VIX

<h2 id="specifications">Specifications</h2>
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 <a href="/facts/Black%E2%80%93Scholes_model/TPPG5YWQ">Black–Scholes model</a> for valuing options.<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a> 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.<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a> In the case of VIX, the option prices used are the S&P 500 index option prices.<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a><a class="footnote-ref" id="fnref:20" href="#fn:20">20</a>
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.<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a> The goal is to estimate the <a href="/facts/Implied_volatility/M5YHByy3">implied volatility</a> of S&P 500 index options at an average expiration of 30 days.<a class="footnote-ref" id="fnref:22" href="#fn:22">22</a>

Given that it is possible to create a hedging position equivalent to a <a href="/facts/Variance_swap/UbUUclLe">variance swap</a> using only vanilla puts and calls (also called "static replication"),<a class="footnote-ref" id="fnref:23" href="#fn:23">23</a> the VIX can also be seen as the square root of the implied volatility of a <a href="/facts/Variance_swap/UbUUclLe">variance swap</a><a class="footnote-ref" id="fnref:24" href="#fn:24">24</a> – and not that of a <a href="/facts/Volatility_swap/MxcfxvNt">volatility swap</a>, volatility being the square root of variance, or <a href="/facts/Standard_deviation/qSug9BRl">standard deviation</a>.
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.<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a>
The VIX is calculated and disseminated in real-time by the <a href="/facts/Chicago_Board_Options_Exchange/l49pf8qj">Chicago Board Options Exchange</a>. On March 26, 2004, trading in futures on the VIX began on CBOE Futures Exchange (CFE).<a class="footnote-ref" id="fnref:26" href="#fn:26">26</a>
On February 24, 2006, it became possible to trade options on the VIX.<a class="footnote-ref" id="fnref:27" href="#fn:27">27</a> Several <a href="/facts/Exchange-traded_fund/ShD4RpcJ">exchange-traded funds</a> 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.<a class="footnote-ref" id="fnref:28" href="#fn:28">28</a>

<h2 id="vix-formula">VIX Formula</h2>
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 <a href="/facts/Put_options/gHQ5NJyL">put options</a> on the S&P 500:

 
 
 
 V
 I
 X
 =
 
 
 
 
 
 2
 
 e
 
 r
 
 
 τ
 
 
 
 τ
 
 
 
 (
 
 
 ∫
 
 0
 
 
 F
 
 
 
 
 
 P
 (
 K
 )
 
 
 K
 
 2
 
 
 
 
 d
 K
 +
 
 ∫
 
 F
 
 
 ∞
 
 
 
 
 
 C
 (
 K
 )
 
 
 K
 
 2
 
 
 
 
 d
 K
 
 )
 
 
 
 
 
 {\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 
 
 
 
 
 τ
 
 
 
 {\displaystyle {\tau }}
 
 is the number of average days in a month (30 days), 
 
 
 
 r
 
 
 {\displaystyle r}
 
 is the risk-free rate, 
 
 
 
 F
 
 
 {\displaystyle F}
 
 is the 30-day forward price on the S&P 500, and 
 
 
 
 P
 (
 K
 )
 
 
 {\displaystyle P(K)}
 
 and 
 
 
 
 C
 (
 K
 )
 
 
 {\displaystyle C(K)}
 
 are prices for puts and calls with strike 
 
 
 
 K
 
 
 {\displaystyle K}
 
 and 30 days to maturity.<a class="footnote-ref" id="fnref:29" href="#fn:29">29</a><a class="footnote-ref" id="fnref:30" href="#fn:30">30</a>

<h2 id="history">History</h2>
The following is a timeline of key events in the history of the VIX Index:[according to whom?] 

