The VIX in Depth: The Formula, the Futures Curve, SOQ Settlement, and Why VIX ETPs Decay

The VIX is Cboe’s index of the market’s expected 30-day volatility of the S&P 500, calculated not from a single option but from the prices of a whole strip of out-of-the-money S&P 500 (SPX) puts and calls. Mathematically it is the square root of a 30-day variance swap rate, expressed in annualized percentage points, so a VIX of 20 means option prices are paying for about 20% annualized volatility over the next 30 calendar days.

In short: the VIX formula weights every out-of-the-money SPX option by one over its strike squared, adds up the result for two expirations that bracket 30 days, and interpolates to exactly 30 days. Because it is built from option prices, it measures what the market charges for volatility, which on average is higher than the volatility that then occurs. The VIX itself cannot be bought. What trades are VIX futures and options, which settle to a special morning calculation called the Special Opening Quotation (SOQ), and exchange-traded products that hold VIX futures. When the futures curve slopes upward, those products lose value steadily even if the VIX goes nowhere.

The basics-level introduction is in implied volatility explained. This article works through the official methodology, a full calculation on a small strip, settlement, and the futures term structure. Nothing here is a recommendation to trade volatility products.

A common misconception: “the VIX is the implied volatility of at-the-money options”

It was, once. Cboe introduced the VIX in 1993 based on at-the-money S&P 100 (OEX) options. In 2003, working with Goldman Sachs, Cboe moved to the current method: S&P 500 options (European-style and cash-settled, see American vs European options) across a wide range of strikes, combined using the variance-swap replication formula from Demeterfi, Derman, Kamal and Zou’s 1999 Goldman Sachs note “More Than You Ever Wanted to Know About Volatility Swaps”, which Cboe’s methodology cites. The new VIX launched on September 22, 2003, with calculated history back to January 1990. Cboe listed VIX futures on its futures exchange (CFE) in March 2004 and VIX options in February 2006.

Because out-of-the-money puts on the S&P 500 trade at higher implied volatilities than at-the-money options (the skew), a strip that includes them produces a number above at-the-money implied volatility. The worked example below shows the size of that difference.

The formula

Everything in this section comes from Cboe’s “Cboe Volatility Index Methodology” (version 6.0, last revised February 26, 2026) and the companion “Cboe Volatility Index Mathematics Methodology” (version 5.0, also February 26, 2026).

For each of two expirations, Cboe computes a variance:

σ² = (2/T) x Σ [ (ΔK_i / K_i²) x e^(RT) x Q(K_i) ] - (1/T) x (F/K_0 - 1)²

where:

T is time to expiration in years, measured in minutes: minutes until expiration divided by 525,600 (the minutes in a 365-day year). Standard monthly SPX options are deemed to expire at 9:30 a.m. ET on their expiration day; weekly SPXW options at 4:00 p.m. ET.
R is a risk-free rate for that expiration, from US Treasury constant-maturity yields, interpolated with a bounded cubic spline and converted to continuous compounding.
F is the forward index level implied by option prices: find the strike where the call and put mid-prices are closest, then F = strike + e^(RT) x (call price - put price).
K_0 is the first listed strike at or below F.
K_i is the strike of the i-th out-of-the-money option: puts below K_0, calls above K_0, and both at K_0 (their prices are averaged).
ΔK_i is half the distance between the strikes on either side of K_i (at the ends of the strip, the distance to the single neighbor).
Q(K_i) is the midpoint of the option’s bid and ask.

The two variances are then interpolated to exactly 30 days:

VIX = 100 x √{ [ T_1σ_1² x (N_T2 - N_30) / (N_T2 - N_T1) + T_2σ_2² x (N_30 - N_T1) / (N_T2 - N_T1) ] x N_365 / N_30 }

where N_T1 and N_T2 are minutes to each expiration, N_30 = 43,200 and N_365 = 525,600.

