VIX

The VIX

Brenner and Galai (1989) New Financial Instruments for Hedging Changes in Volatility proposed the setting up of an index that could be used, in essence, to measure anticipated volatility and provide investors with a tool for hedging risk of a change volatility. In 1992 Amex announced a feasibility study into a novel volatility index and it appeared that a number of parties were convinced of the need to develop a volatility index, in the aftermath of 1987 Crash.

In 1993, Cboe Global Markets introduced the Cboe Volatility Index (VIX® Index), which was originally conceived to measure the market expectation for a 30-day volatility implied by at-the-money S&P 100® Index (OEX® Index) option prices. The VIX Index soon became a leading benchmark for U.S. stock market volatility. It regularly featured in the media and was often referred to as the “fear gauge.”

Today, the VIX, at its core is an index, like the (DJIA), calibrates in a real-time basis throughout each trading day a forward-looking volatility (and not a price). Otherwise however it is not very different to other Financial Indices reported in the Media.

In his paper, Robert Whaley (1993), "Derivatives on Market Volatility Hedging Tools Long Overdue" described the benefits of setting up derivative contracts on the CBOE Market Volatility Index. He noted that a portfolio consisting of securities with option or option-like exposures to volatility could be managed more simply by using dedicated volatility derivatives. The negative correlation of volatility to stock market returns is well documented and suggests a diversification benefit to including volatility in an investment portfolio.

Typically, as stock prices dramatically shift in value, investors endeavor to put in place strategies that reduce the variability of their overall portfolio return. This flight to safety impulse reflected the appetite amongst traders to acquire volatility insurance.

The VIX® Index was introduced in 1993 with two purposes in mind:

(1) provide a benchmark of expected short-term market volatility thus enabling comparisons of the then-current VIX level with historical levels. Minute-by-minute values were estimated employing index option prices dating back to the beginning of January 1986. This dataset was instructive and included the experience of the October 1987 Crash.

(2) the VIX was conceived so as to furnish an index upon which futures and options contracts on volatility could be written. The Chicago Board Options Exchange (CBOE) launched trading of VIX futures contracts in May 2004 and VIX option contracts in February 2006.

Empirically, the VIX index tends to rise when the underlying S&P Index falls, whereas when the market is easing upward in a long-run bull market, the VIX index remains low and steady. The CBOE (2003) methodology for computing the VIX index is no longer unique to the prices of S&P 500 index options. In 2003, Cboe in conjunction with Goldman Sachs, updated the VIX Index to reflect a new way to measure expected volatility. The new VIX Index is based on the S&P 500® Index (SPXSM), the core index for U.S. equities, and estimates expected volatility by aggregating the weighted prices of SPX puts and calls over a wide range of strike prices. The CBOE has already applied the methodology to create a volatility index for the Nasdaq-100® Volatility Index (VXNSM), Cboe DJIA® Volatility Index (VXDSM) and the Cboe Russell 2000® Volatility Index (RVXSM). In addition to these, Cboe calculates several other broad market volatility indexes including the Cboe ShortTerm Volatility Index (VIX9DSM), which reflects 9-day expected volatility of the S&P 500 Index, the Cboe S&P 500® 3-Month Volatility Index (VIX3MSM), Cboe S&P 500® 6-Month Volatility Index (VIX6MSM) and the Cboe S&P 500 1-Year Volatility Index (VIX1YSM). The main requisite is that the underlying index option market has deep and active trading across a broad range of exercise prices or option chain. The NYSE Euronext has applied the CBOE (2003) methodology to index options listed on the AEX (an index of 25 stocks traded in Amsterdam), the BEL20 (an index of 20 Belgium stocks), the CAC40 (an index of 40 French stocks), and the FTSE 100 (an index of 100 stocks traded in the United Kingdom).

The VIX Index Calculation: Step-by-Step

Stock indices, such as the S&P 500, are calculated using the prices of their component stocks. Each index employs rules that govern the selection of component securities and a formula to calculate index values. The VIX Index is a volatility index comprised of options rather than stocks, with the price of each option reflecting the market’s expectation of future volatility. The VIX Index measures 30-day expected volatility of the S&P 500 Index. The components of the VIX Index are near- and next-term put and call options with more than 23 days and less than 37 days to expiration. These include SPX options with “standard” 3rd Friday expiration dates and “weekly” SPX options that expire every Friday, except the 3rd Friday of each month. Once each week, the SPX options used to calculate the VIX Index “roll” to new contract maturities. Below in video clips, I follow Arnold and Earl (2007) who put together a very intuitive spreadsheet. Their paper greatly simplifies the quite technical explanation generally available elsewhere. Some time functions and vlookup are introduced but you are spared any vestige of VBA in that paper. Like conventional indexes, the VIX Index calculation employs rules for selecting component options and a formula to calculate index values. See CBOE VIX White paper (2019).

For those of you who prefer a VBA automated spreadsheet - you should consider the Rouah and Vainberg (2006) text: Option Pricing Models and Volatility. In the third video I include a reference to their Excel VBA generated estimation.

For Python implementation please also see https://github.com/khrapovs/vix