<ul><li>1987 – The Sigma Index was introduced in an academic paper by Brenner and Galai, published in Financial Analysts Journal, July/August 1989.<a class="footnote-ref" id="fnref:31" href="#fn:31">31</a> 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."<a class="footnote-ref" id="fnref:32" href="#fn:32">32</a></li>
<li>1989 – Brenner and Galai's paper is published in Financial Analysts Journal.<a class="footnote-ref" id="fnref:33" href="#fn:33">33</a> Brenner and Galai develop their research further in graduate symposia at <a href="/facts/Hebrew_University_of_Jerusalem/aEpNukpQ">The Hebrew University of Jerusalem</a> and at the <a href="/facts/New_York_University_Stern_School_of_Business/VkEeLgqe">Leonard M. Stern School of Business</a> at <a href="/facts/New_York_University/4UnIkThy">New York University</a>.</li>
<li>1992 – The <a href="/facts/American_Stock_Exchange/v5sMYmFD">American Stock Exchange</a> announced it is conducting a feasibility study on a volatility index, proposed as the "Sigma Index."<a class="footnote-ref" id="fnref:34" href="#fn:34">34</a></li>
<li>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 <a href="/facts/Duke_University/BFMHVjsB">Duke University</a> (now at <a href="/facts/Vanderbilt_University/xut8ASAf">Vanderbilt University</a>), whom the CBOE had commissioned.<a class="footnote-ref" id="fnref:35" href="#fn:35">35</a> This index, now known as the VXO, is a measure of implied volatility calculated using 30-day <a href="/facts/S%26P_100/1kJSLayu">S&P 100</a> index at-the-money options.<a class="footnote-ref" id="fnref:36" href="#fn:36">36</a></li>
<li>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.</li>
<li>2003 – The CBOE introduces a new methodology for the VIX. Working with <a href="/facts/Goldman_Sachs/cKeyh6CP">Goldman Sachs</a>, 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.<a class="footnote-ref" id="fnref:37" href="#fn:37">37</a>[verification needed]</li>
<li>2004 – On March 26, 2004, the first-ever trading in futures on the VIX Index began on the CBOE Futures Exchange (CFE).<a class="footnote-ref" id="fnref:38" href="#fn:38">38</a> VIX is now proposed on different trading platforms, like XTB.</li>
<li>2006 – VIX options were launched in February of this year.<a class="footnote-ref" id="fnref:39" href="#fn:39">39</a></li>
<li>2008 – On October 24, 2008, the VIX reached an intraday high of 89.53.<a class="footnote-ref" id="fnref:40" href="#fn:40">40</a></li>
<li>2008 – On November 21, 2008, the VIX closed at a record 80.74.<a class="footnote-ref" id="fnref:41" href="#fn:41">41</a></li>
<li>2018 – On February 5, 2018, the VIX closed 37.32 (up 103.99% from previous close).<a class="footnote-ref" id="fnref:42" href="#fn:42">42</a></li>
<li>2020 – On March 9, 2020, the VIX hit 62.12, the highest level since the 2008 financial crisis due to a combination of the <a href="/facts/2020_Russia%E2%80%93Saudi_Arabia_oil_price_war/2TdznrDK">2020 Russia–Saudi Arabia oil price war</a> and the <a href="/facts/COVID-19_pandemic/0xTsh7Ut">COVID-19 pandemic</a>.<a class="footnote-ref" id="fnref:43" href="#fn:43">43</a><a class="footnote-ref" id="fnref:44" href="#fn:44">44</a></li>
<li>2020 – During the <a href="/facts/COVID-19_pandemic/0xTsh7Ut">COVID-19 pandemic</a>, on March 12, 2020, the VIX hit and closed at 75.47, exceeding the previous <a href="/facts/Black_Monday_(1987)/nPGfLk7g">Black Monday</a> value, as a travel ban to the US from <a href="/facts/Europe/DTAtrKfh">Europe</a> was announced by <a href="/facts/President_Trump/pqqKY21P">President Trump</a>.<a class="footnote-ref" id="fnref:45" href="#fn:45">45</a></li>
<li>2020 – On March 16, the VIX closed at 82.69, the highest level since its inception in 1990.<a class="footnote-ref" id="fnref:46" href="#fn:46">46</a></li>
<li>2021 – The <a href="/facts/U.S._Securities_and_Exchange_Commission/IM9Pl2gK">U.S. Securities and Exchange Commission</a> fined the <a href="/facts/S%26P_Dow_Jones_Indices/lcQrfV3c">S&P Dow Jones Indices</a> for halting data on February 5, 2018.<a class="footnote-ref" id="fnref:47" href="#fn:47">47</a></li></ul>
<h2 id="interpretation">Interpretation</h2>

