Term Structure Advanced The distribution of realised vol by tenor

Volatility Curve

The single most useful diagnostic picture a volatility trader has, and the one retail traders are almost never shown.

Quick answer: Volatility curve, in the sense that matters to a volatility trader, is the volatility cone — the historical distribution of realised volatility plotted for each window length, its percentile bands narrowing as tenor lengthens, against which today's implied volatilities can be judged cheap or dear at every tenor at once.

In simple words

Pick a window length — say 30 days — and look back over years of NIFTY history at every 30-day realised volatility that has ever occurred. Some were low, some high; write down the median, the middle half, and the extreme ends. Now do the same for 7-day, 14-day, 60-day, 90-day and 180-day windows. Plot all of these and you get a shape that is wide on the left (short windows swing between very calm and very wild) and narrow on the right (long windows average everything out). That funnel is the volatility cone. It tells you what is normal for each tenor.

The reason it is powerful is the overlay. Take today's implied volatilities — the 7-day expiry, the 14-day, the monthly — and drop each one onto the cone at its matching tenor. In one glance you can see whether the market is charging more or less than history says is normal, and crucially you can see it at every tenor simultaneously. Maybe the front weekly is above its 75th percentile (expensive) while the three-month is near its median (fair). That is a picture no single number gives you, and it is almost never put in front of a retail trader.

Not to be confused with: The volatility smile curve — implied volatility plotted across strikes for one expiry. People say volatility curve and mean the smile; this page means something completely different. The smile is a cross-section across strikes at a fixed tenor. The volatility cone is a cross-section across tenors of the distribution of realised volatility. One is about which strike, the other about which window length.

The picture

The cone narrows as the window lengthens

Historical distribution of NIFTY realised volatility at 7, 14, 30, 60, 90 and 180-day windows: median, 25th/75th and 5th/95th percentiles.

The bands are wide at 7 days and squeeze together by 180 days. That narrowing is not a drawing choice — it is arithmetic: a 7-day realised volatility is dominated by a handful of days and can be anything, while a 180-day figure averages so many days that it cannot stray far from the long-run mean. The cone is what lets you say a number is high for its tenor rather than just high.

Professional explanation

The cone is a distribution at each tenor, not a single line

Most volatility pictures show one number per tenor — the current realised volatility, or the current implied. The cone shows a whole distribution per tenor: for each window length it plots the median, the 25th and 75th percentiles, and the 5th and 95th, computed from years of overlapping historical windows. That extra dimension is the entire value of the object. A single realised-volatility line tells you where you are; the cone tells you where you are relative to everywhere you have been at that tenor. Fifteen percent means nothing on its own. Fifteen percent at the 90th percentile of the 7-day cone but the 40th percentile of the 180-day cone means the short end is stretched and the long end is ordinary — a shape, not a level, and shapes are what volatility traders actually trade.

Why the cone narrows — and why that is not optional

The narrowing is a direct consequence of averaging. A 7-day realised volatility is the annualised standard deviation of just five or so trading days' returns, so a single violent session dominates it and it can land almost anywhere between very calm and extreme. A 180-day realised volatility averages roughly 120 sessions, so any single day is diluted to near-irrelevance and the figure is pinned close to the long-run mean by the law of large numbers. The dispersion of an average shrinks with the square root of the number of terms, so the percentile bands must converge as the window grows. This is why the cone is a cone and not a rectangle, and it is why comparing a 7-day implied against a 30-day realised — different tenors — is meaningless: their natural ranges are not even the same width.

The overlay is the whole point

A cone on its own is a history lesson. A cone with today's implied term structure drawn on top of it is a trading tool. Take each listed implied volatility, place it at its own tenor, and read which percentile band it falls in. Now you can see, in one picture, that the front week is priced above its 75th percentile while the quarter is near its median — that the market is paying up for near-term uncertainty but is relaxed further out. That simultaneous, all-tenor verdict is what no scalar like IV Rank delivers, because IV Rank collapses the whole term structure to one point. The cone refuses to collapse it, and that refusal is exactly why a volatility desk keeps the cone on the screen and the retail platform shows a single IV number instead.

