# VolatilityGyan

> The reference library of volatility and options volatility for the Indian market (NIFTY, BANKNIFTY, India VIX). 68 concepts across 8 sections, each explained answer-first with a one-sentence definition, a beginner's explanation, a quantitatively accurate one, the formula with every symbol defined, an original computed diagram, worked NIFTY and BANKNIFTY examples, its advantages, its limitations, common mistakes, professional usage, and 20+ FAQs plus voice-search questions. All diagrams and all calculator output come from one Black-Scholes / statistics engine (volcharts.js), so a tool on this site cannot disagree with a page on this site.
>
> VolatilityGyan is an educational platform only and is NOT a SEBI-registered investment adviser. It publishes no trade calls, no performance claims, no win rates, no backtests and no "sell premium when IV is high" rules. Short-volatility positions carry theoretically unlimited loss; the site says so on every page that discusses them.
>
> KEY DISTINCTION most sources get wrong: "volatility" names at least nine different quantities. Historical and realised volatility are measured backward from prices. Implied volatility is INFERRED by inverting a pricing model against an option's quoted price — it is a price, not a forecast. Expected volatility is somebody's prediction. Forward volatility is derived from two implied volatilities. IV Rank and IV Percentile are context, not measurements, and they routinely disagree because rank is set by two extreme days while percentile counts every day. See https://volatilitygyan.bulansarkar.com/reference/volatility-comparison-matrix

## Core Volatility

Core volatility is the family of measures that quantify how much an asset's price moves, expressed as an annualised standard deviation of its returns. The family splits by what data it is computed from: historical and realised volatility look backward at prices that already happened, implied volatility is extracted forward from option prices, and expected and forward volatility are statements about periods that have not begun.

- [What is Volatility?](https://volatilitygyan.bulansarkar.com/learn/what-is-volatility): What is Volatility? At its core it is the annualised standard deviation of an asset's returns — a measure of how far price typically strays from its own path, which says how much a market moves and deliberately nothing about which direction it moves.
- [Historical Volatility](https://volatilitygyan.bulansarkar.com/learn/historical-volatility): Historical Volatility is the annualised standard deviation of an asset's past close-to-close log returns over a chosen window — a purely backward-looking measurement of how much price actually moved, in which the length of the window silently determines the answer you get.
- [Realized Volatility](https://volatilitygyan.bulansarkar.com/learn/realized-volatility): Realized Volatility is the volatility an asset actually delivered over a past period, measured from its realised price path — the quantity an option seller is short and a delta-hedged book is paid on — and it is estimator-dependent, so close-to-close and high-low methods can report different numbers from the very same days.
- [Implied Volatility](https://volatilitygyan.bulansarkar.com/learn/implied-volatility): Implied volatility is the volatility figure that, when fed into an option pricing model, makes the model output the option's current market price exactly — so it is a restatement of price, not a prediction of it.
- [Expected Volatility](https://volatilitygyan.bulansarkar.com/learn/expected-volatility): Expected volatility is a forecast of how much an asset will move over a future period, produced by a statistical model from the return history — which makes it somebody's prediction, not the market's price, and that distinction is the whole point.
- [Forward Volatility](https://volatilitygyan.bulansarkar.com/learn/forward-volatility): Forward volatility is the volatility the option market implies for a future window between two dates T1 and T2, extracted from the two spot implied volatilities because variance — not volatility — is additive in time.
- [Annualized Volatility](https://volatilitygyan.bulansarkar.com/learn/annualized-volatility): Annualized volatility is a short-period volatility rescaled to a one-year horizon by multiplying by the square root of the number of periods in a year, because variance grows linearly with time while volatility grows with its square root.
- [Intraday Volatility](https://volatilitygyan.bulansarkar.com/learn/intraday-volatility): Intraday volatility is the dispersion of an asset's returns measured within a single trading session, revealing a U-shaped pattern — violent at the open, quiet at midday, rising into the close — that a volatility computed from closing prices never sees.

## Implied Volatility

Implied volatility is the volatility figure that, when fed into an option pricing model, reproduces the option's current market price exactly. It is a re-expression of price, not a prediction, and because every strike and every expiry prints its own implied volatility, the collection of them forms the smile, the skew and the volatility surface.