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?]
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.<a class="footnote-ref" id="fnref:48" href="#fn:48">48</a><a class="footnote-ref" id="fnref:49" href="#fn:49">49</a><a class="footnote-ref" id="fnref:50" href="#fn:50">50</a> However, other works have countered that these critiques failed to correctly implement the more complicated models.<a class="footnote-ref" id="fnref:51" href="#fn:51">51</a>
Some practitioners and <a href="/facts/Portfolio_managers/qbuNEmn7">portfolio managers</a> have questioned the depth of our understanding of the fundamental concept of volatility, itself. For example, <a href="/facts/Daniel_Goldstein/kdymGx5N">Daniel Goldstein</a> and <a href="/facts/Nassim_Taleb/KQTPVVzz">Nassim Taleb</a> famously titled one of their research articles, We Don't Quite Know What We are Talking About When We Talk About Volatility.<a class="footnote-ref" id="fnref:52" href="#fn:52">52</a> Relatedly,[verification needed] <a href="/facts/Emanuel_Derman/gtgQ8PBz">Emanuel Derman</a> has expressed disillusion with empirical models that are unsupported by theory.<a class="footnote-ref" id="fnref:53" href="#fn:53">53</a> 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."
<a href="/facts/Mike_Harris_(entrepreneur)/a4BwnAkJ">Michael Harris</a>, the trader, programmer, price pattern theorist, and author, has argued that VIX just tracks the inverse of price and has no predictive power.<a class="footnote-ref" id="fnref:54" href="#fn:54">54</a><a class="footnote-ref" id="fnref:55" href="#fn:55">55</a>[better source needed]
According to some,[who?] VIX should have predictive power as long as the prices computed by the <a href="/facts/Black-Scholes_equation/AYumL7US">Black–Scholes equation</a> are valid assumptions about the volatility predicted for the future lead time (the remaining time to maturity). <a href="/facts/Robert_J._Shiller/c0D21FQv">Robert J. Shiller</a> has argued that it would be <a href="/facts/Circular_reasoning/Kgac2eUw">circular reasoning</a> 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 <a href="/facts/Great_Depression/5K13wcg0">Great Depression</a>—suggesting that in the case of anomalous conditions, VIX cannot even weakly predict future severe events.<a class="footnote-ref" id="fnref:56" href="#fn:56">56</a>
An academic study from the <a href="/facts/University_of_Texas_at_Austin/6NApstxT">University of Texas at Austin</a> and <a href="/facts/Ohio_State_University/jfSr6u6u">Ohio State University</a> examined potential methods of VIX manipulation.<a class="footnote-ref" id="fnref:57" href="#fn:57">57</a> 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.<a class="footnote-ref" id="fnref:58" href="#fn:58">58</a>

<h2 id="volatility-of-volatility">Volatility of volatility</h2>
In 2012, the CBOE introduced the "VVIX index" (also referred to as "vol of vol"), a measure of the VIX's expected volatility.<a class="footnote-ref" id="fnref:59" href="#fn:59">59</a> VVIX is calculated using the same methodology as VIX, except the inputs are market prices for VIX options instead of stock market options.<a class="footnote-ref" id="fnref:60" href="#fn:60">60</a>
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.<a class="footnote-ref" id="fnref:61" href="#fn:61">61</a>