Which options get in

Expirations. The universe is AM-settled standard SPX options plus PM-settled SPXW options expiring at the end of a week (excluding weeklies that expire on the same date as a standard monthly). Under the “bracket method” with a 30-day constant maturity, the near term is drawn from expirations of 30 days or less and the next term is the expiration immediately after it, so the two bracket 30 days.
Strikes. Starting next to K_0 and moving outward, Cboe includes each out-of-the-money option with a non-zero bid (the current mathematics document says an option with a zero bid or a zero ask is excluded). Once two consecutive strikes have zero bids, no further strikes in that direction are used, even if more distant strikes have bids.
Data source. Quotes from Cboe Options only.
Filtering. To stop a momentary quote gap from printing a misleading value, Cboe applies a filtering algorithm, with a threshold of 0.50 volatility points over two minutes during regular hours. The index is disseminated every 15 seconds, between 9:31 a.m. and 4:15 p.m. ET in regular hours and 3:15 a.m. to 9:25 a.m. ET in global trading hours.

Worked example: computing a VIX on a small strip

Cboe’s methodology includes its own sample calculation (on hypothetical quotes dated September 27, 2022, producing 13.93). Ours uses a deliberately small strip so every number can be checked. Assumptions:

Calculation time: a Tuesday at 10:00 a.m. ET.
Near term: standard AM-settled options expiring in 24 days at 9:30 a.m., so N_T1 = 24 x 1,440 - 30 = 34,530 minutes, T_1 = 34,530 / 525,600 = 0.065696.
Next term: PM-settled weeklies expiring in 31 days at 4:00 p.m., so N_T2 = 31 x 1,440 + 360 = 45,000 minutes, T_2 = 0.085616.
Interest rate 4% for both terms. Hypothetical S&P 500 at 6,000.
Option prices generated from Black-Scholes with a downward-sloping smile that is exactly 17.0% at the money. Strikes every 200 points; options worth under $0.05 are treated as having no bid.

The forward for the near term is 6,015.79 and for the next term 6,020.58, so K_0 = 6,000 in both. Each option’s contribution is (ΔK / K²) x e^(RT) x Q(K), shown here multiplied by one million for readability:

Strike	Option used	Near-term price	Near contribution (x 10^6)	Next-term price	Next contribution (x 10^6)
4,800	Put	0.34	2.96	1.13	9.84
5,000	Put	0.66	5.29	1.90	15.25
5,200	Put	1.54	11.42	3.69	27.39
5,400	Put	4.14	28.47	8.09	55.68
5,600	Put	12.17	77.82	19.29	123.44
5,800	Put	35.94	214.24	47.05	280.69
6,000	Put/call average	104.34	581.22	119.13	664.13
6,200	Call	31.80	165.89	43.78	228.56
6,400	Call	4.52	22.13	8.72	42.72
6,600	Call	0.25	1.15	0.86	3.96
Sum			1,110.59		1,451.67

Step by step for the near term:

2/T_1 x sum = 2 / 0.065696 x 0.00111059 = 0.033810
Forward adjustment: (1/T_1) x (6,015.79 / 6,000 - 1)² = 0.000105
σ_1² = 0.033810 - 0.000105 = 0.033704 (a single-term volatility of 18.36%)

For the next term, 0.033911 - 0.000137 gives σ_2² = 0.033774 (18.38%).

Interpolation weights: (45,000 - 43,200) / (45,000 - 34,530) = 0.1719 on the near term and (43,200 - 34,530) / 10,470 = 0.8281 on the next term. Then:

VIX = 100 x √{ [0.065696 x 0.033704 x 0.1719 + 0.085616 x 0.033774 x 0.8281] x 525,600 / 43,200 } = 18.38

Three observations:

The VIX is above at-the-money volatility. At-the-money implied volatility here is exactly 17.0, but the strip gives about 18.4. The extra comes from the expensive out-of-the-money puts, each weighted by 1/K², so low strikes count for more per dollar of premium.
Strike spacing matters. Rerunning the same smile with 100-point strikes gives 17.89, and with 25-point strikes from 4,500 to 7,500 gives 17.80. Coarse grids overstate the integral. Real SPX strips use 5-point strikes near the money, which is one reason Cboe’s procedure is robust in practice.
The 1/K² weighting is the variance swap. It is the same replicating portfolio Carr and Wu use to synthesize variance swap rates (see the variance risk premium). That is why the VIX squared is best read as a price for 30-day variance, not a forecast of volatility.