The honest part: a percentile is not a floor

Here is the sentence a marketing department would cut. The cone is built from a finite historical sample, and that sample contains regime shifts — a decade with a pandemic crash, a demonetisation, a couple of global risk events, and long stretches of calm that may or may not resemble the next year. So the 5th percentile of the 7-day window is not a floor beneath volatility; it is merely the lowest 7-day realised volatility that has happened to occur in your sample so far. Volatility can and does go below it, and above the 95th, the first time a genuinely new regime arrives. Treating the bands as hard limits — selling because implied is above the 95th percentile, buying because it is below the 5th — is mistaking the edge of your data for the edge of what is possible. The cone describes what has happened, not what can.

Today's implied term structure, dropped onto the cone

The current NIFTY implied volatilities by tenor overlaid on the realised-volatility cone.

Overlaying the implied points on the cone answers the only question that matters — cheap or dear versus this tenor's own history — at every tenor at once. An implied point sitting above the 75th percentile band is expensive for that window; one near the 25th is cheap. This is the diagnostic the whole page is built around, and it turns two abstract curves into a single readable verdict.

Formula

Realised volatility at a window length, the input to every point on the cone

RV_n = √( (252 / n) × Σ r_t² )

Each point on the cone is a percentile of the historical distribution of RV_n for a fixed window length n. This is the close-to-close realised volatility assuming zero mean return, annualised on 252 trading days. Compute it over every overlapping n-day window in your history, then take the median, 25th/75th and 5th/95th percentiles of the resulting set — those five numbers are one vertical slice of the cone.

RV_nRealised volatility measured over a window of n trading days, annualised as a decimal (0.14 = 14%).
nThe window length in trading days — 7, 14, 30, 60, 90 or 180 for the standard cone. This is the tenor axis.
r_tThe log return on day t, ln(P_t / P_{t−1}), where P_t is the closing level of the underlying.
Σ r_t²The sum of squared daily log returns across the n days in the window. The zero-mean assumption means we do not subtract a sample mean.
252Trading days per year, the annualisation factor for realised volatility on this site.

How the band width scales with tenor

spread(percentile bands) ∝ 1 / √n

The width of the cone at tenor n shrinks roughly in proportion to one over the square root of the window length, because a realised volatility is itself an average and the dispersion of an average falls with √n. This is the arithmetic reason the cone narrows, and it is why the 5th–95th gap at 7 days dwarfs the same gap at 180 days.

How to build and read a volatility cone

Gather several years of daily closes for the underlying — NIFTY for the index cone — and compute daily log returns.
For each window length you care about (7, 14, 30, 60, 90, 180 trading days), compute the annualised realised volatility over every overlapping window in the history.
For each window length, take the median, the 25th and 75th percentiles, and the 5th and 95th percentiles of that set of realised volatilities. These five numbers per tenor are the cone.
Plot the percentile bands against tenor. Confirm the bands narrow as tenor grows — if they do not, your window computation has a bug.
Take today's listed implied volatilities and place each at its matching tenor on the same axes.
Read the verdict: an implied point above the 75th percentile band is dear for that tenor, one below the 25th is cheap, and the shape across tenors tells you where the richness lives.
Refuse to treat the outer bands as limits. Note when today's implied is near an extreme, but remember the extreme is the edge of your sample, not a barrier.

Practical example

NIFTY worked example

Suppose the NIFTY cone, built from several years of history, has a 7-day slice with a 5th percentile near 7%, a median near 12%, and a 95th percentile near 28%, while the 180-day slice runs from about 10% at the 5th percentile to 13% median to 19% at the 95th. The 7-day band spans 21 volatility points; the 180-day band spans 9. That is the narrowing, quantified. Now overlay today: the front weekly implied is 15% and the six-month implied is 13%. Drop 15% onto the 7-day slice and it sits above the median but well inside the 75th percentile — mildly elevated, not extreme. Drop 13% onto the 180-day slice and it sits almost exactly on that tenor's median — utterly ordinary. The reading is that the market is paying a small premium for near-term uncertainty and nothing unusual for the long haul. A single IV number, or a single IV Rank, would have hidden that the richness is entirely at the front.