<h2 id="see-also">See also</h2>
<ul>
<li>Business and economics portal</li></ul>

<ul><li><a href="/facts/Economic_Policy_Uncertainty_Index/rjYN1UyR">Economic Policy Uncertainty Index</a></li>
<li><a href="/facts/Greed_and_fear/RKTxVXy8">Greed and fear</a></li>
<li><a href="/facts/Hindenburg_Omen/4VKADyD4">Hindenburg Omen</a></li>
<li><a href="/facts/IVX/IlD8W8gt">IVX</a></li>
<li><a href="/facts/Market_trend/5C1BeRrp">Market trend</a></li>
<li><a href="/facts/Option_on_realized_variance/HFhYkaEV">Option on realized variance</a></li>
<li><a href="/facts/Probability_of_default/tL7MH87q">Probability of default</a></li>
<li><a href="/facts/S%26P/ASX_200_VIX/03KnEbg1">S&P/ASX 200 VIX</a></li>
<li><a href="/facts/SKEW/GnMDAxk8">SKEW</a></li>
<li><a href="/facts/Volfefe_index/XColz9ft">Volfefe index</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li><a href="/facts/Fischer_Black/7CDCxCSB">Black, Fischer</a> and <a href="/facts/Myron_Scholes/U5x5bhx6">Myron Scholes</a>. "The Pricing of Options and Corporate Liabilities." Journal of Political Economy (May/June 1973), pp. 637–659.</li>
<li>Brenner, Menachem; Galai, Dan (July–August 1989). <a href="http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf">"New Financial Instruments for Hedging Changes in Volatility"</a> (PDF). <a href="/facts/Financial_Analysts_Journal/JqcJM2yy">Financial Analysts Journal</a>. 45 (4): 61–65. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.2469%2Ffaj.v45.n4.61">10.2469/faj.v45.n4.61</a>.</li>
<li>Brenner, Menachem; Galai, Dan (Fall 1993). <a href="http://people.stern.nyu.edu/mbrenner/research/JOD_article_of_Vol_Index_Computation.pdf">"Hedging Volatility in Foreign Currencies"</a> (PDF). The Journal of Derivatives. 1 (1): 53–58. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.3905%2Fjod.1993.407870">10.3905/jod.1993.407870</a>.</li>
<li>"Amex Explores Volatility Options," <a href="http://people.stern.nyu.edu/mbrenner/research/IFR_report_on_Brenner-Galai_Sigma_Index.pdf">International Financing Review</a>, August 8, 1992.</li>
<li>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).</li>
<li>Connors, Larry. "A Volatile Idea." Futures (July 1999): pp. 36–37.</li>
<li>Connors, Larry. "Timing Your S&P Trades with the VIX." Futures (June 2002): pp. 46–47.</li>
<li>Copeland, Maggie. "Market Timing: Style and Size Rotation Using the VIX." Financial Analysts Journal, (Mar/Apr 1999); pp. 73–82.</li>
<li>Daigler, Robert T., and Laura Rossi. "A Portfolio of Stocks and Volatility." The Journal of Investing. (Summer 2006).</li>
<li>Fleming, Jeff, Barbara Ostdiek, and <a href="/facts/Robert_E._Whaley/BBsRnYwC">Robert E. Whaley</a>, "Predicting Stock Market Volatility: A New Measure," The Journal of Futures Markets 15 (May 1995), pp. 265–302.</li>
<li><a href="/facts/Mark_Hulbert/hVkv3f1y">Hulbert, Mark</a>, <a href="http://online.barrons.com/article/SB50001424052748703464104576616983309689062.html">"The Misuse of the Stock Market's Fear Index,"</a> Barron's, October 7, 2011.</li>
<li>Mele, Antonio and Yoshiki Obayashi. "The Price of Fixed Income Market Volatility." Springer Verlag: Springer Finance Series, New York (2015).</li>
<li>Moran, Matthew T., "Review of the VIX Index and VIX Futures.," Journal of Indexes, (October/November 2004). pp. 16–19.</li>
<li>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).</li>
<li>Szado, Ed. "VIX Futures and Options—A Case Study of Portfolio Diversification During the 2008 Financial Crisis." (June 2009).</li>
<li>Tan, Kopin. "The ABCs of VIX." Barron's (Mar 15, 2004): p. MW16.</li>
<li>Tracy, Tennille. "Trading Soars on Financials As Volatility Index Hits Record." Wall Street Journal. (Sept. 30, 2008) p. C6.</li>
<li><a href="/facts/Robert_E._Whaley/BBsRnYwC">Whaley, Robert E</a>., <a href="http://rewconsulting.files.wordpress.com/2012/09/jd93.pdf">"Derivatives on Market Volatility: Hedging Tools Long Overdue,"</a> The Journal of Derivatives 1 (Fall 1993), pp. 71–84.</li>
<li><a href="/facts/Robert_E._Whaley/BBsRnYwC">Whaley, Robert E</a>., "The Investor Fear Gauge," The Journal of Portfolio Management 26 (Spring 2000), pp. 12–17.</li>
