🌊 Implied volatility and India VIX

🎯 In 30 seconds: Volatility measures how much a price swings, stated as a yearly percentage. Historical volatility is calculated from past prices. Implied volatility (IV) is worked backwards from today's option prices: it is the swing the market is paying for. India VIX, published by NSE, turns Nifty option prices into one number for the expected volatility over the next 30 calendar days. A rough rule: IV x square root of (days / 365) gives a one-standard-deviation move. With VIX at 14 and Nifty at 24,000, that is about 465 points over a week. IV usually rises before known events and falls after them, which can make an option buyer lose even when right about direction.

Volatility in plain numbers

Think of two auto-rickshaw rides to the same office. One driver takes the same road every day and arrives within two minutes of the usual time. The other takes shortcuts and arrives anywhere from 15 minutes early to 25 minutes late. The average time might be the same. The second ride is more volatile.

For prices, volatility is the standard deviation of returns, scaled to a year. "Nifty volatility is 14%" means that, if moves follow a normal pattern, the Nifty's return over a year would land within 14% either side of its average about two years in three. Volatility says nothing about direction. It measures the size of the swings.

To get a shorter period, multiply by the square root of the time as a fraction of a year. This chapter uses calendar days, matching how India VIX is described:

• 1 day: 14% x √(1/365) = about 0.73%
• 7 days: 14% x √(7/365) = about 1.94%
• 30 days: 14% x √(30/365) = about 4.01%

Some traders use 252 trading days instead of 365 calendar days. Both are approximations; the point is the method, not the second decimal.

Historical volatility: what already happened

Historical (or realised) volatility is calculated from past closing prices:

1. Take daily closes for, say, the last 30 trading days.
2. Compute each day's return: today's close divided by yesterday's, minus 1 (or the natural log of that ratio).
3. Take the standard deviation of those returns.
4. Multiply by √252 to annualise, since there are about 252 trading days a year.

A spreadsheet does this in four columns. NSE publishes daily historical index data you can download for the purpose. Historical volatility tells you how jumpy the market has been. It does not tell you what the market expects next.

Implied volatility: what the market is paying for

An option price depends on the underlying's price, the strike, time to expiry, interest rates and volatility. All but volatility can be looked up. So if you know the option's price, you can work backwards through a pricing model to find the volatility that makes the model match the price. That number is implied volatility.

NSE's option chain shows an IV for each strike. When options get more expensive with nothing else changing, IV has risen: buyers are paying more for protection or for a bet on a big move. When options get cheaper, IV has fallen.

IV is a price, not a prediction you can trust blindly. It reflects supply and demand for options as well as genuine expectations. Option sellers argue that, on average, implied volatility sits above the volatility that actually follows, and that this gap is what they earn. It is not guaranteed in any given week, and this chapter does not cite a study measuring it for India.

Turning IV into an expected move

A one-standard-deviation expected move is: price x IV x √(days / 365).

With the Nifty at 24,000 and IV of 14%:

• Over 1 day: 24,000 x 0.14 x √(1/365) = about 176 points.
• Over 7 days: about 465 points.
• Over 30 days: about 963 points.

Under the model, the Nifty would end inside those ranges about two times in three and outside them about one time in three. Real markets produce big moves more often than a normal curve suggests, so treat the outer third as fatter than it looks.

A faster method from the chain: add the prices of the ATM call and ATM put for an expiry. That sum, the ATM straddle, is roughly the move the market is pricing by expiry. If the 24,000 call is 200 and the put is 172 with a week to go, the straddle is 372 points, about 1.55% of the Nifty. Straddles and strangles builds on this.

India VIX: the market's fear gauge

NSE describes India VIX as "a volatility index based on the NIFTY Index Option prices". From the best bid and ask prices of Nifty options, it calculates a volatility figure in percent that indicates the expected market volatility over the next 30 calendar days. NSE says it uses the computation method of the US Cboe VIX, adapted to the Nifty options order book. NSE's methodology document and white paper describe the steps.

How to read it:

• Higher VIX, bigger expected swings. A VIX of 20 implies expected moves about two-thirds larger than a VIX of 12.
• It is about size, not direction. VIX tends to rise when markets fall, because demand for put protection pushes option prices up. It can also rise before a big scheduled event in a calm market.
• Use it as an expected-move input. VIX of 14 means roughly the same thing as a 14% IV in the method above: about 4% either way over 30 days.

