A modified volatility construction for weeks-to-months regimes

Implied and historical volatility

Historical volatility is the standard deviation of an asset's rates of return, equal to the square root of return variance. Implied volatility is the volatility input that makes a chosen option pricing model match the option's observed market price.

Those two estimates can differ at the same moment. A listed composite built from implied volatility therefore does not automatically restate contemporaneous statistical volatility.

The listed volatility index

The volatility index is a composite of implied volatilities from eight near-the-money nearby and second-nearby S&P 100 calls and puts, adjusted for remaining time and moneyness.

Option-premium analysis judges whether those listed index options are expensive or cheap relative to their own history by mapping the level of that composite. When the index is very high, the options used to compute it are expensive relative to their historical prices. When the index is very low, those options are cheap.

How the raw index behaved

In the historical window described, the index reached a high of 150 in 1987 and a low of about 8 in 1993-94. Extreme lows clustered at 8% to 9%, while readings greater than 20% were described as fairly uncommon in the then-recent period.

The index generally declined during orderly equity advances and rose during declines. Steeper and more abrupt declines were associated with higher readings.

The modified two-factor series

A modified-volatility-construction is a two-factor series that combines cash-index distance from a selected moving average with the volatility-index close and a 252-day annualization factor. In the archive workflow the cash input is the S&P 100 or S&P 500 close's distance from a 21-day moving average, and 252 is treated as the approximate number of trading days in a year.

If the cash index equals its moving average, the construction prints zero regardless of the volatility-index level. The options factor cannot, on its own, pull the hybrid off that zero print.

Bands that locate a market regime

The modified series is framed with a 252-day exponential moving average and standard-deviation-bands at one, one and a half, and two standard deviations that center about zero. Those dynamic envelopes mark unusual readings of the hybrid.

A market regime, in this workflow, is a weeks-to-months state describing whether implied volatility and option premium are elevated, depressed, or mid-range relative to recent history and the cash index's location.

Two-standard-deviation penetrations of the modified series accompanied extreme raw-index readings. In early 1994 and August-September 1994 the raw index stayed low while the modified series moved first ahead of a potential decline.