<li><a href="/facts/Robert_E._Whaley/BBsRnYwC">Whaley, Robert E</a>., "Understanding the VIX." The Journal of Portfolio Management 35 (Spring 2009), pp. 98–105.</li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="https://www.cboe.com/tradable_products/vix/">Official website</a> at CBOE</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn: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. <a href="http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf" target="_blank">http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Brenner, Menachem; Galai, Dan (Fall 1993). "Hedging Volatility in Foreign Currencies" (PDF). The Journal of Derivatives. 1 (1): 53–58. doi:10.3905/jod.1993.407870. <a href="http://people.stern.nyu.edu/mbrenner/research/JOD_article_of_Vol_Index_Computation.pdf" target="_blank">http://people.stern.nyu.edu/mbrenner/research/JOD_article_of_Vol_Index_Computation.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Brenner, Menachem; Galai, Dan (1989). "New Financial Instruments for Hedging Changes in Volatility". Financial Analysts Journal. 45 (4): 61–65. doi:10.2469/faj.v45.n4.61. ISSN 0015-198X. JSTOR 4479241. <a href="https://www.jstor.org/stable/4479241" target="_blank">https://www.jstor.org/stable/4479241</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Pisani, Bob (29 March 2020). "Father of Wall Street's 'fear gauge' sees wild volatility continuing until coronavirus cases peak". CNBC. Retrieved 29 March 2020. <a href="https://www.cnbc.com/2020/03/29/father-of-wall-streets-fear-gauge-sees-wild-volatility-continuing-until-coronavirus-cases-peak.html" target="_blank">https://www.cnbc.com/2020/03/29/father-of-wall-streets-fear-gauge-sees-wild-volatility-continuing-until-coronavirus-cases-peak.html</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Kuepper, Justin. "CBOE Volatility Index (VIX) Definition". Investopedia. Retrieved 2020-04-10. <a href="https://www.investopedia.com/terms/v/vix.asp" target="_blank">https://www.investopedia.com/terms/v/vix.asp</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Kuepper, Justin. "CBOE Volatility Index (VIX) Definition". Investopedia. Retrieved 2020-04-10. <a href="https://www.investopedia.com/terms/v/vix.asp" target="_blank">https://www.investopedia.com/terms/v/vix.asp</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">"Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. 2019. Retrieved 26 February 2020.[page needed] <a href="https://cdn.cboe.com/resources/vix/vixwhite.pdf" target="_blank">https://cdn.cboe.com/resources/vix/vixwhite.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">"Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. 2019. Retrieved 26 February 2020.[page needed] <a href="https://cdn.cboe.com/resources/vix/vixwhite.pdf" target="_blank">https://cdn.cboe.com/resources/vix/vixwhite.pdf</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">"Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. 2019. Retrieved 26 February 2020.[page needed] <a href="https://cdn.cboe.com/resources/vix/vixwhite.pdf" target="_blank">https://cdn.cboe.com/resources/vix/vixwhite.pdf</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">"How Does the Cboe's VIX® Index Work? | Six Figure Investing". sixfigureinvesting.com. 10 July 2014. Retrieved 2020-04-10. <a href="https://sixfigureinvesting.com/2014/07/how-does-the-vix-index-work/" target="_blank">https://sixfigureinvesting.com/2014/07/how-does-the-vix-index-work/</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Iachini, Michael. "VIX ETFs: The Facts and Risks". Schwab Brokerage. Retrieved 2020-04-10. <a href="https://www.schwab.com/resource-center/insights/content/vix-etfs-facts-and-risks" target="_blank">https://www.schwab.com/resource-center/insights/content/vix-etfs-facts-and-risks</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Reiff, Nathan. "How to Use a VIX ETF in Your Portfolio". Investopedia. Retrieved 2020-04-10. <a href="https://www.investopedia.com/investing/use-vix-etf-in-your-portfolio/" target="_blank">https://www.investopedia.com/investing/use-vix-etf-in-your-portfolio/</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">"Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. 2019. Retrieved 26 February 2020.[page needed] <a href="https://cdn.cboe.com/resources/vix/vixwhite.pdf" target="_blank">https://cdn.cboe.com/resources/vix/vixwhite.pdf</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">"How Does the Cboe's VIX® Index Work? | Six Figure Investing". sixfigureinvesting.com. 10 July 2014. Retrieved 2020-04-10. <a href="https://sixfigureinvesting.com/2014/07/how-does-the-vix-index-work/" target="_blank">https://sixfigureinvesting.com/2014/07/how-does-the-vix-index-work/</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">"Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. 2019. Retrieved 26 February 2020.[page needed] <a href="https://cdn.cboe.com/resources/vix/vixwhite.pdf" target="_blank">https://cdn.cboe.com/resources/vix/vixwhite.pdf</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">"Cboe Index Dashboard". www.cboe.com. Retrieved 2020-09-02. <a href="http://www.cboe.com/index/dashboard/vvix#vvix-overview" target="_blank">http://www.cboe.com/index/dashboard/vvix#vvix-overview</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">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. <a href="http://www.jstor.org/stable/1831029" target="_blank">http://www.jstor.org/stable/1831029</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">Nickolas, Steven. "Implied Volatility". Investopedia. Retrieved 2020-08-18. <a href="https://www.investopedia.com/ask/answers/032515/what-options-implied-volatility-and-how-it-calculated.asp" target="_blank">https://www.investopedia.com/ask/answers/032515/what-options-implied-volatility-and-how-it-calculated.asp</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