- [How IV is Calculated](https://volatilitygyan.bulansarkar.com/learn/how-iv-is-calculated): How IV is calculated comes down to inversion: you fix every observable input to a pricing model and search numerically for the single volatility that makes the model reproduce the option's market price, because that volatility cannot be solved for in closed form.
- [Why IV Changes](https://volatilitygyan.bulansarkar.com/learn/why-iv-changes): Why IV changes is a question about order flow, not opinion: implied volatility rises and falls because the demand for options relative to their supply rises and falls, and it responds to who needs to buy or sell protection rather than to anyone revising a forecast of future movement.
- [IV Expansion](https://volatilitygyan.bulansarkar.com/learn/iv-expansion): IV expansion is a sustained, persistent rise in implied volatility in which the market re-rates the entire distribution of future outcomes upward and keeps it there — as opposed to a one-day spike that mean-reverts within weeks.
- [IV Crush](https://volatilitygyan.bulansarkar.com/learn/iv-crush): IV crush is the sudden, one-print collapse of implied volatility that occurs the instant a scheduled event resolves, as the option stops charging for uncertainty that no longer exists — which is why a long option bought into the event can lose money even when the underlying moves in the predicted direction.
- [Event Volatility](https://volatilitygyan.bulansarkar.com/learn/event-volatility): Event volatility is the portion of an option's implied volatility attributable to a single scheduled event — such as an RBI decision or the Union Budget — isolated by treating total variance as the sum of an ordinary diffusive component and a concentrated one-day event component.
- [Earnings Volatility](https://volatilitygyan.bulansarkar.com/learn/earnings-volatility): Earnings volatility is the pronounced rise and subsequent collapse of a single stock's implied volatility around its quarterly results release, driven by the concentrated, company-specific uncertainty that one report resolves in a single session.
- [Volatility Smile](https://volatilitygyan.bulansarkar.com/learn/volatility-smile): The volatility smile is the U-shaped curve you get when you plot each strike's implied volatility against its strike price, in which both out-of-the-money puts and out-of-the-money calls print a higher implied volatility than the at-the-money option — evidence that the market prices fat tails on both sides that Black–Scholes assumes away.
- [Volatility Skew](https://volatilitygyan.bulansarkar.com/learn/volatility-skew): The volatility skew is the downward-sloping implied-volatility curve that equity indices print, in which out-of-the-money puts are systematically dearer — in volatility terms — than out-of-the-money calls, so the market charges more to insure a fall than to bet on a rise.
- [Volatility Surface](https://volatilitygyan.bulansarkar.com/learn/volatility-surface): The volatility surface is the two-dimensional map of implied volatility plotted over both strike and time to expiry — the full object that any single quoted "IV" is merely one point on, and the thing Black–Scholes assumes is a flat horizontal plane despite it never having been one.
- [Sticky Strike](https://volatilitygyan.bulansarkar.com/learn/sticky-strike): Sticky strike is the volatility-surface regime in which each strike keeps its own implied volatility fixed as spot moves, so the curve stays glued to strikes and the at-the-money option — now a different point on that fixed downward-sloping curve — prints a lower implied volatility when spot rises.
- [Sticky Delta](https://volatilitygyan.bulansarkar.com/learn/sticky-delta): Sticky delta is the volatility-surface regime — also called sticky moneyness — in which the entire smile slides sideways along with spot, so the at-the-money implied volatility stays unchanged while every individual strike's implied volatility moves as its distance from spot changes.

## Volatility Metrics

Volatility metrics are the standardised measurements that place a raw volatility reading in context: IV Rank and IV Percentile locate today's implied volatility within its own history, HV versus IV compares the forward-looking figure with the backward-looking one, the volatility risk premium measures the gap between them, and expected move converts an implied volatility into a price range.

