Gaps and Volatility Bands: How a Jump Enters the Range

A stock closes at 100 and the next session opens at 105. Nothing traded in between, so the chart shows a hole where a continuous path would be. A trader looking at the volatility band on that chart can reasonably ask what it just did with the jump, and whether the answer depends on how the band was built.

It does depend, and the difference is mechanical rather than a matter of opinion. The same five-point jump is one data point to one kind of band and a lasting step to another.

A gap is a return before it is a hole

A return-space band works on percentage moves from one close to the next. Oisigma's How It Works page describes the method as return space, "percentage moves anchored to the prior close," then projected back onto price. In that frame a gap has no special status. It is part of the move between two closes, and it enters the series only through where the close ends up. A gap that is fully reversed by the close leaves almost no mark on a daily close-to-close return; one that holds becomes a large return.

That is the same logic as the one in why closing prices matter: the series is built from settlements, so the path inside the bar, including where it opened, is not scored. On an intraday chart the bookkeeping is the same but the unit is smaller. Mechanically, the first bar of a session is measured against the previous session's last close, so the overnight move arrives inside that one bar's return.

What a price-space band does with the same jump

A band built on price levels has to average and measure the dispersion of the levels themselves. Take a deliberately simple, constructed example, not market data: a 20-bar window, price flat at 100, then a gap to 105, then flat again. Ten bars after the gap, the window holds ten closes at 100 and ten at 105.

The average of those closes is 102.5. Price sits at 105 and has not moved for ten bars, yet the midline sits 2.5 points below it. The dispersion of the levels is 2.5 points as well, because the step is read as spread, so a two-standard-deviation band is roughly ten points wide on a chart where nothing has changed since the gap. Both distortions last for as long as the pre-gap closes remain in the window. This is the same structural lag described in the Bollinger Band drift problem: an average of levels takes time to absorb a level shift, in varying degrees at any window length.

How a gap sits in a return-space window

In a return-space window the same event is one observation among many. Oisigma's FAQ describes the canonical window as 60 bars, about a calendar quarter on daily. A five percent gap is one large return among sixty. While it stays in the window it widens the band, which is reasonable, since a large percentage move did just occur.

Two features follow from the construction. The midline does not lag the jump, because the range is projected from the prior close rather than from an average of old levels. And the effect has a clock: sixty bars later the observation leaves the window and the band can narrow on a day when nothing unusual happened. The return space versus price space post covers why that structure matters in general; the gap is the cleanest case of it.

The gap day itself

None of this helps on the gap day. The band for any bar is built from information available at the prior close only, which is what makes it causal, so a gap cannot be in the band that it lands against. A large gap can put the close well outside a range that described the previous quarter accurately. A small gap, relative to recent moves, can land comfortably inside it. Which of the two a given gap turns out to be is only known once the bar has closed.

That is the same limit as the crisis-onset case. The working paper reports that on crisis-onset days, defined as the VIX above 30, inner-band containment fell to about 65%, against about 71% normally. That is historical calibration measured on BTM only, and past behavior is not a guarantee of future results. It is also conditioned on the VIX, not on gaps, so it should not be read as a gap statistic. The crisis-onset post covers the limit and the reasons for it.

What has not been published

The honest boundary is narrow but real. Oisigma's published results are scored on consecutive closes. None of them splits days by gap size, or compares gap days against non-gap days. The intraday result on the intraday post covers one instrument, SPY, with a 15-minute floor, and does not separate the session-open bar.

So everything above is the arithmetic of how each construction handles a jump, not a measured effect on containment. That arithmetic is checkable by anyone with a spreadsheet, which is the point of stating it this way. How much a gap moves calibration in practice is a question the published record does not answer, and this site does not claim to know.

The takeaway

A gap is a return to a return-space band and a step in the levels to a price-space band. In the first it is one observation that enters, widens the range for a defined period, and leaves. In the second it shifts the average and inflates the spread for as long as the old levels remain in the window. Neither version can know about the gap on the day it happens, and no published Oisigma result measures how often gap days land outside the range.

Frequently asked questions

Does ATR include gaps? Yes, by definition: true range is the largest of the bar's high-low distance and the distances from the prior close to the high and to the low, so a gap from the prior close is counted. ATR measures how far price travelled, an intraday quantity, while standard deviation of returns is calibrated against close-to-close moves. Which is appropriate depends on the type of quantity being measured; the order block and liquidity sweep study covers that domain split.

If a gap fills by the close, does it still affect the band? On a daily chart, the return depends only on the two closes. A gap that opens and is fully reversed within the session leaves the close where it started, and the intraday excursion is not in a close-to-close series at all. That is a property of the construction, described in why closing prices matter, and not a statement about how often gaps reverse.

Does a longer window make gaps matter less? Each observation carries less weight in a longer window, since it is one of more bars, but it also stays in the window longer. The reactive-versus-steady trade-off is the one covered in what rolling volatility is; the FAQ page describes shorter windows as more reactive but noisier, and longer ones as smoother but slower through regime changes.

Does a close outside the band after a gap say what happens next? No. The range is an expected range, not a claim that price reverses at its edges, and it does not predict direction. The working paper validates the range's calibration, not the profitability of any use, and whether any use delivers value after real-world costs is an open question. No published result conditions on gaps.

A gap is one of the easier events to watch against a calibrated range, because the jump and its size are visible the moment the bar prints. BTM draws a close-based expected range on any TradingView symbol, and you can start a free 30-day trial to see how it handles the next gap on the markets you already follow.