<li id="fn:19">"VIX Options". www.cboe.com. Retrieved 2020-08-18. <a href="http://www.cboe.com/products/vix-index-volatility/vix-options-and-futures/vix-options" target="_blank">http://www.cboe.com/products/vix-index-volatility/vix-options-and-futures/vix-options</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></li>
<li id="fn:20">"Olymp Trade promo code". Honestdigitalreview.com. 24 August 2019. Retrieved 2020-07-22. <a href="https://honestdigitalreview.com/2019/08/olymptrade-coupon-code-promo-code-bonus.html" target="_blank">https://honestdigitalreview.com/2019/08/olymptrade-coupon-code-promo-code-bonus.html</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></li>
<li id="fn:21">"Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. 2019. Retrieved 26 February 2020.[page needed] <a href="https://cdn.cboe.com/resources/vix/vixwhite.pdf" target="_blank">https://cdn.cboe.com/resources/vix/vixwhite.pdf</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">"Cboe Tradable Products". www.cboe.com. <a href="https://www.cboe.com/tradable_products/" target="_blank">https://www.cboe.com/tradable_products/</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">"Just what you need to know about Variance Swaps" (PDF). May 2005. <a href="http://spekulant.com.pl/article/Volatility%20products/JP%20Morgan%20Chase%20-%20Variance%20Swap%20introduction.pdf" target="_blank">http://spekulant.com.pl/article/Volatility%20products/JP%20Morgan%20Chase%20-%20Variance%20Swap%20introduction.pdf</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
<li id="fn:24">Kanas, Angelos (2013-06-01). "The risk-return relation and VIX: evidence from the S&P 500". Empirical Economics. 44 (3): 1291–1314. doi:10.1007/s00181-012-0639-4. ISSN 1435-8921. <a href="https://doi.org/10.1007/s00181-012-0639-4" target="_blank">https://doi.org/10.1007/s00181-012-0639-4</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></li>
<li id="fn:25">"White Paper Cboe Volatility Index" (PDF). Retrieved 15 March 2024. <a href="https://www.sfu.ca/~poitras/419_VIX.pdf" target="_blank">https://www.sfu.ca/~poitras/419_VIX.pdf</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></li>
<li id="fn:26">Lin, Yueh-Neng (November 2013). "VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation". Journal of Banking & Finance. 37 (11): 4432–4446. doi:10.1016/j.jbankfin.2013.03.006. <a href="https://doi.org/10.1016/j.jbankfin.2013.03.006" target="_blank">https://doi.org/10.1016/j.jbankfin.2013.03.006</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></li>
<li id="fn:27">Lin, Yueh-Neng (November 2013). "VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation". Journal of Banking & Finance. 37 (11): 4432–4446. doi:10.1016/j.jbankfin.2013.03.006. <a href="https://doi.org/10.1016/j.jbankfin.2013.03.006" target="_blank">https://doi.org/10.1016/j.jbankfin.2013.03.006</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></li>
<li id="fn:28">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. <a href="https://www.barrons.com/articles/no-your-etf-doesnt-track-the-vix-volatility-index-and-here-are-the-numbers-1403010972" target="_blank">https://www.barrons.com/articles/no-your-etf-doesnt-track-the-vix-volatility-index-and-here-are-the-numbers-1403010972</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></li>
<li id="fn:29">"Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. 2019. Retrieved 26 February 2020.[page needed] <a href="https://cdn.cboe.com/resources/vix/vixwhite.pdf" target="_blank">https://cdn.cboe.com/resources/vix/vixwhite.pdf</a> <a href="#fnref:29" class="footnote-back-ref">↩</a></li>
<li id="fn:30">Papanicolaou, Andrew (5 April 2016). "Identifying Links Between the S&P500 and VIX Derivatives". Institute for Pure & Applied Mathematics. UCLA. Retrieved 10 April 2020. <a href="https://www.ipam.ucla.edu/research-articles/identifying-links-between-the-sp500-and-vix-derivatives/" target="_blank">https://www.ipam.ucla.edu/research-articles/identifying-links-between-the-sp500-and-vix-derivatives/</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></li>
