The VIX Volatility Index - A Very Thorough Look at It

Abstract

The CBOE Volatility Index, known by its ticker symbol VIX, is a popular measure of the stock market’s expectation of volatility implied by S&P 500 index options, calculated and published by the Chicago Board Options Exchange (CBOE). It is colloquially referred to as the fear index or the fear gauge. 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. Despite its theoretical foundation in option price theory, CBOE’s Volatility Index is prone to inadvertent and deliberate errors. We shed light on many claims that have been brought up against the VIX in recent years. Replicating the VIX index by using empirical options data from CBOE we show which one of those claims are justified and lead to meaningful alterations of the VIX. Three main areas can be identified: Eight different alteration possibilities of the current VIX formula, three deficiencies in the theoretical derivation of the VIX and two major issues with the market microstructure of the VIX and its derivatives. First, eight theoretically possible ways of altering the current VIX formula are identified. We will thoroughly investigate those ways both from a theoretical point of view and using empirical data. The two major alteration possibilities are identified and their potential impact on the VIX calculation is shown using actual option quote data from the CBOE. Second, the theoretical derivation behind the VIX formula has three major flaws. We show their importance based on an empirical analysis of the VIX and the underlying options on the S&P 500. Our analysis helps to understand and put into context previous claims that were brought up against the VIX. Third, the market microstructure behind the pricing of VIX derivatives appears to be flawed. Very liquid derivatives are priced off an illiquid auction mechanism of out-of-the-money put and call options. To make matters worse, those derivatives are cash-settled and the settlement value of the VIX, as used for the pricing of its derivatives, is based on a different calculation than the regular VIX index. Finally, we also investigate claims that the settlement values can substantially deviate from the previous-day close. We show that those claims are based on a wide-spread misunderstanding of how the settlement values and the VIX index are calculated and that they are not justified in the way that they are brought up at the moment. Our empirical methodology is based on replicating the VIX based on the underlying quote data. Our conclusion is that the VIX needs a thorough review of both its theoretical foundations, its calculations and the market mechanism behind computing the value of its derivatives. Furthermore, some of the claims brought up against the VIX are more of a theoretical nature and not important, but some might have a dramatic impact on the value of the VIX as well as the pricing of its derivatives. To our knowledge, that is the first comprehensive study of the VIX index and its shortcomings that is both based on theoretical and empirical observations. We are confident that our analysis will lead to new ways of how to make the VIX index safer for investors and market participants as well as less prone to manipulation and errors.