BANKNIFTY worked example

The BANKNIFTY cone teaches a lesson about mean level, not just shape. Because BANKNIFTY is a concentrated basket of lenders, it genuinely realises more volatility than NIFTY, so its entire cone sits higher: a BANKNIFTY 30-day realised volatility might have a median around 17% where NIFTY's sits near 12%. This matters because a trader who memorises NIFTY cone levels and applies them to BANKNIFTY will call BANKNIFTY implied volatility expensive when it is merely normal for BANKNIFTY. Each underlying needs its own cone. It also matters at the short end: BANKNIFTY's 7-day cone is wider than NIFTY's because a single bank-results day or a rate decision moves the narrow index harder, so the 95th percentile of BANKNIFTY's weekly realised volatility is a genuinely large number, and an implied that looks extreme against NIFTY's cone can be mid-range against BANKNIFTY's own.

Lot sizes used above (NIFTY 75, BANKNIFTY 30) are those in force at the time of writing; NSE revises them periodically. Figures exclude brokerage, STT, exchange charges, stamp duty and GST. Examples are teaching scenarios built on round numbers — they are not historical quotes, not backtests and not trade calls.

Risk note. The cone is frequently used to justify systematic option selling: implied is above the 75th percentile of realised, therefore sell. The dangerous step is hidden in the word therefore. The cone's percentiles are drawn from a sample that has not yet contained the next regime, so an implied volatility above the 95th percentile can still be too low if a shock larger than anything in the history is coming. Selling volatility because it is high in the sample is selling insurance because claims have been rare lately, and the position that harvests the calm is the same position that is largest when the regime breaks.

Advantages & limitations

What it is good for

It contextualises any volatility reading against that tenor's own history, so you can say a number is high for its window rather than just high in the abstract.
It shows all tenors at once. Overlaying the implied term structure reveals where in the curve the richness or cheapness lives, which a single scalar like IV Rank cannot.
It makes like-for-like comparison automatic. Because each implied point is judged against realised of the same window length, it prevents the classic error of comparing a short implied against a long realised.
It exposes the shape of the whole distribution, not just the middle. Seeing the 5th and 95th percentiles tells you how fat the tail of realised volatility is at each tenor — information a median hides.
It is model-free on the realised side. The cone's bands come from actual historical price movement, not from any option-pricing assumption, so they are a clean benchmark for the model-dependent implied numbers laid over them.

Where it breaks down

It is built from a finite sample, so its percentiles describe only what has happened in your history — the 5th percentile is the lowest observed, not a floor, and volatility can go beyond either edge.
The sample mixes regimes. A cone spanning a crash, a demonetisation and long calm blends distributions that may not describe the coming year, so a percentile is an average over incompatible worlds.
It uses overlapping windows, which makes the historical realised volatilities highly autocorrelated. That understates the true uncertainty in the percentile estimates and makes the bands look tighter and more precise than they are.
It compares realised against implied, which are not the same object — implied carries a volatility risk premium, so implied sitting above the median of realised is normal and expected, not automatically a signal.
It is silent on direction and on skew. The cone is an at-the-money, magnitude-only picture; it says nothing about which way the market will move or about the shape across strikes at any tenor.

Common mistakes

Confusing this volatility curve with the volatility smile. The smile is implied volatility across strikes at one expiry; the cone is the distribution of realised volatility across tenors. They share a word and nothing else.
Treating the outer percentile bands as hard floors and ceilings. Selling because implied is above the 95th percentile assumes the next move fits inside the sample, and the moves that hurt are precisely the ones that do not.
Comparing a 7-day implied against a 30-day realised because both are on the same screen. Different tenors have different natural ranges; the cone exists specifically to stop this comparison.
Applying NIFTY cone levels to BANKNIFTY or a single stock. Each underlying realises a different amount of volatility, so each needs its own cone; a shared cone mislabels normal as extreme.
Forgetting that overlapping windows make the bands falsely tight. The percentiles are estimated from autocorrelated data, so treating them as precise to the point is overconfidence built into the method.
Reading implied above the median of realised as a sell signal. Implied usually sits above realised because of the volatility risk premium; that gap is the normal state, not an edge on its own.

Professional usage

Volatility desks keep the cone on the screen as their primary value diagnostic, precisely because it refuses to collapse the term structure into a scalar. A relative-value trader looks at where each listed implied sits in its own tenor's cone and structures trades that are long the cheap tenor and short the dear one — a calendar or a variance spread — rather than taking an outright view. Because the cone judges every implied against realised of the matching window, it is the natural frame for deciding not whether to be long or short volatility outright, but where on the curve the mispricing is concentrated, which is the question a book of vega across expiries actually poses.

