Volatility simply means how much a price swings. There are two very different ways to measure it, and options traders use both:
- Historical volatility (HV), also called realised or statistical volatility, measures how much the price actually moved over a past period.
- Implied volatility (IV) measures how much movement the option prices assume from now until expiry. It is worked out from option prices, as explained in the implied volatility guide.
HV is a fact about the past. IV is the market's price for the future. The gap between them tells you whether options are expensive or cheap compared with how the underlying has been behaving.
How historical volatility is calculated
HV is the standard deviation of daily returns, scaled up to a year:
- Take the daily closing prices for the period, often the last 20 or 30 trading days.
- Work out each day's return: today's close divided by yesterday's, minus 1. (Many traders use the natural log of that ratio, which gives almost the same numbers for small moves.)
- Find the standard deviation of those returns: how spread out they are around their average.
- Multiply by the square root of the number of trading days in a year, about 250, which is close to 16.
HV (yearly %) = standard deviation of daily returns × √250 (≈ 16)
Example: if NIFTY's daily returns over the last 20 sessions have a standard deviation of 0.75%, HV is about 0.75 × 15.8 ≈ 11.9%. If NIFTY's at-the-money IV is 13% at the same time, options are priced for a little more movement than NIFTY has recently delivered.
A note on conventions: HV is usually scaled by trading days (√250), while IV quotes often assume calendar days (√365). The yearly figures line up because both describe a year; the daily conversions differ slightly. Use one convention consistently when you compare.
Why IV is usually a little above HV
Over long periods, index implied volatility has tended to sit above the volatility that followed. The reason is simple: option sellers take on the risk of rare but large moves, and they ask to be paid for it. This extra is called the volatility risk premium. It is the reason option selling earns money on many quiet days, and also why it can lose heavily on the few days when a big move arrives. The premium is not constant: after a crash, realised volatility can run well above the IV that was priced beforehand.
A live example: priced movement against real movement
India VIX is the market's implied volatility for NIFTY. Here it is with its rank against the past year:
To compare it with real movement, look back at NIFTY's recent daily changes. If NIFTY has been moving around 0.5% a day while VIX implies about 0.75%, options are priced for more than recent movement. The expected move to expiry shows the same comparison in points:
When the expiry arrives, check whether NIFTY finished inside the range. Over many expiries, that tells you whether IV has been over- or under-pricing actual movement.
Reading the gap between IV and HV
| Situation | What it usually means | Things to check |
|---|---|---|
| IV well above HV | Options are pricing more movement than recently seen. Often before results or events. | Is there a known event? Is the market nervous for a reason? |
| IV close to HV | Options priced roughly in line with recent movement. | Upcoming calendar; trend in both. |
| IV below HV | Options are pricing less movement than recently delivered. Often right after a sharp move, or when sellers are crowded. | Has the big move ended, or is it continuing? |
None of these is a trade signal on its own. HV describes a period that has already ended, and a calm stock can become volatile overnight.
Choosing the look-back period
HV changes a lot with the window you choose. A 10-day HV reacts fast to a single big day. A 60-day HV is smoother but slow to notice change. Traders often compare IV for an option with HV over a similar span: for a weekly option, the last 5 to 10 sessions; for a monthly, 20 to 30. Looking at several windows side by side shows whether movement is speeding up or slowing down.
HV also ignores intraday swings when it uses closing prices only. A day that ranges 2% but closes flat counts as zero. Measures that use highs and lows, such as the average true range, capture that.
A worked example with a stock
Take a large private bank whose shares trade at ₹1,800. Over the last 20 sessions, its daily returns have a standard deviation of 1.1%, so its 20-day HV is about 1.1 × 15.8 ≈ 17%. Its monthly at-the-money options trade at an IV of 24%, and its quarterly results are due in a week.
- At 17% HV, the stock has been moving about ₹20 a day (1.1% of ₹1,800).
- At 24% IV, using the same trading-day yardstick, the options are pricing about 24 ÷ 15.8 ≈ 1.5% a session on average, about ₹27, and that average has to cover the results day too.
- The 7-point gap between IV and HV is mostly the results premium. After results, IV would usually settle closer to the stock's normal level, unless the news changes how the stock trades.
So "IV is high" here does not mean the options are mispriced. It means a known event is being paid for. The useful question is whether the results move will be bigger or smaller than that premium, which past results can hint at but never settle. The IV crush guide follows a similar example through results day.
How traders use HV and IV together
- Option sellers look for IV well above both recent HV and the symbol's normal IV, with a clear reason why IV should fall (an event passing). They still need a plan for a big move.
- Option buyers look for IV at or below recent HV, when options look cheap against real movement, and ideally a reason for movement to pick up.
- Everyone uses HV to sense how far a stock usually moves, which helps place stop-losses and choose strikes realistically.
The IV leaders page lists stocks whose options carry the highest IV right now, a starting point for this comparison.
Common mistakes
- Expecting HV to predict the future. It summarises the past. Results, news and global shocks reset it quickly.
- Comparing IV with an HV from a very different window. A weekly option's IV against a one-year HV mixes two different questions.
- Ignoring gaps. Overnight gaps count in close-to-close HV, but they cannot be traded during the session.
- Assuming the volatility risk premium is free money. It exists because the risk is real.