<li id="fn:31">"Volatility" (PDF). people.stern.nyu.edu. Retrieved 2020-02-26. <a href="http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf" target="_blank">http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf</a> <a href="#fnref:31" class="footnote-back-ref">↩</a></li>
<li id="fn:32">Brenner, Menachem; Galai, Dan (1989). "New Financial Instruments for Hedging Changes in Volatility". Financial Analysts Journal. 45 (4): 61–65. doi:10.2469/faj.v45.n4.61. ISSN 0015-198X. JSTOR 4479241. <a href="https://www.jstor.org/stable/4479241" target="_blank">https://www.jstor.org/stable/4479241</a> <a href="#fnref:32" class="footnote-back-ref">↩</a></li>
<li id="fn:33">Brenner, Menachem; Galai, Dan (1989). "New Financial Instruments for Hedging Changes in Volatility". Financial Analysts Journal. 45 (4): 61–65. doi:10.2469/faj.v45.n4.61. ISSN 0015-198X. JSTOR 4479241. <a href="https://www.jstor.org/stable/4479241" target="_blank">https://www.jstor.org/stable/4479241</a> <a href="#fnref:33" class="footnote-back-ref">↩</a></li>
<li id="fn:34">"IFR report" (PDF). people.stern.nyu.edu. 1992. Retrieved 2020-02-26. <a href="http://people.stern.nyu.edu/mbrenner/research/IFR_report_on_Brenner-Galai_Sigma_Index.pdf" target="_blank">http://people.stern.nyu.edu/mbrenner/research/IFR_report_on_Brenner-Galai_Sigma_Index.pdf</a> <a href="#fnref:34" class="footnote-back-ref">↩</a></li>
<li id="fn:35">"Derivatives on market volatility" (PDF). rewconsulting.files.wordpress.com. 2012. Retrieved 2020-02-26. <a href="http://rewconsulting.files.wordpress.com/2012/09/jd93.pdf" target="_blank">http://rewconsulting.files.wordpress.com/2012/09/jd93.pdf</a> <a href="#fnref:35" class="footnote-back-ref">↩</a></li>
<li id="fn:36">Mehta, Salil (July 2015). "Volatility in motion" (blog). Statistical Ideas. Retrieved 26 February 2020 – via Statisticalideas.blogspot.com. <a href="http://statisticalideas.blogspot.com/2015/07/volatility-in-motion.html" target="_blank">http://statisticalideas.blogspot.com/2015/07/volatility-in-motion.html</a> <a href="#fnref:36" class="footnote-back-ref">↩</a></li>
<li id="fn:37">"Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. 2019. Retrieved 26 February 2020.[page needed] <a href="https://cdn.cboe.com/resources/vix/vixwhite.pdf" target="_blank">https://cdn.cboe.com/resources/vix/vixwhite.pdf</a> <a href="#fnref:37" class="footnote-back-ref">↩</a></li>
<li id="fn:38">"History". www.cboe.com. Retrieved 2021-11-20. <a href="https://www.cboe.com/about/history/" target="_blank">https://www.cboe.com/about/history/</a> <a href="#fnref:38" class="footnote-back-ref">↩</a></li>
<li id="fn:39">"History". www.cboe.com. Retrieved 2021-11-20. <a href="https://www.cboe.com/about/history/" target="_blank">https://www.cboe.com/about/history/</a> <a href="#fnref:39" class="footnote-back-ref">↩</a></li>
<li id="fn:40">"Update: 3-Volatility index below 30 for 1st time since Sept". Reuters. 2009-05-19. Retrieved 2021-11-20. <a href="https://www.reuters.com/article/markets-stocks-vix-idUSN1945357120090519" target="_blank">https://www.reuters.com/article/markets-stocks-vix-idUSN1945357120090519</a> <a href="#fnref:40" class="footnote-back-ref">↩</a></li>
<li id="fn:41">Li, Yun (March 16, 2020). "Wall Street's fear gauge closes at highest level ever, surpassing even financial crisis peak". MSNBC. Retrieved March 17, 2020. <a href="https://www.cnbc.com/2020/03/16/wall-streets-fear-gauge-hits-highest-level-ever.html" target="_blank">https://www.cnbc.com/2020/03/16/wall-streets-fear-gauge-hits-highest-level-ever.html</a> <a href="#fnref:41" class="footnote-back-ref">↩</a></li>
<li id="fn:42">"CBOE Volatility Index". MarketWatch. February 7, 2018. Archived from the original on February 7, 2018. Retrieved August 23, 2020. <a href="https://web.archive.org/web/20180207005155/https://www.marketwatch.com/investing/index/VIX" target="_blank">https://web.archive.org/web/20180207005155/https://www.marketwatch.com/investing/index/VIX</a> <a href="#fnref:42" class="footnote-back-ref">↩</a></li>
<li id="fn:43">Peterseil, Yakob (March 9, 2020). "VIX Spikes to Highest Since 2008 in Manic Monday Trading". Bloomburg. Retrieved March 9, 2020. <a href="https://www.bloomberg.com/news/articles/2020-03-09/vix-futures-spike-to-highest-since-2009-in-manic-monday-trading" target="_blank">https://www.bloomberg.com/news/articles/2020-03-09/vix-futures-spike-to-highest-since-2009-in-manic-monday-trading</a> <a href="#fnref:43" class="footnote-back-ref">↩</a></li>
<li id="fn:44">Evans, Pete (March 9, 2020). "'This is basically panic selling': Stock markets plunge as coronavirus fear spreads". CBC. Retrieved March 9, 2020. <a href="https://www.cbc.ca/news/business/markets-stocks-oil-1.5490697" target="_blank">https://www.cbc.ca/news/business/markets-stocks-oil-1.5490697</a> <a href="#fnref:44" class="footnote-back-ref">↩</a></li>