- [IV Rank](https://volatilitygyan.bulansarkar.com/learn/iv-rank): IV Rank locates today's implied volatility inside its own trailing 52-week range, scoring it from 0 at the year's low to 100 at the year's high — so it answers "is this reading high or low for this underlying?" using only the highest and lowest points of the year.
- [IV Percentile](https://volatilitygyan.bulansarkar.com/learn/iv-percentile): IV Percentile is the fraction of trading days in the past year on which implied volatility closed below today's level, expressed from 0 to 100 — so it answers "how many recent days were calmer than now?" using every observation, not just the year's high and low.
- [HV vs IV](https://volatilitygyan.bulansarkar.com/learn/hv-vs-iv): HV vs IV is the comparison between historical volatility — how much the underlying actually moved in the past — and implied volatility — how much option prices say it will move in the future, and the gap between them is the market's price for uncertainty rather than a mispricing to be harvested.
- [Volatility Risk Premium](https://volatilitygyan.bulansarkar.com/learn/volatility-risk-premium): The volatility risk premium is the systematic gap by which implied volatility exceeds the volatility that subsequently realises, typically one to four volatility points on liquid index options — a small, frequent, positive edge that exists precisely because it is occasionally overwhelmed by a large, rare, negative one.
- [Expected Move](https://volatilitygyan.bulansarkar.com/learn/expected-move): Expected move is the one-standard-deviation price range that an option's implied volatility is pricing over a chosen number of days, computed as spot × implied volatility × √(days ÷ 365), and it is a price the market is charging rather than a forecast it is making.
- [Standard Deviation](https://volatilitygyan.bulansarkar.com/learn/standard-deviation): Standard deviation is the typical distance of a set of numbers from their average, and in finance it is the exact quantity that volatility measures — specifically the standard deviation of an asset's returns, not of its prices.
- [Variance](https://volatilitygyan.bulansarkar.com/learn/variance): Variance is the square of volatility — the average of the squared deviations of returns from their mean — and it is the quantity that adds across independent time periods and independent positions, which volatility does not.
- [Realized Variance](https://volatilitygyan.bulansarkar.com/learn/realized-variance): Realized variance is the sum of the squared returns of an asset over a period, and because squaring makes the largest moves dominate the total, it is less an average of the period than a summary of its handful of worst days.

## Term Structure

The volatility term structure is the curve of implied volatility plotted against time to expiry. When it slopes upward, near-dated options are cheaper than long-dated ones and the market is in contango, its normal calm state. When it slopes downward it is in backwardation, which signals current stress the market expects to subside.

- [What is Term Structure?](https://volatilitygyan.bulansarkar.com/learn/what-is-term-structure): The volatility term structure is the curve you get when you plot at-the-money implied volatility against days to expiry — and its slope, not its level, tells you whether the market thinks the current volatility is here to stay or here to pass.
- [Contango](https://volatilitygyan.bulansarkar.com/learn/contango): Contango is the market's default state, in which the volatility term structure slopes upward — near-dated implied volatility trades below long-dated — so a position that is long volatility loses value as its contracts roll down the curve toward a lower spot, even if the underlying never moves at all.
- [Backwardation](https://volatilitygyan.bulansarkar.com/learn/backwardation): Backwardation is the inverted volatility term structure — near-dated implied volatility trading above long-dated — that appears in selloffs and crises when the market believes the current stress is real but temporary, so the near expiry carries the panic and the downward slope says it is expected to subside.
- [Calendar Structure](https://volatilitygyan.bulansarkar.com/learn/calendar-structure): Calendar structure is the implied-volatility relationship between two expiries that a calendar spread actually trades — sell a near-dated option, buy a far-dated one at the same strike — so the position is not a bet on the level of volatility but on the spread between two points on the term-structure curve and on the underlying staying near the strike.
- [Expiry Structure](https://volatilitygyan.bulansarkar.com/learn/expiry-structure): Expiry structure is the implied volatility read off each individual listed expiry of an index, and on NIFTY it forms a saw-tooth — every weekly and the monthly carrying its own event content — rather than the smooth upward curve that interpolation pretends exists between them.
- [Volatility Curve](https://volatilitygyan.bulansarkar.com/learn/volatility-curve): 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.
- [Event Premium](https://volatilitygyan.bulansarkar.com/learn/event-premium): Event premium is the extra variance that a single scheduled event — an RBI decision, the Union Budget, election counting — injects into an option's total implied variance, and separating it out lets you back out the one-day move the option market is actually pricing for that event day.
- [Rolling Volatility](https://volatilitygyan.bulansarkar.com/learn/rolling-volatility): Rolling volatility is the realised volatility of an underlying computed over a moving window of the most recent days, re-estimated each day as the window slides forward — so its level depends as much on the window length you chose as on what the market actually did.

## Volatility Indices

A volatility index is a model-free measure of the volatility that an index's option chain is currently pricing over a fixed forward window, usually 30 days, quoted as an annualised percentage. India VIX does this for NIFTY and CBOE's VIX does it for the S&P 500. Both measure expected magnitude of movement, not its direction.