Risk managers use the cone to sanity-check both their own volatility assumptions and the market's. When an implied volatility is far outside its historical cone, that is a flag to investigate — either a genuine regime change is being priced, or a quote is stale, and the cone tells them which tenors to look at first. Systematic volatility strategies use the cone as a conditioning variable: a rule might scale exposure by where current implied sits in the cone, sizing smaller when implied is already at an extreme of its historical band. In every case the professional use hinges on the same feature — the cone benchmarks against the specific tenor's own past, so it is a like-for-like ruler in a domain where mismatched comparisons are the default error.

Key takeaways

The volatility curve that matters to a volatility trader is the volatility cone: the historical distribution of realised volatility at each window length, shown as percentile bands.
The cone narrows with tenor because a realised volatility is an average, and the dispersion of an average shrinks with the square root of the number of days it covers.
The power is in the overlay: dropping today's implied term structure onto the cone shows cheap-or-dear at every tenor simultaneously, which no single number like IV Rank can do.
A percentile band is not a limit. The 5th percentile is the lowest realised volatility in your sample, not a floor, and a new regime can push volatility straight through either edge.
This is not the volatility smile. The smile is across strikes; the cone is across tenors of the realised-volatility distribution.

The volatility cone is the picture that turns a volatility number into a verdict. On its own, 15% is just a number; on the cone, it is elevated at the front and ordinary at the back, and that shape is a trade. Build the cone from real history, overlay today's implied term structure, and read where the market is paying up and where it is relaxed — at every tenor at once. Then remember the one thing the picture cannot show you: the bands are the edge of your data, not the edge of what the market can do, and the regime that breaks them will not warn you first.

Frequently asked questions

What is a volatility cone?

A volatility cone is the historical distribution of realised volatility plotted for each window length — 7, 14, 30, 60, 90, 180 days — showing the median and percentile bands at each tenor. It is called a cone because the bands narrow as the window lengthens, forming a funnel shape.

Why does the volatility cone narrow as tenor increases?

Because a realised volatility is an average, and the dispersion of an average shrinks with the square root of the number of days it covers. A 7-day figure is dominated by a few sessions and can land anywhere, while a 180-day figure averages away any single day and stays near the long-run mean.

How do I use the cone to tell if options are cheap or dear?

Overlay today's implied volatilities on the cone at their matching tenors and read which percentile band each falls in. An implied point above the 75th percentile is expensive for that window, one below the 25th is cheap, and you see this at every tenor at once.

Is the volatility cone the same as the volatility smile?

No, and confusing them is common. The smile is implied volatility across strikes for one expiry; the cone is the distribution of realised volatility across tenors. The smile is about which strike, the cone about which window length — they share a word and nothing else.

What does the 5th percentile of the cone mean?

It means only that 5% of the historical realised volatilities at that window length were lower — it is the lowest normal in your sample, not a floor. Volatility can and does go below it the first time a genuinely calmer regime arrives; the band is the edge of your data, not of what is possible.

How is each point on the cone calculated?

For a given window length, compute the annualised realised volatility over every overlapping window in your history, then take the median, 25th/75th and 5th/95th percentiles of that set. Those five numbers form one vertical slice of the cone at that tenor.

Why is implied volatility usually above the median of the realised cone?

Because implied volatility carries a volatility risk premium — option sellers charge above the expected cost of the movement, like insurers. So implied sitting a little above the realised median is the normal state, not automatically a sell signal; the premium is expected, not an edge.

Can I compare a 7-day implied against a 30-day realised volatility?

No — that is exactly the error the cone is built to prevent. Different tenors have different natural ranges, so a 7-day and a 30-day number are not on the same scale. Always judge an implied against realised of the same window length.

Does the NIFTY cone work for BANKNIFTY?

No. BANKNIFTY is a concentrated basket of lenders that realises more volatility than NIFTY, so its whole cone sits higher. Applying NIFTY levels to BANKNIFTY labels normal BANKNIFTY volatility as expensive; each underlying needs its own cone.

What window lengths should a volatility cone use?

The standard set is 7, 14, 30, 60, 90 and 180 trading days, which spans from the near weeklies to a six-month view. The exact choice is a convention; the important thing is that each implied you overlay is compared against realised of the same window.

Why are overlapping windows a problem for the cone?