What the VIX number means, with history

Because the VIX is the square root of a risk-neutral variance, it includes a premium for volatility risk. From Cboe’s daily history (our calculation, January 2, 1990 to November 9, 2026), the average VIX close was 19.42 and the median 17.56. Over the same period, the S&P 500’s realized volatility over the 21 trading days following each date averaged about 15.3.

Settled extremes, from the same data:

Event	Date	VIX
Highest intraday	October 24, 2008	89.53 (closed 79.13)
Highest close	March 16, 2020	82.69
Lowest close	November 3, 2017	9.14
Largest jump in the 2018 selloff	February 5, 2018	closed 37.32, from 17.31 on February 2

A useful conversion: dividing the VIX by √12 (about 3.46) gives the one-standard-deviation 30-day move implied by option prices. A VIX of 20 implies about 5.8% over a month. Dividing by √252 (about 15.9) gives a daily figure: about 1.26% at a VIX of 20.

VIX futures

From Cboe’s VIX product specifications:

Contract size: $1,000 times the VIX futures price. A minimum price increment of 0.05 points is worth $50.
Final settlement date (monthly contracts): the Wednesday that is 30 days before the third Friday of the following calendar month, so that the SPX options used for settlement have exactly 30 days to run. Weekly futures settle on the Wednesday of the week in their ticker.
Last trading: trading in an expiring contract ends at 8:00 a.m. Chicago time on the final settlement date.
Settlement: cash, on the business day after the final settlement date, at the SOQ.

Why futures do not track spot

The VIX is not an asset you can buy and store, so the usual cost-of-carry link between spot and futures does not exist. A VIX future is the market’s price today for where the SOQ will print on its settlement date, including a risk premium. Since the VIX tends to revert toward its long-run average, futures typically sit between spot and that average: above spot when the VIX is low, below it when the VIX is high. The contracts are listed on CFE and cleared like other exchange-traded derivatives (see how options markets work).

A real term structure, two days apart

From Cboe Futures Exchange daily settlement data:

Contract (settlement date)	Days to settle from Nov 9	Settle, Nov 6, 2026	Settle, Nov 9, 2026
Spot VIX (close)	0	25.64	19.92
Nov 2026 (Nov 18)	9	23.69	20.01
Dec 2026 (Dec 16)	37	22.18	19.49
Jan 2027 (Jan 20)	72	22.05	20.10
Feb 2027 (Feb 17)	100	21.94	20.46
Mar 2027 (Mar 17)	128	21.70	20.61
Apr 2027 (Apr 21)	163	21.78	20.89
Jun 2027 (Jun 16)	219	21.68	21.03

On Friday, November 6, 2026, the curve was inverted (backwardation): spot at 25.64 above every future, and later contracts generally lower. By the following Monday the spot VIX had fallen almost 6 points, the front futures fell much less, and the curve was close to flat with a mild upward slope from December onward. Two lessons follow. Futures move less than spot, especially far out the curve: on November 9, spot fell 5.72 points, the November future 3.69, and the June 2027 future 0.65. And the shape can flip in a single session.

VIX options and the SOQ

VIX options are European-style, cash-settled options on the VIX, with a $100 multiplier. Their last trading day is the business day before the morning on which the settlement value is calculated, and they settle to the same SOQ as the VIX future with the same settlement date. That has an important consequence: since the option and the future settle to the same number on the same morning, the correct underlying for pricing a VIX option is the VIX future of that expiration, not the spot VIX. A VIX call can look cheap against spot and be fairly priced against its future.

