Jumps Are Loud but Forgettable: Roughing It Up

Barndorff-Nielsen and Shephard had handed the profession a scalpel: a way to take a day's realized volatility and cut it cleanly into two pieces, the continuous churn of ordinary trading and the discontinuous jumps caused by sudden news.

A scalpel is only interesting if you use it on something. In 2007, Torben Andersen, Tim Bollerslev and Francis Diebold used it, across exchange rates, stock indices and bond yields, and asked the question everyone wanted answered: does knowing whether yesterday's volatility came from grinding or from jumping help you forecast tomorrow?

The answer is yes, and the reason why is genuinely surprising.

The problem: your forecast is being poisoned by one-off events

Every volatility forecasting model in existence works on the same principle: volatility clusters, so a volatile yesterday implies a volatile tomorrow. Feed it a big number today and it will forecast a big number tomorrow.

But consider a specific, very common scenario. The market is calm all day. Then at 2pm a central bank surprises everyone, the price gaps violently in ninety seconds, and then everything settles back down and the rest of the afternoon is as sleepy as the morning.

Your realized volatility for that day is enormous, because it contains the gap. Your model dutifully forecasts an enormous volatility for tomorrow. And it is wrong, because nothing about the market has actually changed. There was one violent moment, caused by an event that has now passed, and the underlying state of the market is exactly what it was yesterday.

Multiply that by every macro announcement, every earnings surprise, every geopolitical shock, and your forecasts are being systematically contaminated by events that carry no information about the future.

The key idea via analogy: the drum and the gong

Think of the market's volatility as two instruments playing at once.

There is a drum, beating steadily. Its tempo speeds up and slows down over weeks and months, and it does so gradually. When the drum is fast today, it will very likely still be fast tomorrow, and probably fairly fast next month too. The drum has momentum.

And there is a gong. Every so often, someone hits it. It is loud, far louder than the drum, and it dominates any recording of the room in the moment it is struck. But it fades in seconds. Being struck today tells you nothing about whether it will be struck tomorrow.

Realized volatility records the room. It hears the drum and the gong mixed together. If you use it naively, a gong strike makes you think the drum sped up, and you predict a loud tomorrow when in fact the drum is beating at exactly its old tempo.

The authors' contribution is to separate the recording into a drum track and a gong track (using bipower variation to isolate the drum, and the difference to isolate the gong), and then forecast using both tracks separately. Practically, this means building a HAR-style regression, but with the continuous component and the jump component entering as their own variables, each with its own coefficient.

The finding: persistence lives entirely in the drum

This is what they discovered, and it is the heart of the paper.

The continuous component is enormously persistent. A high level of ordinary churn today strongly predicts a high level tomorrow, next week and next month. This is where all the familiar volatility clustering lives.

The jump component is barely persistent at all. A jump today tells you almost nothing about volatility tomorrow. Jumps arrive, do their damage, and are forgotten.

Once you see that, the practical implication is obvious. The two components deserve very different weights in a forecast. The continuous part should get a large coefficient. The jump part should get a small one. And when the authors tested this out of sample, splitting the components produced significant improvements in volatility forecasts compared with using undifferentiated realized volatility.

They also went looking for what causes the jumps, and found a satisfying answer: many of them line up with scheduled macroeconomic news announcements. Jumps are not random acts of god. They are, to a considerable extent, the market repricing on the arrival of specific, identifiable information.

Why it mattered

• It turned a measurement idea into a forecasting gain. Bipower variation was elegant theory. This paper is the demonstration that the theory pays.
• It reshaped the standard model. The HAR-CJ specification, HAR with separate continuous and jump components, became a workhorse of applied realized volatility work.
• It sharpened a conceptual distinction. "Volatility" is not one thing. Diffusive risk and jump risk behave differently, persist differently and should be managed differently. This paper is the clearest empirical statement of that.
• It connected volatility to the news calendar. Linking jumps to macro announcements gave a concrete, testable economic story for where the discontinuities come from.

The honest limitations

• The split depends entirely on the jump test. Whether a given day contains a "jump" is the output of a statistical test with a chosen significance level. Change the threshold and you change the decomposition, and therefore the forecasts. There is unavoidable arbitrariness here.
• Sampling frequency defines what a jump is. A move that unfolds over two minutes is a jump at five-minute sampling and a burst of high volatility at ten-second sampling. The continuous-versus-jump distinction is partly an artefact of how often you look.
• Microstructure noise contaminates both pieces. Both realized volatility and bipower variation are distorted by the bid-ask bounce, and the distortions do not cancel.
• "Jumps do not predict volatility" is not "jumps do not matter." A jump can wipe out a portfolio. The finding is about forecasting the level of volatility, not about the importance of jump risk. For tail risk, options pricing and hedging, jumps are enormously consequential.
• Gains are real but not revolutionary. The forecast improvement from splitting the components is statistically significant and worth having, but it does not transform a mediocre model into a great one.

The one-line takeaway

Andersen, Bollerslev and Diebold split realized volatility into the market's steady grind and its sudden shocks, and found that all the predictability lives in the grind: a jump is loud on the day and forgotten by the next, so a forecasting model that treats the two the same is systematically fooled every time a central bank speaks.