets plunge as coronavirus fear spreads". CBC. Retrieved March 9, 2020.
24. ^ Nicholas Jasinski (March 12, 2020). "The VIX Fear Gauge Is Soaring. It's Unlikely to Come Down Anytime Soon". Barron's. Retrieved March 12, 2020.
25. ^ Li, Yun (March 16, 2020). "Wall Street's fear gauge closes at highest level ever, surpassing even financial crisis peak". cnbc.com. Retrieved March 19, 2020.
26. ^ Cumby, R.; Figlewski, S.; Hasbrouck, J. (1993). "Forecasting Volatility and Correlations with EGARCH models". Journal of Derivatives. 1 (2): 51–63. doi:10.3905/jod.1993.407877. S2CID 154028452.
27. ^ Jorion, P. (1995). "Predicting Volatility in Foreign Exchange Market". Journal of Finance. 50 (2): 507–528. doi:10.1111/j.1540-6261.1995.tb04793.x. JSTOR 2329417.
28. ^ Adhikari, B.; Hilliard, J. (2014). "The VIX, VXO and realised volatility: a test of lagged and contemporaneous relationships". International Journal of Financial Markets and Derivatives. 3 (3): 222–240. doi:10.1504/IJFMD.2014.059637.
29. ^ Andersen, Torben G.; Bollerslev, Tim (1998). "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts". International Economic Review. 39 (4): 885–905. doi:10.2307/2527343. JSTOR 2527343.
30. ^ Goldstein, Daniel G.; Taleb, Nassim Nicholas (28 March 2007). "We Don't Quite Know What We are Talking About When We Talk About Volatility". Journal of Portfolio Management. 33 (4). doi:10.3905/jpm.2007.690609. S2CID 153535794. SSRN 970480.
31. ^ Derman, Emanuel (2011). Models Behaving Badly: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life. New York, NY: Simon and Schuster. pp. unknown page nos. ISBN 9781439165010. Retrieved 25 February 2020.
32. ^ Harris, Michael (21 August 2012). "On the Zero Predictive Capacity of VIX—Price Action Lab Blog" (self-published blog). PriceActionLab.com. Retrieved 25 February 2020.
33. ^ Harris, Michael (25 August 2012). "Further Analytical Evidence that VIX Just Tracks the Inverse of Price" (self-published blog). PriceActionLab.com. Retrieved 25 February 2020.
34. ^ Shiller, Robert (30 March 2011). "Econ 252-11: Financial Markets [Lecture 17—Options Markets]". New Haven, CT: Yale University. Archived from the original (college course content) on 22 September 2016. Retrieved 26 February 2020 – via OYC.Yale.edu.
35. ^ Griffin, John M.; Shams, Amin (May 23, 2017). "Manipulation in the VIX?". SSRN.com. doi:10.2139/ssrn.2972979. S2CID 157586475. SSRN 2972979. Retrieved 25 February 2020.
36. ^ Cornish, Chloe (13 February 2018). "Anonymous 'Whistleblower' Claims 'Rampant Manipulation' of Vix Index". Financial Times. Retrieved 26 February 2020 – via FT.com.
37. ^ BBOE Staff (March 13, 2012). "Double the Fun with CBOE's VVIX Index" (PDF). CBOE.com. Retrieved November 19, 2019.
38. ^ "Cboe Index Dashboard". www.cboe.com. Retrieved 2020-09-02.

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