Method · 4 min read

The volatility projection

Understanding what the band drawn beyond the last candle shows: a measured estimate of how far price could move, not a prediction of direction.

The essentials

Beyond the last candle, the chart can draw a cone: a band that widens progressively and shows the price levels considered likely at the horizons ahead. It combines the displayed asset’s recent volatility, measured live, with a calibration established once and for all on a long market history. That calibration is not recomputed separately for each asset: doing so requires a depth of history that not every listed asset has yet.

The middle line of the cone is perfectly flat, and that is not an oversight: it stays equal to the last known price at every horizon. Nobody — not this model, not any other — knows which way a crypto price will move in the hours or days ahead. What can be estimated is how far it might move around that current price. The cone answers "how much can the price move?", never "up or down?".

The narrow band (50%): half of past moves of this magnitude stayed inside it.
The wide band (80%): four out of five past moves stayed inside — one in five went outside, in either direction.
The further the horizon, the wider the band: uncertainty about the size of the move grows with elapsed time.

Interactive lab

Draw possible futures and count

The cone says "by how much" the price may move, never "which way". Draw random paths: about 8 in 10 should end inside the wide band.

today

Futures drawn

Inside the 80% band

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Inside the 50% band

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With only a few draws, the count varies a lot. Keep going: the more you draw, the closer it gets to 80% and 50%.

Illustration: these paths are drawn at random to show what an 80% band means. This is not the app's method, whose calibration is measured on real price histories.

Check what you learned

The price leaves the cone's 80% band. What does that mean?

Going further: measured calibration

These bands are not set by assumption: they are measured. A validation bench replays long market histories and counts, for each time range, how often price actually stayed inside each band — over disjoint windows, that is, tests independent of one another. Here is what the measurement gives.

1 day: 50% band achieved 49.9%, 80% band 79.4%.
7 days: 50% band achieved 49.8%, 80% band 79.4%.
1 month: 50% band achieved 50.4%, 80% band 79.5%.
3 months: 50% band achieved 51.0%, 80% band 79.7%.
1 year: 50% band achieved 51.8%, 80% band 82.1%.

A band advertised at 50% that actually covers 49.9% of cases, and an 80% band covering 79.4%, is what you expect from honest calibration: the gap between promise and reality is a fraction of a point.

Expert: the statistical choices behind the cone

Volatility is measured with an estimator that uses each candle’s open, high, low and close rather than closes alone. The selection criterion was independence from drift: several classic estimators assume zero price drift over the period and therefore mistake a marked trend for volatility, overestimating it. A liquid crypto is almost always trending, if only moderately, over the windows involved here.

The cone’s bounds do not come from a known probability law: they are empirical quantiles, measured directly on the gaps actually observed between the price at the horizon and the starting price. This is not cosmetic. The study that preceded this work compared the usual parametric laws against real data: none fits both the centre and the tails of the distribution of crypto moves, and using one would produce bands visibly too wide or too narrow depending on where you read them.

The validation bench applies two statistical tests standard in the field. The Kupiec test (1995) checks that the observed breach rate matches the expected rate on average. The Christoffersen test (1998) additionally checks that breaches are independent over time: a good risk model must not merely be wrong at the right rate on average, it must also avoid being wrong twenty times in a row while a market collapses, which would make the band dangerously optimistic exactly when it matters most.