Overlapping windows share most of their days, so consecutive realised volatilities are highly autocorrelated. That autocorrelation understates the true uncertainty in the percentile estimates, making the bands look tighter and more precise than the data actually supports.

Does the cone predict future volatility?

Not directly. It describes the historical distribution of realised volatility at each tenor, which is a benchmark, not a forecast. Volatility clusters and mean-reverts, so the cone hints at plausible ranges, but any single future window can land outside the historical bands.

What is realised volatility in the cone context?

Realised volatility is the annualised standard deviation of the underlying's daily log returns over a window, computed from actual past prices. Each point on the cone is a percentile of the historical set of these realised volatilities for a fixed window length.

How many years of data do I need to build a useful cone?

Enough to contain a range of regimes — several years at least, so that both calm and stressed periods are represented. Too short a history gives a narrow cone that has simply never seen a shock; too long risks blending regimes that no longer describe the market.

Why is the cone almost never shown to retail traders?

Because it refuses to collapse volatility into a single number, and retail platforms prefer a scalar like IV or IV Rank. The cone shows a whole distribution at every tenor, which is more informative but less tidy, so it stays on professional screens.

What does it mean if today's implied sits at the top of the cone?

It means implied is high relative to that tenor's own history, so options are expensive for that window. It does not mean they are overpriced — a new, more volatile regime can make even a top-of-cone implied too low, because the band is only the edge of the past sample.

Should I sell options when implied is above the 95th percentile of the cone?

Be cautious — that is exactly the trade the cone can lure you into. The 95th percentile is drawn from a sample that has not yet contained the next shock, so an extreme reading can still be too low, and the short-volatility position is largest exactly when the regime breaks.

How does the cone relate to IV Rank and IV Percentile?

IV Rank and IV Percentile collapse the whole term structure to one point's position in its own history. The cone does the same comparison but keeps every tenor separate, so it shows where in the curve the richness lives rather than averaging it into a single figure.

Is the cone model-dependent?

The realised side is model-free — it comes from actual price movement, not from any option-pricing assumption. The implied volatilities you overlay are model-dependent, so the cone is a clean historical ruler against which the model-based numbers are measured.

Can the implied term structure sit entirely below the cone median?

Yes, in very calm periods implied volatility across all tenors can sit at the low end of the cone. That says options are cheap versus history at every tenor, but cheap options that expire worthless still lose their full premium, and calm is when short-volatility risk quietly accumulates.

Does the cone say anything about direction?

No. The cone is a magnitude-only, at-the-money picture built from squared returns, which discard sign. It tells you how large moves have been at each tenor, never which way the market went or will go.

Voice search & related questions

Natural-language questions people ask about volatility curve.

Why is the volatility cone shaped like a funnel?

Because short windows can be anything and long windows cannot. A 7-day realised volatility is decided by a handful of days, so it swings from very calm to very wild; a 180-day figure averages so many days that it barely moves off the long-run mean. Wide on the left, narrow on the right — that is the funnel.

How does the cone help me decide if options are worth buying?

Drop today's implied volatilities onto the cone at their own tenors and see where they land. If the tenor you want to buy is sitting near the bottom of its band, options are cheap for that window versus history — a starting point, not a green light, since a cheap option that expires worthless still loses everything.

Is this the same curve as the volatility smile?

No, and it is a very common mix-up. The smile plots implied volatility across strikes for a single expiry. The cone plots the distribution of realised volatility across window lengths. Different axis, different meaning — one is about strikes, the other about time horizons.

Can volatility fall below the bottom of the cone?

Yes. The bottom band is just the lowest realised volatility your history happens to contain, not a hard floor. The first time the market gets calmer than anything in your sample, volatility drops straight through it — the cone shows what has happened, not what can.

Why do the pros use the cone when retail gets a single IV number?

Because a single number hides where the action is. The cone keeps every tenor separate, so a desk can see the front week is expensive while the quarter is fair and trade that shape. A scalar like IV Rank averages all of that into one figure and throws the shape away.

Should I use one cone for NIFTY and BANKNIFTY?

No, build a separate cone for each. BANKNIFTY realises more volatility than NIFTY, so its whole cone sits higher up. Use NIFTY's cone on BANKNIFTY and you will keep calling normal BANKNIFTY volatility expensive, which is not what the number is telling you.

Sources & references

Last reviewed 10 July 2026. Educational content only — not investment advice.