- [India VIX](https://volatilitygyan.bulansarkar.com/learn/india-vix): India VIX is NSE's volatility index — a model-free measure of the volatility the near-dated NIFTY option chain is pricing over a fixed forward 30-day window, quoted as an annualised percentage and computed from a strip of option prices rather than by inverting Black–Scholes on any one option.
- [CBOE VIX](https://volatilitygyan.bulansarkar.com/learn/cboe-vix): CBOE VIX is the Chicago Board Options Exchange's volatility index — a model-free measure of the volatility the near-dated S&P 500 option chain is pricing over a constant 30-day window, and the original index on whose methodology India VIX is directly modelled.
- [VVIX](https://volatilitygyan.bulansarkar.com/learn/vvix): VVIX is the volatility of the volatility index — a model-free measure of how much the VIX itself is expected to move over the next 30 days, computed from the prices of options on the VIX exactly as the VIX is computed from options on the index.
- [VIX Futures](https://volatilitygyan.bulansarkar.com/learn/vix-futures): VIX futures are exchange-traded contracts on the future value of a volatility index, and because volatility mean-reverts they price toward its long-run average rather than toward today's spot — which is why the curve normally slopes upward in calm markets and inverts in stress.
- [VIX Options](https://volatilitygyan.bulansarkar.com/learn/vix-options): VIX options are options written on a volatility index that settle against the VIX future of matching expiry rather than against spot VIX, which — together with their upward call skew — makes them behave unlike any equity index option.
- [VIX Term Structure](https://volatilitygyan.bulansarkar.com/learn/vix-term-structure): VIX term structure is the curve of a volatility index across expiries — VIX9D, VIX, VIX3M and VIX6M — whose slope reveals whether the market believes today's level of fear is temporary or permanent, information the single headline number throws away.
- [Fear Index](https://volatilitygyan.bulansarkar.com/learn/fear-index): Fear Index is the popular nickname for a volatility index such as India VIX, and it is a misnomer — the index measures the price of optionality, meaning the expected magnitude of movement, not fear, not direction, and not whether the market is safe.
- [Market Sentiment](https://volatilitygyan.bulansarkar.com/learn/market-sentiment): Market sentiment, read through volatility, is what option prices reveal about crowd positioning — via the put-call ratio, the skew, and the term-structure slope — and every one of those readings is a description of where the market has already been, confirmed only after the regime has changed.

## Volatility Strategies

Volatility strategies are positions whose profit and loss depend primarily on the magnitude of an underlying's movement, or on changes in implied volatility, rather than on direction. Long volatility positions pay a known premium for an unbounded payoff; short volatility positions collect a known premium and accept an unbounded loss.

- [Long Volatility](https://volatilitygyan.bulansarkar.com/learn/long-volatility): Long volatility is any position built to gain when volatility increases — typically by owning options — so that its maximum loss is the known premium paid while its profit has no structural ceiling, at the cost of losing a little value to time decay almost every single day.
- [Short Volatility](https://volatilitygyan.bulansarkar.com/learn/short-volatility): Short volatility is any position built to gain when volatility falls — typically by selling options and collecting premium — so that its maximum profit is capped at the premium received while its loss has no structural floor, giving it the exact payoff profile of an insurer that wins small and often and loses large and rarely.
- [Long Vega](https://volatilitygyan.bulansarkar.com/learn/long-vega): Long vega is a position whose value rises when the LEVEL of implied volatility rises, independent of whether the underlying actually moves — an exposure that scales with the square root of time to expiry, so a bet on the volatility level is naturally a long-dated trade rather than a short-dated one.
- [Short Vega](https://volatilitygyan.bulansarkar.com/learn/short-vega): Short vega is a position whose value falls when implied volatility rises, giving it a steeply asymmetric exposure in which the entire upside lives in a narrow sliver of the volatility distribution and the entire downside lives in the unbounded tail — an asymmetry that grows worse through vomma, because a short-vega position is also short volatility convexity.
- [Gamma Scalping](https://volatilitygyan.bulansarkar.com/learn/gamma-scalping): Gamma scalping is the practice of holding a delta-hedged long-gamma position and re-hedging it back to flat as the underlying moves, which converts the difference between realised and implied volatility into cash — and pays only when realised movement exceeds the implied volatility that was paid for.
- [Delta Hedging](https://volatilitygyan.bulansarkar.com/learn/delta-hedging): Delta hedging is the practice of holding a position in the underlying that offsets the directional exposure of an option, so that small moves in the spot price no longer change the combined value — a neutrality that Black–Scholes assumes is continuous and free, and that every real desk pays for in spreads and re-hedges.
- [Volatility Arbitrage](https://volatilitygyan.bulansarkar.com/learn/volatility-arbitrage): Volatility arbitrage is buying an option believed cheap on volatility, or selling one believed expensive, and delta-hedging it so that direction is stripped out and only the difference between realised and implied volatility is left — a positive-expectancy bet with fat-tailed losses, not the riskless profit the word 'arbitrage' implies.
- [Dispersion Trading](https://volatilitygyan.bulansarkar.com/learn/dispersion-trading): Dispersion trading is selling volatility on an index and buying it on the index's constituents, a position that profits when the individual names move more than the index does and that is therefore fundamentally a short bet on correlation — which rises toward one in precisely the crash the trade cannot survive.
- [Calendar Trading Concepts](https://volatilitygyan.bulansarkar.com/learn/calendar-trading): Calendar trading is taking opposing option positions at the same strike but different expiries, so the trade is not a bet on the level of implied volatility but on the spread between two points on the term-structure curve and how that spread changes — a position that is net long vega yet short gamma near the strike, which surprises traders who expected a clean long-volatility bet.

