The volatility cheat sheet

Everything on this site, compressed to one screen: the nine facts that do most of the work, the five regimes, the three shapes, and the things that are never true.

Quick answer: 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.

The whole of VolatilityGyan, compressed. Everything below links to the page that derives it, explains where it fails, and works an example.

The nine facts that do most of the work

Fact	Expression	Why it matters
Annualising volatility	σ_annual = σ_daily × √252	Volatility scales with the square root of time, so a month is not four times a week.
Expected move (1σ)	S × σ × √(days ÷ 365)	The range the option market is pricing about 68% of the time.
Straddle shortcut	expected move ≈ ATM straddle × 1.25	Works on a screen, with no calculator, to within a few percent.
Variance adds; volatility does not	σ²_total = σ²₁ + σ²₂	This is why forward volatility is higher than the spot volatility spanning it.
Vega scales with √T	vega ∝ √(time to expiry)	Long-dated options are the way to trade the LEVEL of implied volatility.
Gamma scales with 1/√T	gamma ∝ 1 ÷ √(time to expiry)	Short-dated options are the way to trade MOVEMENT.
Theta and gamma are the same trade	θ ≈ −½ Γ S² σ²	Every rupee of decay you collect is convexity you are short.
IV Rank	(IV − 52w low) ÷ (52w high − 52w low) × 100	Two days set the answer. One spike distorts it for a year.
IV Percentile	share of the last 252 days with IV below today	Every day counts once. Usually reads higher than rank.

Which volatility is this?

Say the word "volatility" to five people and get five quantities. The comparison matrix pulls them apart in full; the short version:

Historical — computed from past closes. Backward-looking. Depends entirely on the window you chose.
Realised — what the market actually did. Same idea, usually a finer estimator.
Implied — solved backwards out of an option's price. Forward-looking. It is a price, not a prediction.
Forward — what the term structure implies about a window that has not started.
India VIX — the whole NIFTY chain compressed to one 30-day number.

Regime at a glance

India VIX	Regime	Term structure	What it is telling you
< 11	Complacent	Steep contango	Options are cheap. That is a statement about price, not about safety.
11–15	Normal	Contango	Premium roughly fair. NIFTY lives here.
15–20	Elevated	Flattening	Expensive, and usually deservedly so.
20–28	Stressed	Backwardation	The market is frightened now and expects to stop being frightened.
> 28	Crisis	Steep backwardation	Liquidity has left the wings. Quoted prices for far strikes mean little.

The three shapes to recognise

Skew — implied volatility across strikes

One expiry, spot 24,000.

Downside protection costs more than upside participation, because index crashes are faster and more correlated than index rallies.

Term structure — implied volatility across expiries

The same underlying in two regimes.

The slope of this curve is the single most informative number a volatility trader looks at, and it is invisible if you only read the headline VIX.

IV crush — implied volatility through an event

A scheduled event, twenty sessions before to fourteen after.

The build-up is gradual and the collapse is a single print. Being right about direction does not save a long option from the crush.

The library

Section	What it covers	Pages
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…	8
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 …	11
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…	8
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 cheape…	8
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 3…	8
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 vol…	9
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 t…	9
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, s…	7

Things that are never true

No amount of volatility analysis produces a reliable income. High implied volatility does not mean options are overpriced — it usually means the market is about to move more. Low implied volatility does not mean the market is safe. Mean reversion does not stop a reading from doubling before it reverts. A positive volatility risk premium on average does not mean a positive one this month. And nothing on this page, or this site, is investment advice.

Frequently asked questions

What is the most useful volatility formula to memorise?

The expected move: S × σ × √(days ÷ 365). It converts an implied volatility into the price range the option market is pricing, which is the question most traders actually have.

What is the fastest way to estimate the expected move?

Read the at-the-money straddle price and multiply by 1.25. It is a rearrangement of the Brenner–Subrahmanyam approximation and it needs nothing you cannot see on the option chain.

Why does volatility scale with the square root of time?

Because variance scales linearly with time under independent returns, and volatility is the square root of variance. Doubling the horizon multiplies expected dispersion by 1.41, not by 2.

What is the difference between vega and gamma scaling?

Vega grows with the square root of time to expiry and gamma shrinks with it. So long-dated options are the instrument for trading the LEVEL of implied volatility, and short-dated options for trading realised MOVEMENT.

Are the volatility regime bands official?

No. Under 11 complacent, 11–15 normal, 15–20 elevated, 20–28 stressed and above 28 crisis are conventions calibrated to NIFTY and India VIX. A reading of 20 is elevated for an index and unremarkable for a mid-cap stock.

Is high implied volatility a reason to sell options?

No. High implied volatility usually means the market is about to move more, and it moves most in the periods when short-option positions are largest. High IV is not an edge; the gap between IV and subsequently realised volatility is, and it is small, positive on average and occasionally catastrophically negative.

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