Friday's VIX Rose 21.45%; Its Squared Reading Rose 47.49%

Friday's VIX Rose 21.45%; Its Squared Reading Rose 47.49%

Cboe's VIX closed at 19.99 on Friday, 16 October 2026, compared with 16.46 on Thursday. Its VIX market page displayed a 3.53-point increase and a 21.45% daily change. Those numbers describe a change in a volatility index. A worksheet measuring the relative change in its squared reading needs a different answer: about 47.49%.

Both calculations can be correct. Volatility is expressed on a square-root scale; variance uses the squared scale. Carrying the same percentage from one to the other changes the measurement.

The distinction matters when a research note says that implied variance rose by the same percentage as VIX. Check which quantity the note calculated before comparing it with another risk measure.

Keep the published closes beside the calculation

Cboe's market page reports the 16 October reading and its previous close. Its historical-data page links daily closing history. These two published readings are the inputs:

Thursday, 15 October 2026: VIX close 16.46 index points. Expressed as annualised volatility in decimal form, the reading is 0.1646. Its square is 0.02709316.

Friday, 16 October 2026: VIX close 19.99 index points. The corresponding decimal volatility is 0.1999. Its square is 0.03996001.

Subtracting the published closes gives 19.99 - 16.46 = 3.53 volatility points. Dividing by the earlier close gives 100 x (19.99 / 16.46 - 1) = 21.4459...%, which rounds to Cboe's displayed 21.45%.

For the squared readings, the calculation is 100 x (0.03996001 / 0.02709316 - 1) = 47.4911...%. That is author arithmetic from the published two-decimal closes. Cboe did not publish a separate 47.49% variance-change statistic in the records used here, and the calculation does not recover additional precision from the underlying option quotes.

Why squaring changes a percentage

Cboe's VIX FAQ describes a constant 30-day expected-volatility measure derived from SPX option prices. Its mathematics methodology combines variance terms, annualises the result and takes a square root to express the index in volatility units, multiplied by 100.

Reversing that scale gives (VIX / 100)^2, an option-implied annualised variance scale. The decimal square is a variance quantity, not an ordinary percentage return. The 47.49% figure above is the relative percentage change between two such quantities.

If volatility rises by a decimal fraction r, its new level is 1 + r times the old level. The squared level changes by (1 + r)^2 - 1 = 2r + r^2. Doubling the volatility percentage omits the final squared term. Here, twice the unrounded volatility change is about 42.89%; the extra term contributes about 4.60 percentage points to the squared-reading change.

Two fictional records make the nonlinearity easier to check. Each starts from an invented volatility reading of 20, with no real dates, options or market path.

Fictional upward record: the reading moves from 20 to 24, a 20% increase. Decimal volatility moves from 0.20 to 0.24; its square moves from 0.0400 to 0.0576, a 44% increase.

Fictional downward record: the reading moves from 20 to 16, a 20% decrease. Decimal volatility moves from 0.20 to 0.16; its square moves from 0.0400 to 0.0256, a 36% decrease.

The equal-sized volatility changes produce unequal variance changes. These are separate comparisons with the same starting value, not successive legs of a round trip or forecasts for VIX.

Two closes have two rolling windows

The comparison spans one completed session, while each VIX reading looks forward over its own 30-day window. Thursday's and Friday's windows begin at different times. Their difference does not isolate the variance assigned to Friday, the next trading day or any one scheduled announcement.

Our earlier VIX horizon comparison examines total variance across different index horizons. This calculation instead compares the relative changes in one index and its square across two observation dates. Neither calculation alone measures a realised S&P 500 return or proves why option prices changed.

This article was prepared at 07:11:48 Australia/Brisbane on Sunday, 18 October. Friday, 16 October was the latest completed relevant U.S. regular options session: Cboe's dated statistics contained a populated 3:15 p.m. Central row. Its C1 hours put regular-session close at 4:15 p.m. Eastern Daylight Time, or 06:15 Brisbane on Saturday, 17 October. The daily CSV supplies observation dates, not a separately verified upload second. No later session close is assumed.

A squared index reading does not price a position

The 21.45% change supplies no return on a VIX derivative, and 47.49% supplies no variance-contract return. Neither is a probability or a forecast that the S&P 500 will move by that amount. A higher squared reading describes the option-implied scale being compared; it does not establish the variance that will subsequently occur.

Nor can a researcher apply either percentage to every option premium. A contract has its own underlying, strike, expiration, exercise and settlement terms, quote time, bid, ask and available size. The options-chain guide and liquidity guide explain that separate evidence. The implied-volatility guide covers the volatility input itself.

Options Matrix Pro publishes this article and offers commercial options-analysis software. This is general education, not personal financial, legal or tax advice or a recommendation to trade. Buyers can lose their premium; some short positions can lose much more, including theoretically unlimited loss on an uncovered call. Exercise, assignment, settlement and funding obligations, limited liquidity, transaction costs, concentration and taxes remain product- and account-specific. Options are unsuitable when the investor cannot tolerate the relevant losses or fund the obligations. Review FINRA's options guidance and the OCC disclosure gateway.

Sources and method

Sources were accessed on 18 October 2026 Australia/Brisbane. Cboe's market page, historical-data page and daily history supply the observed readings. Its VIX FAQ and mathematics methodology supply the horizon and scale. Dated statistics and hours establish the completed-session boundary. FINRA supplies the risk guidance; OCC's gateway directs readers to the standardised-options disclosures.

Label the worksheet column before entering the change: 3.53 volatility points, 21.45% relative change in VIX, or 47.49% relative change in its squared reading. Retain both observation dates and the published-close precision beside it.