## Volatility & Options

Implied volatility enters an option's price through the time-value component, so a change in implied volatility changes the premium of every option that still has time value, with the effect measured by vega. Theta and vega both scale with implied volatility, which is why a high-IV environment simultaneously offers more decay to a seller and more risk per point of movement.

- [IV and Option Premium](https://volatilitygyan.bulansarkar.com/learn/iv-and-option-premium): IV and option premium are linked through the option's time value: raising implied volatility widens the distribution of possible outcomes and therefore raises the premium, but the shape of that relationship — near-linear at the money, gentle in the money, convex out of the money — depends entirely on which strike you hold.
- [IV and Theta](https://volatilitygyan.bulansarkar.com/learn/iv-and-theta): IV and theta are tied together because a higher implied volatility means more time value to decay away and a wider expected daily move, so an option's theta — the rupees of premium it loses per calendar day — grows almost linearly with implied volatility, and that extra decay is the exact compensation for a proportionally larger gamma exposure.
- [IV and Vega](https://volatilitygyan.bulansarkar.com/learn/iv-and-vega): IV and vega are connected because vega is the rupees of premium an option gains or loses for a one-percentage-point change in implied volatility, and its size — a hump centred at the money, near zero in both wings, and growing with the square root of time to expiry — tells you exactly where on the option chain a position is exposed to the level of IV.
- [IV Before Expiry](https://volatilitygyan.bulansarkar.com/learn/iv-before-expiry): IV before expiry becomes an increasingly unstable quantity as the at-the-money premium collapses toward zero with the square root of remaining time, so that a single tick of price movement implies an enormous change in σ — which is why an implied volatility computed in the final sessions is a division by almost nothing and should never anchor an IV Rank, a screener alert, or a trade.
- [IV After Expiry](https://volatilitygyan.bulansarkar.com/learn/iv-after-expiry): IV after expiry does not exist, because implied volatility is a property of a specific option contract rather than a continuous quantity attached to the underlying: the expiring contract's IV simply ceases, and the next contract begins its own series.
- [IV Around Events](https://volatilitygyan.bulansarkar.com/learn/iv-around-events): IV around events is the predictable arc an option's implied volatility traces as a scheduled announcement approaches: it rises convexly while the uncertain day sits inside the option's remaining life, peaks on the eve, and collapses the instant the outcome is public — because the option correctly stops charging for a risk that no longer exists.
- [IV Around RBI Policy](https://volatilitygyan.bulansarkar.com/learn/iv-around-rbi-policy): IV around RBI policy is the modest, staged implied-volatility arc surrounding a Monetary Policy Committee decision — mild because the rate move is usually telegraphed, so what the option market is really pricing is the tone of the statement and any shift in the policy stance.
- [IV Around the Union Budget](https://volatilitygyan.bulansarkar.com/learn/iv-around-budget): IV around the Union Budget is the long, roughly month-long implied-volatility build-up and deep post-speech crush surrounding the government's annual fiscal statement, larger than an RBI meeting because a single speech can change capital-gains taxation, the securities transaction tax, sectoral allocations and the fiscal path with none of it known in advance.
- [IV Around Election Results](https://volatilitygyan.bulansarkar.com/learn/iv-around-election-results): IV around election results is the largest scheduled volatility event in the Indian market, building toward roughly 28.5% implied volatility on the eve of counting day and then crushing only part-way — settling above where it began — because the new political configuration itself introduces fresh policy uncertainty that the count resolves but does not remove.