How the SOQ differs from the spot VIX

Per section 3.4 of Cboe’s VIX methodology, the settlement calculation differs from the live index in four ways:

One expiration, no interpolation. It uses SPX or SPXW options from the single expiration 30 calendar days after the settlement day.
A fixed strike range. Cboe determines and announces the highest call strike and lowest put strike in advance, rather than applying the two-consecutive-zero-bids rule.
Zero-bid options can count. Options inside that range are eligible even with a zero bid.
Opening trade prices, not mid-quotes. Each option’s price is its opening trade price in a special opening auction Cboe runs on settlement days. Only if an option has no opening trade does Cboe use the midpoint of the best bid and offer at the open.

The result is that the SOQ is a real, tradable set of prints rather than a quote snapshot, which is what allows a hedger to offset a futures position into settlement by trading the actual SPX strip in the auction. It also means the SOQ can differ noticeably from the prior evening’s VIX or the VIX a few minutes after the open, because it reflects a single auction’s prices.

Why long VIX ETPs decay

Exchange-traded products that offer “VIX exposure” cannot hold the VIX. They hold futures, usually following an S&P Dow Jones index such as the S&P 500 VIX Short-Term Futures Index, which S&P DJI describes as rolling from the first-month to the second-month VIX future every day in equal fractional amounts, to maintain a constant one-month maturity.

When the curve slopes upward (contango), every future gradually slides down toward the lower spot level as it ages. A constant-maturity holder keeps selling the cheaper near contract and buying the dearer next one, and loses that slide.

Worked example: a month in which nothing happens

Take a hypothetical calm curve that does not change for 30 days: spot VIX 15.0, the 30-day point 17.0, the 60-day point 18.3 (linear between those points). The fund holds a blend of the two nearest futures with an average maturity of 30 days, shifting a slice from the first to the second each day.

The first-month future slides down at 2.0 / 30 = 0.067 points per day; the second-month at 1.3 / 30 = 0.043 points per day.
Averaged over the month, the blend loses about 0.055 points a day, or about 1.65 points over 30 days on a level near 17.
Compounding the daily changes exactly (with the near-month weight falling from 1 to 0 over the month) gives a loss of about 9.4% in 30 days, with the VIX unchanged at 15.

That is the cost of holding volatility insurance through futures in calm markets. In backwardation (as on November 6, 2026 above), the roll works the other way and a long position gains from the slide. Over long periods, contango has been the more common state, which is why long VIX futures products have tended to lose value between spikes. Inverse and short VIX products earn this roll in calm periods and face the opposite risk: the 115.6% one-day rise in the VIX on February 5, 2018 shows how quickly that can reverse.

What can go wrong

Treating the VIX as tradable. A view that “the VIX is too low” can be right and still lose money in futures, because the futures already price mean reversion.
Pricing VIX options off spot. Always use the matching future. The difference can be several volatility points.
Settlement surprises. The SOQ comes from one opening auction. Positions held into settlement are exposed to that print, which can differ from the previous close or the live index.
Roll decay compounds. Holding long VIX futures products as a long-term hedge has historically been expensive in calm years.
Volatility of volatility. The VIX can double in a day. Leveraged or inverse volatility products can lose most of their value in a single session.

The short version

The VIX is the square root of a 30-day variance swap rate built from out-of-the-money SPX options, weighted by 1/K² and interpolated between two expirations measured in minutes. Our small-strip calculation turns an at-the-money volatility of 17.0 into a VIX of about 18.4, because the strip prices the skew. VIX futures ($1,000 multiplier) and VIX options ($100 multiplier, priced off the futures) settle on Wednesday mornings to the SOQ, computed from opening auction trade prices in a single 30-day SPX expiration. Futures do not track spot because the VIX cannot be stored, and in contango a constant-maturity long position loses roll yield: about 9.4% in a month in our calm-curve example, with the VIX unchanged.