The variance risk premium in Nifty

Why variance and not volatility? A variance swap, the contract this idea comes from, pays the realised variance against a fixed price, so the premium is the fixed price less the variance that came. India has no listed variance swap. The theory still sits under India VIX, whose formula is a variance one, and under every short option position.

That framing matters in India. SEBI's August 2026 study of individual F&O traders in FY26 found that 87.7% of them lost money. The other side of those trades is not charity. A seller who borrows the average without the capital and the tail management behind it is not collecting the same premium as a firm that has both.

In variance:
VRP = IV^2-RV^2
In vol points:
gap = IV-RV
RV over the next 20 sessions
Variance swap, seller:
  N * (K^2-RV^2)
  K: the strike in vol
India VIX, variance formula:
s^2 = (2/T) * sum(dK/K^2
      * e^(rT) * Q(K))
   -(1/T)*(F/K0-1)^2

Vol points understate the asymmetry. A seller of variance is paid the squared gap, so a month of high realised volatility costs more than an equal month of low realised volatility earns. That curvature is why the next sections count in both units.

Read the chart by sliding the realised line twenty sessions back. The implied level on 27 Feb 2026 was priced against the realised line of early April, far higher at 26.17. The implied level on 30 Mar 2026, 29.22, was priced against the realised line of late April, far lower at 18.81. Implied peaked at 29.22 and realised peaked later at 29.46, because a trailing window forgets slowly. That lag is why I always say which window a realised figure is.

I keep both numbers on one page when I look at this: the implied level that was sold and the realised level that arrived, with the date of each. A premium quoted without its dates is a slogan. Two choices decide the answer. The first is the estimator: realised volatility from closes, from ranges or from NSE's weighted file gives different levels for the same days, so use one estimator on both sides of any comparison. The second is the implied side: the at the money figure and India VIX are not the same measure, because VIX weighs the whole strip of out of the money strikes. A premium measured against VIX is usually larger than one measured against the at the money option, for the same index and days.

Counting every start date, not just every twentieth, implied was above what followed on most of them. Overlap makes that count look more certain than it is, which is why I count windows that do not overlap. The whole file points the same way: the mean 30 day implied volatility is 12.42 and the mean twenty session realised volatility is 11.53, a difference of 0.89 vol points. India VIX, which includes the wings of the smile, averages higher still at 13.49.

The losses did not arrive alone. The windows of 22 Jan, 19 Feb and 20 Mar 2026 ran back to back, at 3.28, 8.85 and 2.76 points against the seller. Volatility clusters, as the forecasting lesson shows, so a seller who is wrong once is often wrong again before a calm month returns. Implied was also not a safe sign. The highest implied level of the file, 29.22 on 30 Mar 2026, paid the seller 10.41 points. The window of 20 Mar 2026, with implied at 22.23, also high, cost 2.76.

To see the size in rupees, price each gap at the vega of one lot of the at the money straddle on the 10 Jun 2026 chain, Rs 2,813 for each vol point. The average window is worth 2.5 thousand rupees, the best 12.9 thousand, and the worst lost 24.9 thousand. The vega of each past date was different, so read the bars as a size and not as a record. The point stands: a loss ten times the average is not an outlier, it is the other side of the premium.

Nothing here says the premium will be positive in the next window. Four windows in fourteen show it does not have to be, and the file is only about fifteen months long with one stress episode in it. A longer record would hold more episodes, and a gentler or harsher average. I read the file as a worked example of the shape, not an estimate of the size.

A seller does not have to carry the whole tail. A bought option further out caps the loss, as in the credit spread lesson, and the lesson on hedging an option selling book goes through the trade offs. Capping the tail gives up part of the premium. Whether that is worth it depends on the size of the account, and nothing in this file says which way it falls.

The margins lesson shows what is blocked. The bigger cost is the risk of the window that returns the year's gains in a month, which a retail account rarely has capital to sit through. A seller who sizes by the average has sized for a month that does not exist.