From 1993 to 2003, the VIX was constructed using Black-Scholes implied volatilities from options on the S&P 100 index. Since 2003, however, the VIX has been constructed using model-free implied volatility from options on the S&P 500 index.
Among measures of asset price volatility, two types can be distinguished. Historical volatility is estimated using historical asset prices. Implied volatility is estimated from option prices, by equating market prices of options to those obtained with an option-pricing model.
Historical volatilities are retrospective estimates, but implied volatilities are prospective estimates because they are estimated from option prices. Hence, many analysts prefer implied volatilities because they reflect future expectations about volatility, rather than past realizations.
Often the Black-Scholes model is used to obtain implied volatility, which creates two problems. The first is that this approach assumes the Black-Scholes model to be the correct one for pricing options. It is well- known, however, that the assumptions underlying the Black-Scholes model are rarely met in practice. The second problem is that Black-Scholes implied volatilities are usually constructed by using options that are near-the-money, and by excluding all deep in-the-money and out-of-the-money options.
Hence, all the information embedded in the excluded options is lost. Model-free implied volatility is a recent innovation that uses the entire cross-section of option prices to calculate implied volatility and that is not dependent on a particular parametric model for option prices.
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| The volatility index (VIX) |
