Index volatility alignment, skews, and butterfly construction

Align related index gauges

Implied volatility is the variability the options market has already priced into premiums, as distinct from variability later observed in the underlying. Option premium analysis compares what is paid across related indexes, strikes, and expirations to test whether two gauges sit on the same volatility scale and where demand or event risk has distorted the surface.

After 22 September 2003, a widely quoted equity-index implied-volatility gauge was recalculated from S&P 500 options rather than S&P 100 options, while the original S&P 100 formulation remained available as a separate series.

S&P 100 and S&P 500 prices and day-to-day volatility typically move together, so option premiums on the two indexes generally embed similar implied-volatility levels. When the S&P 500 implied-volatility gauge sits near 12, S&P 100 option implied volatility is expected near that same level rather than near 34, and a multi-fold rise in the former is expected to be matched by a similar rise in the latter.

Read price and time skews

A price skew is a same-expiration pattern in which implied volatility differs by strike, often with far out-of-the-money index puts richer than nearer strikes. After the 1987 equity crash, demand for deep out-of-the-money index puts as portfolio protection lifted their implied volatility above at-the-money and in-the-money options and left puts more expensive than calls.

A time skew is a calendar pattern in which implied volatility differs by expiration month, often with short-dated options richer when a near-term catalyst is being priced. Short-dated options often carry higher implied volatility than longer-dated options when a near-term catalyst such as an earnings release raises the chance of a large short-horizon move.

Construct the butterfly

A butterfly spread is a three-strike, same-right structure that sells two at-the-money options and buys one in-the-money and one out-of-the-money wing, combining a bull spread and a bear spread. A standard butterfly is built entirely with calls or entirely with puts by selling two at-the-money contracts and buying one in-the-money and one out-of-the-money contract of the same type.

An iron butterfly is a four-leg mixed-right structure that sells the at-the-money put and call and buys the out-of-the-money put and call, sharing the same rangebound, decay-dependent objective as a standard butterfly. Both butterfly constructions are intended for a rangebound underlying so that the short option premium decays with the passage of time.