Friday 8 May 2026. The Nifty fell 0.62% that day, a quiet one. Yet the twenty session realised volatility dropped from 18.48 to 13.45 percent a year in one session, a fall of 5.03 points, and nothing that day caused it. A big day from 8 Apr 2026 had simply left the window. That is one reason I never quote a realised volatility without three things next to it: the window, the estimator and the annualising factor. This lesson sets out the four estimators I use on an index, where each one fails, and what changes when you change a choice. Every figure comes from NSE end of day files, so nothing here is live and nothing is a view on where volatility goes next.
3By the end you can
- Name the four estimators and the part of the day each one reads.
- Explain why a window figure can fall on a quiet day.
- State the window, estimator and annualising factor behind any realised volatility.
The idea, plainly
Realised volatility measures how much the index actually moved. Take the daily returns of a window, find how spread out they are, and scale the result to a year. The first volatility lesson separated three names: historical looks back over a window that ends today, implied reads an option price, and realised is what happened after the option was priced. This lesson is about how the backward looking figure is built.
Each estimator uses more of the day than the one before
- Close to close. The sample standard deviation of the log return from each close to the next, times the square root of the days in a year. It needs closes only. It counts gaps, because the close to the next close includes the overnight jump. It is noisy, because it uses one number a day.
- Parkinson (1980). Uses the high and the low of each day. A day's range says more about how much the price moved than its close does. The paper shows it extracts the same information from roughly a fifth of the days, under its assumptions: no drift, no gaps, trading all day.
- Garman Klass (1980). Adds the open and the close to the range. Under the same assumptions it is more efficient again. It shares the weakness: it sees only what happened inside the session.
- Yang Zhang (2000). Adds the overnight gap and the open to close move to a range term, in a mix that stays sound when the price drifts and when it jumps at the open.
- The window. Ten sessions react fast and bounce about. A hundred and twenty sessions are steady and late. Twenty sessions, about a month, is the common middle.
- The mean. Close to close can subtract the average return or assume it is zero. The zero mean version is closer to what an exchange risk file does, and it reads a little differently on a trending window.
- The annualising factor. The square root of 252 trading days is standard for an index. NSE's own volatility file for F&O underlyings uses a weighted average of past squared returns, which favours recent days, and scales to a year with the square root of 365. Same returns, a figure about a fifth higher.
3 terms this section turns on
Read 6 more paragraphs, 272 words
Historical, implied and realised: what is the difference? Historical and realised use the same arithmetic on different dates. Historical ends on the day you look. Realised starts on the day an option was priced and runs forward. Implied is not measured from returns at all. The question page gives the short answer.
Four estimators cover most needs. Each one uses more of the day than the one before.
That weakness matters in India. NSE's index trades from 09:15 to 15:30. Between the close and the next open the index can jump on news from elsewhere, and the high and low of the session know nothing about it. Range estimators that ignore the gap tend to read low in a gappy period. Close to close reads the gap in, and Yang Zhang is built to.
Three more choices change any of them.
None of these is wrong. They answer slightly different questions, and the answer you need depends on what you will compare the number with. Compare an implied volatility for the next thirty calendar days with a twenty session figure and the same factor, and say so.
Use follows purpose. To set an option's implied volatility against what the index has just done, I match the window to the option's life: a one month option, a twenty session window. To look for a change of regime, I read a short and a long window together. When the ten session figure sits well above the hundred and twenty session one, volatility has been rising. When it sits well below, it has been fading. That describes the recent past. It is not a forecast.
Worked example: the 8 Apr 2026 day, twice
On 8 Apr 2026 the Nifty rose 3.78%, from 23,123.65 to 23,997.35. The twenty session realised volatility moved from 26.04 to 29.46 on that day alone. Twenty sessions later, on 8 May 2026, the same day dropped out of the window and the estimate fell from 18.48 to 13.45, on a day the index fell 0.62%.
The same day moves the estimate twice, once going in and once leaving
The shorter the window, the wider the swings in realised volatility
Same returns, two factors: 7.27 against 8.75
Day Open High Low Close 1 100.0 101.5 99.2 100.8 2 100.5 102.2 100.1 101.9 3 102.6 103.4 101.0 101.4 4 101.2 102.0 99.9 100.3 5 100.9 102.5 100.4 102.1 6 102.0 102.9 100.8 101.3
Four estimators, four answers from the same six invented days
Read 7 more paragraphs, 374 words
One day carried the estimate for twenty sessions, then vanished. The index did not become calmer on 8 May. The window forgot a day. A slower, weighted estimator softens that cliff. A short window makes it worse. A long window mutes it, but reacts late to a real change.
Now the window itself, on one date. The cone below shows, for each window length, the range of close to close readings across the file, from 1 Jul 2025 to 15 Sep 2026, and where each stood at the end.
Same index, same date, five different realised numbers, one for each window. Which is right? All of them. The twenty session reading was 7.27. Over the whole file the twenty session figure averaged 11.53 percent, against 12.42 for the 30 day implied volatility, so implied sat above realised on average.
A window figure also carries sampling error. Twenty returns give a rough estimate, with an error of roughly one part in six if the returns were independent and normal. On the 7.27 reading that is about 1.2 points either way. A figure from a short window deserves a wide band around it.
The factor is a choice that hides in plain sight. The returns behind the 7.27 reading have a daily standard deviation of about 0.46 percent. Annualise them the exchange way and they read 8.75.
Last, the four estimators on one set of bars. The data files behind these lessons keep closes only, so I use six invented days of open, high, low and close. The numbers are made up for the exercise and are not market data. A real run would take the daily open, high, low and close from NSE's index end of day files.
The four answers sit within a couple of points of each other. Garman Klass reads above Parkinson because on five of the six days the close sat near the open compared with the day's range, and its formula then leans harder on the range. Yang Zhang adds the gaps at the open of the third and fifth days. With six invented days the order says nothing about the market. Real series of hundreds of days narrow that spread and show which estimator suits your use.
The common mistake
The claim: Realised volatility is the true volatility, and implied volatility is only a guess about it.
There is no one realised figure to be true to. On 15 Sep 2026 the same twenty sessions of Nifty returns read 7.27 with one annualising factor and 8.75 with another. The next day the window forgets a day and the figure moves with no new news. Four estimators on the same six invented days gave four answers. Realised volatility is a measurement, and a measurement comes with a method. Say the window, the estimator and the factor, and compare like with like.
Key takeaways
- Realised volatility is a measurement, and it comes with a method.
- A big day moves a window figure twice: entering and leaving.
- Range estimators miss the overnight gap. Close to close and Yang Zhang see it.
- Window length trades speed against steadiness.
- Calendar days in the factor read about a fifth higher than trading days.
- Compare like with like: same window, estimator and factor.
Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study