**VIX** is a popular measure of the implied volatility of S&P 500 index options. Often referred to as the ** fear index **or the

*fear gauge*, it represents one measure of the market’s expectation of stock market volatility over the next 30 day period.

Based on the history of index option prices, Prof. Whaley computed daily VIX levels in a data series commencing January 1986, available on the CBOE website. Prof. Whaley’s research for the CBOE appeared in the Journal of Derivatives.

The VIX is quoted in percentage points and translates, roughly, to the expected movement in the S&P 500 index over the upcoming 30-day period, which is then annualized. “VIX” is a registered trademark of the CBOE.

The VIX is calculated as the square root of the par variance swap rate for a 30 day term initiated today. Note that 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). Avariance 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. The VIX is quoted as an annualized standard deviation.The VIX has replaced the older VXO as the preferred volatility index used by the media. VXO was a measure of implied volatility calculated using 30-day S&P 100 index at-the-money options.

The VIX is quoted in percentage points and translates, roughly, to the expected movement in the S&P 500 index over the next 30-day period, which is then annualized. For example, if the VIX is 15, this represents an expected annualized change of 15% over the next 30 days; thus one can infer that the index option markets expect the S&P 500 to move up or down 15%/√12 = 4.33% over the next 30-day period. That is, index options are priced with the assumption of a 68% likelihood (one standard deviation) that the magnitude of the change in the S&P 500 in 30-days will be less than 4.33% (up or down).

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 (or lower) volatility of the underlying security makes an option more (or less) valuable, because there is a greater (or smaller) probability that the option will expire in the money (i.e., with a market value above zero). Thus, a higher option price implies greater volatility, other things being equal.

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