VIX


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 Index is a volatility index derived from S&P 500 options, with the price of each option representing the market's expectation of 30-day forward-looking volatility. 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.
Like conventional indexes, the VIX Index calculation employs rules for selecting component options and a formula to calculate index values. Unlike other market products, VIX cannot be bought or sold directly. Instead, VIX is traded and exchanged via derivative contracts, or derived Exchange-traded fund, and exchange-traded notes which most commonly track VIX futures indexes.
In addition to VIX, CBOE uses the same methodology to compute the following related products:
Cboe also calculates the Nasdaq-100® Volatility Index, Cboe DJIA® Volatility Index and the Cboe Russell 2000® Volatility Index.

Specifications

The concept of computing implied volatility or an implied volatility index dates back to the publication of the option valuation model by Black and Scholes in 1973. 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. In the case of VIX, the option prices are the S&P 500 index option prices.
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. The goal is to estimate the implied volatility of S&P 500 index options at an average expiration of 30 days.
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. A variance swap can be perfectly statically replicated through vanilla puts and calls, whereas a volatility swap requires dynamic hedging. 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.
The VIX is calculated and disseminated in real-time by the Chicago Board Options Exchange. On March 26, 2004, trading in futures on the VIX began on CBOE Futures Exchange.
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.

VIX Formula

The VIX is a 30-day predictor of volatility given by a weighted portfolio of out-of-the-money European options on the S&P 500:
where is the number of average days in a month, is the risk-free rate, is the 30-day forward price on the S&P 500, and and are prices for puts and calls with strike and 30 days to maturity.

History

The following is a timeline of key events in the history of the VIX Index:
VIX is sometimes criticized as a prediction of future volatility. Instead it is described as a measure of the current price of index options.
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. However, other works have countered that these critiques failed to correctly implement the more complicated models.
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. Relatedly, Emanuel Derman has expressed disillusion with empirical models that are unsupported by theory. He argues that, while "theories are attempts to uncover the hidden principles underpinning the world around us... models are metaphors—analogies that describe one thing relative to another."
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.
According to some, 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. 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.
An academic study from the University of Texas at Austin and Ohio State University examined potential methods of VIX manipulation. 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.

Interpretation

The VIX is quoted in percentage points and represents the expected range of movement in the S&P 500 index over the next month, at a 68% confidence level. For example, if the VIX is 15, this represents an expected annualized change, with a 68% probability, of less than 15% up or down. The expected volatility range for a single month can be calculated from this figure by dividing the VIX figure of 15 not by 12, but by which would imply a range of +/- 4.33% over the next 30-day period. Similarly, expected volatility for a week would be 15 divided by, or +/- 2.08%. The VIX uses calendar day annualization so the conversion of 15% is 15 divided by, or +/- 0.79% per day. The calendar day approach does not account for the number trading days in a calendar year. Trading days typically amount to 252 days out of a given calendar year.
The price of call and put options can be used to calculate implied volatility, because volatility is one of the factors used to calculate the value of these options. Higher volatility of the underlying security makes an option more valuable, because there is a greater probability that the option will expire in the money. Thus, a higher option price implies greater volatility, other things being equal.
Even though the VIX is quoted as a percentage rather than a dollar amount, multiple VIX-based derivative instruments are in existence, including:
Similar indices for bonds include the MOVE and LBPX indices.
Although the VIX is often called the "fear index", a high VIX is not necessarily bearish for stocks. 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. Option buyers are willing to pay such high premiums only if similarly anticipating a large upside move. The resulting aggregate of increases in upside stock option call prices raises the VIX just as the aggregate growth in downside stock put option premiums that occurs when option buyers and sellers anticipate a likely sharp move to the downside. When the market is believed as likely to soar as to plummet, writing any option that will cost the writer in the event of a sudden large move in either direction may look equally risky.
Hence high VIX readings mean investors see significant risk that the market will move sharply, whether downward or upward. The highest VIX readings occur when investors anticipate that huge moves in either direction are likely. Only when investors perceive neither significant downside risk nor significant upside potential will the VIX be low.
The Black–Scholes formula uses a model of stock price dynamics to estimate how an option's value depends on the volatility of the underlying assets.

Volatility of Volatility

In 2012, the CBOE introduced the "VVIX index", a measure of the VIX's expected volatility. VVIX is calculated the same as VIX, except the inputs are market prices for VIX options, instead of stock market options.