## Market Regimes

A volatility regime is a persistent market state characterised by a typical level of volatility and a typical behaviour of it. Volatility clusters, so calm days follow calm days and violent days follow violent ones, and it mean-reverts, so no regime is permanent. Regimes are diagnostic descriptions of where the market has been, not signals about where it is going.

- [Low Volatility Markets](https://volatilitygyan.bulansarkar.com/learn/low-volatility-markets): Low volatility markets are regimes in which daily price moves stay small — realised volatility around 10% annualised — options are cheap, and short-volatility strategies look effortless, precisely the conditions under which leverage accumulates quietly across the whole market.
- [High Volatility Markets](https://volatilitygyan.bulansarkar.com/learn/high-volatility-markets): High volatility markets are turbulent regimes of several-percent sessions with no reliable direction — realised volatility around 26% annualised — in which options are expensive in absolute terms but not necessarily overpriced, because the movement that arrives is often large enough to justify the premium and sometimes larger.
- [Trending Markets](https://volatilitygyan.bulansarkar.com/learn/trending-markets): Trending markets are regimes of persistent direction with modest daily dispersion, where a run of small same-signed moves compounds into a large total return without ever producing a single dramatic day — because volatility measures the size of daily moves, not their direction.
- [Range-bound Markets](https://volatilitygyan.bulansarkar.com/learn/range-bound-markets): Range-bound markets are regimes of oscillation around a centre, where daily volatility can stay high while the multi-month return collapses toward zero — because the moves alternate in sign and cancel, the mirror image of a trend.
- [Crisis Volatility](https://volatilitygyan.bulansarkar.com/learn/crisis-volatility): Crisis volatility is the behaviour of a market in dislocation — the term structure inverts into backwardation, skew goes vertical, correlation across constituents goes to one, and margin rises mechanically — all driven by a sudden collapse in the willingness to sell insurance that rebuilds far more slowly than it evaporated.
- [Mean Reversion in Volatility](https://volatilitygyan.bulansarkar.com/learn/mean-reversion-in-volatility): Mean reversion in volatility is the persistent tendency of volatility to be pulled back toward a long-run level — around 14% annualised for NIFTY — with excursions above the mean that are violent and short-lived and excursions below it that are shallow and long-lasting, an asymmetry that gives the distribution of volatility its long right tail.
- [Volatility Clustering](https://volatilitygyan.bulansarkar.com/learn/volatility-clustering): Volatility clustering is the empirical regularity — noted by Mandelbrot in 1963 and formalised by Engle's ARCH in 1982 — that large price changes tend to be followed by large changes of either sign and small changes by small changes, so the magnitude of returns is persistent and forecastable while their direction is very nearly not.