A dated example from history. On 24 March 2020, during the COVID-19 sell-off, Business Standard reported that India VIX touched 86.63 during the day, above its previous closing peak of 85.13 from November 2008, and closed at 81.9. A VIX of about 82 implies a 30-day one-standard-deviation move of around 23%, which shows how extreme that period was.

You can see the current value and download history from NSE's India VIX page. This course does not quote today's level because it changes every few seconds during market hours.

IV vs historical volatility: is the market paying up?

Comparing IV with recent historical volatility tells you whether options look rich or cheap relative to the recent past:

• IV well above historical volatility: the market expects more movement than it has seen lately, often because of a coming event, or is nervous. Option buyers pay a lot for time value.
• IV close to or below historical volatility: options are priced for a quieter future than the recent past. Buyers pay less, sellers collect less.

Neither is a signal on its own. IV can stay high for weeks in a falling market and be right to do so.

IV rank and IV percentile

Two common ways to put today's IV in context:

• IV rank = (today's IV - lowest IV in the past year) / (highest - lowest) x 100. If a stock's IV ranged from 20% to 60% over the year and is 30% today, IV rank is 25.
• IV percentile = share of days in the past year when IV was lower than today. An IV percentile of 80 means IV was lower on 80% of days.

Some broker platforms show these. They are descriptions, not forecasts. A high IV rank before results is normal and does not by itself mean options are "too expensive".

Event volatility in India

Some days are known in advance to carry larger than usual moves, and option prices reflect that before the day:

• Company results: a stock's IV for the expiry covering its results date usually rises in the days before the announcement.
• RBI monetary policy: the policy dates are published by the RBI in advance. Rate-sensitive stocks and Nifty Bank options can carry extra IV into the announcement.
• Union Budget: presented on 1 February in recent years. Index IV often rises into Budget day.
• Election results: counting days for general and major state elections are announced in advance, and index IV tends to rise ahead of them.

After the event, the uncertainty is resolved, and IV usually falls quickly. Trading news and events covers the events themselves.

IV crush: a worked results example

Hypothetical Sharma Foods Ltd at ₹1,000, results tomorrow. Hypothetical lot of 1,500 shares. The 1,000 call with 10 days to expiry trades at ₹30.51 with IV of 45%; the 1,000 put at ₹28.87. The straddle is ₹59.38, so the market is pricing roughly a 6% move by expiry.

You buy one lot of calls for ₹30.51 x 1,500 = ₹45,765. Results come out. Next morning IV has dropped to 25%, a typical post-event fall. Here is the call's value at four share prices, with 9 days left:

With the share flat, the call lost almost half its value overnight, purely from the drop in IV. A 3% rise, a decent result, produced only a modest gain. The buyer needed a move bigger than the market had priced to do well. This is why buying options just before results is often a losing habit: you pay for the expected move upfront, and the expected move is usually about right.

Volatility skew

IV is not the same at every strike. For Nifty options, lower strikes usually show higher IV than higher strikes. You can see this on NSE's option chain: OTM puts carry more IV than OTM calls the same distance away. This is called skew. It exists because investors pay up for crash protection, and because markets tend to fall faster than they rise. Skew means OTM puts are relatively expensive and OTM calls relatively cheap, compared with a model that uses one IV for all strikes.

Try it

Open NSE's India VIX page and note today's value. Then open the Nifty option chain for the nearest weekly expiry and add the ATM call and put prices to get the straddle. Use VIX to compute the expected move to that expiry with the formula above, and compare it with the straddle. Download a month of Nifty closing prices from NSE's historical data and compute historical volatility in a spreadsheet. Is the market's IV above or below what actually happened last month? Finally, find a company with results due in the next two weeks and record its ATM option IV on the day before and the day after results.

Sources

• NSE: India VIX
• NSE: White paper on India VIX (PDF)
• NSE: India VIX computation methodology (PDF)
• Business Standard: Covid-19 impact: India VIX touches 86.63 level, breaches 2008 peaks (24 March 2020)
• NSE: Option chain
• NSE: Nifty 50 futures and options, contract specifications