Implied Volatility (IV) & The VIX Index

Four modules in this book deal with volatility, and readers routinely blur them into one. It is worth drawing the boundaries before any of the detail. This module is about the level. What implied volatility is, how it is extracted from a traded premium, how it differs from the volatility the underlying has actually delivered, and what India VIX measures when it prints 13.4 or 21.8. Everything here treats IV as a single number attached to a moment in time. That is a simplification, and the next three modules each remove one part of it.

The IV Rank and IV Percentile module takes the same number and asks a question this module cannot answer: is 18 per cent high? On its own, 18 means nothing. Against a stock that has spent the last year between 15 and 20, it is elevated. Against one that has ranged from 25 to 70, it is unusually quiet. That comparison against an instrument’s own history is a separate calculation with two competing versions, and it gets its own module because the two versions frequently disagree.

The volatility skew and term structure module removes the idea that there is one IV at all. Every strike on the chain carries its own implied volatility, and they are not equal — the downside puts almost always price richer than the equivalent upside calls. Implied volatility also differs across expiries, and the shape of that curve changes under stress. The IV crush module then narrows all the way down to one scheduled event and traces the premium through it: inflated the evening before results, collapsed the next morning. Four questions, four modules, one underlying quantity.

Implied volatility is quoted as an annualised percentage, and it describes a one-standard-deviation move. Both of those phrases need unpacking. Annualised means the figure has been scaled up to a full year even when the option expires in six sessions, purely so that every contract can be quoted on one comparable scale. One standard deviation means the middle band of outcomes — roughly two chances in three that the underlying finishes inside that band, and roughly one in three that it finishes outside it, split between the two sides. An IV of 14 per cent on NIFTY is therefore a statement about a range, expressed on an annual scale, that you have to rescale to the horizon you are actually trading.

That rescaling is the single most useful calculation in this module, because it converts an abstract percentage into index points you can compare against a strike. Volatility scales with the square root of time, not with time itself. Doubling the horizon does not double the expected move; it multiplies it by about 1.41. This is the same square-root relationship that makes far-dated options expensive in absolute terms but cheap per day, and it is why a weekly option and a monthly option quoted at the same IV are pricing very different rupee ranges.

Note what the number does not contain: direction. An implied volatility of 14 per cent says the market is pricing a band around 24,500, not that NIFTY is going up or down. A collapse of 900 points and a rally of 900 points are the same event to an IV reading. This is why implied volatility can rise on a day the index rises, and why a trader who is right about direction can still be wrong about the trade. Direction is priced by delta, covered in its own module. Volatility is priced by vega.

There is no formula that gives you implied volatility directly. Black-Scholes maps volatility to a price; it cannot be rearranged to map a price back to volatility. So the calculation is done by search. The software assumes a volatility, prices the option, compares that theoretical price with the premium the strike is actually trading at, adjusts the assumption, and repeats until the two match to within a tiny tolerance. Modern terminals do this for every strike on the chain in milliseconds, which is why the IV column refreshes as fast as the LTP column beside it.

The consequence is that implied volatility inherits every flaw in the price it was derived from. If the premium used is a stale print from twenty minutes ago, the IV is stale. If the strike is illiquid and the bid-ask spread is wide — say a bid of ₹1.20 against an ask of ₹2.05 — then the IV computed off the bid and the IV computed off the ask are meaningfully different numbers, and neither is more true than the other. This is the same family of problem covered in the module on deviations between theoretical and market prices, and it is the reason far out-of-the-money strikes on the chain often display implied volatilities that look absurd.

It also means implied volatility is not an independent opinion about the future. It is the option’s own price, translated. When a commentator says implied volatility has risen, they are saying option premiums have risen faster than the model can explain through spot, strike, time and rates. Nothing has been forecast. A crowd has paid up, and the IV column is where that shows. Treating it as a prediction that must come true is the most common misreading in this entire module.

Realised volatility — also called historical volatility — is a completely different animal that happens to be quoted in the same unit. It is arithmetic performed on the underlying’s own closing prices: take the daily returns over the last twenty sessions, compute their standard deviation, annualise it. No options are involved, no model is inverted, and no expectation enters. It tells you how much RELIANCE or NIFTY has actually been moving. Implied volatility tells you what the option market is charging for movement over a future window. One is a measurement, the other is a price.

The gap between them is where option traders live. If NIFTY has been realising 10 per cent while the chain implies 16 per cent, buyers of those options are paying for a wider range than the index has recently delivered. That does not make them wrong — the range may be about to widen, and it usually widens for a reason the whole market can see, such as a policy meeting or an election count. Equally, implied can sit below realised when a violent move is already underway and the market treats it as spent. There is no rule that one must be above the other, and this book will not quote you an average gap, because any such figure depends entirely on the instrument, the window and the period chosen.