## Calculators (all client-side; no data leaves the browser)

- [Implied Volatility Calculator](https://volatilitygyan.bulansarkar.com/tools/implied-volatility-calculator): The implied volatility calculator solves for the single volatility figure that makes the Black–Scholes price of an option equal the market price you type in. It uses bisection, so it converges for deep out-of-the-money options and near expiry, where Newton's method fails.
- [Expected Move Calculator](https://volatilitygyan.bulansarkar.com/tools/expected-move-calculator): The expected move calculator converts an implied volatility into a price range: the one-standard-deviation band the option market is pricing for the period you specify, which historically contains the outcome roughly 68% of the time.
- [Standard Deviation Calculator](https://volatilitygyan.bulansarkar.com/tools/standard-deviation-calculator): The standard deviation calculator takes a series of closing prices, converts them to daily log returns, computes the sample standard deviation of those returns, and annualises it by multiplying by the square root of 252 — which is exactly how historical volatility is defined.
- [IV Rank Calculator](https://volatilitygyan.bulansarkar.com/tools/iv-rank-calculator): IV Rank measures where today's implied volatility sits between its 52-week low and its 52-week high, on a scale of 0 to 100. It ignores every observation except those two, which is both its simplicity and its central flaw.
- [IV Percentile Calculator](https://volatilitygyan.bulansarkar.com/tools/iv-percentile-calculator): IV Percentile is the share of days in the lookback window whose implied volatility closed below today's. Unlike IV Rank it uses every observation, which makes it robust to the single spike that can distort a 52-week range for a year.
- [Volatility Converter](https://volatilitygyan.bulansarkar.com/tools/volatility-converter): The volatility converter rescales a volatility figure between horizons using the square-root-of-time rule: to move from one period to another, multiply by the square root of the ratio of their lengths. Doubling the horizon multiplies volatility by 1.41, not by 2.
- [Volatility Comparison Tool](https://volatilitygyan.bulansarkar.com/tools/volatility-comparison-tool): The volatility comparison tool places an implied volatility beside a realised volatility over a matched window and reports the gap between them — the volatility risk premium — in volatility points, as a ratio, and as the difference in the price range each implies.
- [Expected Range Calculator](https://volatilitygyan.bulansarkar.com/tools/expected-range-calculator): The expected range calculator converts an implied volatility into the full set of expiry bands — one, two and three standard deviations — and computes the model probability that the underlying finishes beyond any strike you nominate.
- [Volatility Regime Dashboard](https://volatilitygyan.bulansarkar.com/tools/volatility-regime-dashboard): The volatility regime dashboard combines a volatility index level, the slope of the implied-volatility term structure, and the gap between implied and realised volatility into a single description of the market's current volatility state — which is a description, not a signal.
- [Options Premium Sensitivity Tool](https://volatilitygyan.bulansarkar.com/tools/options-premium-sensitivity): The premium sensitivity tool prices an option under Black–Scholes and decomposes what moves it: delta for a move in the underlying, gamma for the change in delta, vega for a one-point change in implied volatility, and theta for one calendar day of decay.

## Reference sheets

- [Volatility Cheat Sheet](https://volatilitygyan.bulansarkar.com/reference/volatility-cheat-sheet): The volatility cheat sheet condenses the whole of VolatilityGyan into one page: the nine identities that do most of the practical work, a table separating the nine different quantities called volatility, the five regime bands, and the three chart shapes — skew, term structure and IV crush — that every options trader must be able to read on sight.
- [IV Cheat Sheet](https://volatilitygyan.bulansarkar.com/reference/iv-cheat-sheet): The IV cheat sheet states what implied volatility is — the volatility that makes a pricing model reproduce an option's market price — lists the seven events that move it and in which direction, shows why IV Rank and IV Percentile routinely disagree, and gives the five working rules that follow from implied volatility being a price rather than a forecast.
- [Volatility Formula Reference](https://volatilitygyan.bulansarkar.com/reference/volatility-formula-reference): The volatility formula reference lists every formula used anywhere on VolatilityGyan, pulled directly from the concept pages at build time so it cannot drift from them, together with a single definition for every symbol and an explicit statement of the conventions — 252 trading days for annualising volatility, 365 calendar days for time to expiry.
- [IV Decision Tree](https://volatilitygyan.bulansarkar.com/reference/iv-decision-tree): The IV decision tree asks five questions in order — which volatility is this, high compared with what, does a scheduled event sit inside the option's life, what does the term structure say, and what is realised volatility doing — and narrows what you are looking at without ever telling you what to do about it.
- [Volatility Comparison Matrix](https://volatilitygyan.bulansarkar.com/reference/volatility-comparison-matrix): The volatility comparison matrix separates the nine distinct quantities that all get called volatility, showing for each what it is computed from, whether it looks backward or forward, what it actually says, its units, and what dominates it — because most disagreements between two correct volatility numbers come from comparing two different quantities.
- [Volatility Regime Guide](https://volatilitygyan.bulansarkar.com/reference/volatility-regime-guide): The volatility regime guide describes five market states — complacent, normal, elevated, stressed and crisis — and what changes across them: the slope of the term structure, the steepness of the skew, the relationship between implied and realised volatility, what decays fastest, and where the risk is actually hiding.

## Index & glossary

- [All 68 concepts A–Z](https://volatilitygyan.bulansarkar.com/learn)
- [Glossary — 106 terms](https://volatilitygyan.bulansarkar.com/glossary)

## About & legal

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- [Methodology — the model, the conventions, and where each fails](https://volatilitygyan.bulansarkar.com/methodology)
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- Author: Bulan Sarkar · hello@bulansarkar.com