<li id="fn:45">Jasinski, Nicholas (March 12, 2020). "The VIX Fear Gauge Is Soaring. It's Unlikely to Come Down Anytime Soon". Barron's. Retrieved March 12, 2020. <a href="https://www.barrons.com/articles/the-vix-fear-gauge-is-soaring-its-unlikely-to-come-down-anytime-soon-51584050364" target="_blank">https://www.barrons.com/articles/the-vix-fear-gauge-is-soaring-its-unlikely-to-come-down-anytime-soon-51584050364</a> <a href="#fnref:45" class="footnote-back-ref">↩</a></li>
<li id="fn:46">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. <a href="https://www.cnbc.com/2020/03/16/wall-streets-fear-gauge-hits-highest-level-ever.html" target="_blank">https://www.cnbc.com/2020/03/16/wall-streets-fear-gauge-hits-highest-level-ever.html</a> <a href="#fnref:46" class="footnote-back-ref">↩</a></li>
<li id="fn:47">Jonathan Stempel. (17 May 2021). "S&P Dow Jones Indices is fined by SEC over U.S. 'volatility' crash". Yahoo Finance website. Retrieved 18 May 2021. <a href="https://finance.yahoo.com/news/p-dow-jones-indices-fined-152400340.html" target="_blank">https://finance.yahoo.com/news/p-dow-jones-indices-fined-152400340.html</a> <a href="#fnref:47" class="footnote-back-ref">↩</a></li>
<li id="fn:48">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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:48" class="footnote-back-ref">↩</a></li>
<li id="fn:49">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. <a href="/wiki/Journal_of_Finance" target="_blank">/wiki/Journal_of_Finance</a> <a href="#fnref:49" class="footnote-back-ref">↩</a></li>
<li id="fn:50">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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:50" class="footnote-back-ref">↩</a></li>
<li id="fn:51">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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:51" class="footnote-back-ref">↩</a></li>
<li id="fn:52">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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:52" class="footnote-back-ref">↩</a></li>
<li id="fn:53">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. <a href="9781439165010" target="_blank">9781439165010</a> <a href="#fnref:53" class="footnote-back-ref">↩</a></li>
<li id="fn:54">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. <a href="http://www.priceactionlab.com/Blog/2012/08/on-the-zero-predictive-capacity-of-vix/" target="_blank">http://www.priceactionlab.com/Blog/2012/08/on-the-zero-predictive-capacity-of-vix/</a> <a href="#fnref:54" class="footnote-back-ref">↩</a></li>
<li id="fn:55">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. <a href="http://www.priceactionlab.com/Blog/2012/08/further-analytical-evidence-that-vix-just-tracks-the-inverse-of-price/" target="_blank">http://www.priceactionlab.com/Blog/2012/08/further-analytical-evidence-that-vix-just-tracks-the-inverse-of-price/</a> <a href="#fnref:55" class="footnote-back-ref">↩</a></li>
<li id="fn:56">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. <a href="/wiki/Robert_J._Shiller" target="_blank">/wiki/Robert_J._Shiller</a> <a href="#fnref:56" class="footnote-back-ref">↩</a></li>
<li id="fn:57">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. <a href="https://ssrn.com/abstract=2972979" target="_blank">https://ssrn.com/abstract=2972979</a> <a href="#fnref:57" class="footnote-back-ref">↩</a></li>
<li id="fn:58">Cornish, Chloe (13 February 2018). "Anonymous 'Whistleblower' Claims 'Rampant Manipulation' of Vix Index". Financial Times. Retrieved 26 February 2020 – via FT.com. <a href="https://www.ft.com/content/a89eba68-10b4-11e8-940e-08320fc2a277" target="_blank">https://www.ft.com/content/a89eba68-10b4-11e8-940e-08320fc2a277</a> <a href="#fnref:58" class="footnote-back-ref">↩</a></li>
<li id="fn:59">"Double the Fun with CBOE's VVIX Index" (PDF). CBOE.com. March 13, 2012. Retrieved November 19, 2019. <a href="http://www.cboe.com/micro/vvix/documents/vvix-termstructure.pdf" target="_blank">http://www.cboe.com/micro/vvix/documents/vvix-termstructure.pdf</a> <a href="#fnref:59" class="footnote-back-ref">↩</a></li>
<li id="fn:60">"Cboe Index Dashboard". www.cboe.com. Retrieved 2020-09-02. <a href="http://www.cboe.com/index/dashboard/vvix#vvix-overview" target="_blank">http://www.cboe.com/index/dashboard/vvix#vvix-overview</a> <a href="#fnref:60" class="footnote-back-ref">↩</a></li>
<li id="fn:61">"What is the VVIX (Cboe VVIX Index)?". VIXFAQ.com. Retrieved 2024-04-29. <a href="https://www.vixfaq.com/what-is-the-cboe-vvix-index/" target="_blank">https://www.vixfaq.com/what-is-the-cboe-vvix-index/</a> <a href="#fnref:61" class="footnote-back-ref">↩</a></li>
</ol>

VIX open-in-new

VIX