What the comparison genuinely gives you is a sanity check on your own thesis. A trader buying a long straddle is stating that the underlying will move more than the chain is charging for. Putting implied and realised side by side makes that statement explicit and testable rather than a feeling. It is also the reason vega, the Greek that measures sensitivity to implied volatility, deserves its own module — a position can be flat on delta and still be fully exposed to the difference between what was priced and what arrives.

India VIX is NSE’s volatility index for NIFTY. Rather than reading the implied volatility off one strike, it pulls the bid and ask quotes of a wide strip of out-of-the-money NIFTY options across the near and next expiries and blends them into a single annualised figure for the coming 30 calendar days. Out-of-the-money contracts are used because they are pure time value, with no intrinsic value muddying the reading. The construction follows the methodology CBOE developed for its own volatility index, adapted to Indian contract conventions. NSE introduced it in 2008, and it is disseminated live through the trading session alongside NIFTY itself.

Reading a print is the same square-root-of-time exercise from earlier in this module. India VIX at 14 is an annualised 14 per cent. Over 30 days that is 14 × √(30 ÷ 365) ≈ 4.0 per cent, and on a NIFTY of 24,500 that is roughly 985 points either side. So a VIX of 14 is the market pricing a one-standard-deviation NIFTY range of about 23,515 to 25,485 over the coming month. Do that conversion once and the index stops being an abstract number on a ticker. It becomes a range you can hold against the strikes you were about to trade.

India VIX and NIFTY generally move in opposite directions, and the reason is structural rather than mystical. Indian equity portfolios are overwhelmingly long. When the index falls, those portfolios need protection, protection means buying puts, and buying puts bids up premiums — which is exactly what an implied volatility index measures. When the index grinds higher, hedging demand thins out and the reading drifts down. The index is popularly called a fear gauge, but it is more precisely a price of protection. That distinction matters, and it is developed properly in the volatility skew module.

It lifts both sides of the chain at once, and this is the part that surprises people. A call and a put are both claims on movement. If the market starts pricing a wider range, a wider range is worth more whichever way it points, so the 24,500 call and the 24,500 put both get more expensive on the same tick. Traders who assume rising VIX must mean puts up and calls down are importing a directional idea into a number that has none. The asymmetry does exist — puts typically gain more than calls do — but that is skew, and it sits in the next module but one.

The clean way to see the effect is to freeze everything except volatility. Take an at-the-money NIFTY 24,500 call with seven calendar days to expiry, hold the index perfectly still at 24,500, and move only the implied volatility. The premium moves anyway. That movement is not a directional profit or loss; it is a volatility profit or loss, and it belongs entirely to vega. The table below isolates it. It is illustrative — the figures come from a standard pricing model at three volatility levels, not from a live chain — but the mechanism is exact.

The mirror image applies to anyone short premium. A trader who has sold a strangle and watches India VIX jump from 12 to 17 will see the position marked against them before NIFTY has gone anywhere at all. The mark-to-market loss is real, the margin requirement typically rises with it, and both can force an exit that the eventual index move would never have justified. This is why volatility expansion is treated as a first-class risk in the margin and position-sizing modules rather than as a footnote to direction.

The first trap is treating IV as a forecast that owes you an outcome. It does not. If the chain prices a 980-point NIFTY range over a month and NIFTY moves 300 points, the market was not wrong in any meaningful sense — it charged for a distribution and one draw from that distribution came in narrow. Traders who conclude that high IV is therefore always overpriced are generalising from a sample of one. The honest framing is that a buyer at elevated IV needs movement to arrive in size, not merely in the right direction, and a seller at elevated IV is being paid to carry the risk that it does.

The second trap is comparing raw IV across different instruments. A midcap chemical stock implying 42 per cent and NIFTY implying 14 per cent tells you nothing about which is expensive. Individual stocks are structurally more volatile than a 50-stock index, so their normal IV lives at a higher level. The only way to say whether either is expensive is to compare each against its own history — which is precisely the job of IV Rank and IV Percentile in the next module, and the reason that module exists at all.

The third trap is the phrase "the IV" itself. Open any NIFTY chain and the IV column shows a different figure at every strike, sometimes several points apart between a deep put and an equally distant call. There is no single implied volatility for an underlying; there is a surface. Quoting one number is a convenience, and India VIX is a carefully constructed version of that convenience. Knowing that the surface exists, and that its shape carries information, is the bridge into the skew and term structure module.