Wednesday 11 Jun 2025. The Nifty monthly with 15 days left priced the at the money option at 12.83 percent. The monthly with 50 days left priced it at 13.46 percent. So what did the market price for the 35 days between them? Not 13.46, the far vol. Not 13.14, the average. The answer was 13.72 percent. Two prices carry a third, and it is the one a calendar spread leans on. This module works the arithmetic, shows when it breaks, and says what the answer is and is not. Every figure comes from NSE end of day files, dated, so nothing here is live and nothing is a view on the next fortnight.
3By the end you can
- Compute the forward volatility between two expiries from their implied vols and days to expiry.
- Check that total variance rises with the expiry, and say what a failed check means.
- Explain why forward volatility is a price for the days between, and not a forecast or an average.
The idea, plainly
What is forward volatility?
An implied volatility is an average over the whole life of an expiry. The far expiry's average covers the near expiry's days as well as the days after them. To isolate the days after, take the variance of each expiry, which is the volatility squared times the time in years, and subtract.
Forward variance =
(w2 - w1) / (T2 - T1)
with w = vol^2 x T
Forward vol =
square root of the
forward variance
Two quotes in, one forward volatility out
The maths: why the subtraction works
Suppose the market prices variance as a rate that can change from day to day. The variance between today and the near expiry is the sum of the daily rates over those days, and the variance to the far expiry is the same sum over more days. An implied volatility quotes that total, so:
w1 = vol1^2 x T1
w2 = vol2^2 x T2
w2 = w1 + (variance between)
Rearranged, the variance between is w2 less w1. Divide by T2 less T1 to turn it back into a yearly rate, and take the root to get a volatility. The same day count has to be used for both expiries. This page uses calendar days over a year. NSE measures time to expiry in minutes for India VIX. A trading day count shifts both vols a little, and the forward with them, so pick one and keep it.
The step needs w2 to exceed w1. If it does not, the number under the root is negative and no volatility between the two dates can reproduce both prices.
Read one more paragraph, 103 words
The result is a yearly rate for the days between the two expiries, and nothing else. The term structure and event variance module reads the whole curve. This one reads two points on it. Like any implied vol, the forward vol is quoted per year even though it covers a few weeks. To turn it into a move over the span, multiply by the square root of the days over a year. For the pair below, 13.72 percent over 35 days is a one standard deviation move of 4.25 percent over that stretch, measured from wherever the index stands on the near expiry.
Why is it not an average?
Because the near days sit inside both numbers. Think of two stretches of a journey: if the first 15 days averaged 12.83 percent and all 50 averaged 13.46 percent, the last 35 days had to run faster than 13.46 percent to pull the whole up. The steps for 11 Jun 2025:
| Step | Near | Far |
|---|---|---|
| Implied vol, percent | 12.83 | 13.46 |
| Days left | 15 | 50 |
| Total variance | 0.000676 | 0.002482 |
On an upward curve the forward vol sits above the far vol
Read 2 more paragraphs, 81 words
The variance between is 0.002482 less 0.000676, which is 0.001806. Over the 35 days between, that is a yearly forward variance of 0.01884, and its square root is 13.72 percent. The average of the two vols, 13.14 percent, and the far vol, 13.46 percent, both understate it.
The chart steps through every expiry, weeklies included, so its dashed steps are shorter than the pair worked above, which runs from the 26 Jun monthly to the 31 Jul monthly.
Worked example: three shapes, three forwards
I picked three dates because they show the three cases: a rising curve, a nearly flat one and a falling one. Each pair is two monthlies, two to three weeks and about seven weeks out, so that both expiries are read at the future and the day count is the only moving part.
What does the forward do on a flat or a falling curve?
Run the same steps on two more dated pairs. On 10 Jun 2026 the 20 day monthly priced 15.03 percent and the 48 day monthly 14.77 percent. The far total variance was 2.3 times the near one. The forward vol for the 28 days between is 14.58 percent, below both vols and below their average of 14.90 percent.
| Step | 10 Jun 2026 | 7 Apr 2025 |
|---|---|---|
| Near total variance | 0.001238 | 0.002921 |
| Far total variance | 0.002868 | 0.005535 |
| Variance between | 0.001630 | 0.002613 |
| Forward variance | 0.02125 | 0.02725 |
The forward sits above the far vol on a rising curve and below it on a falling one
Read 2 more paragraphs, 94 words
On 7 Apr 2025, a stress session, the 17 day monthly priced 25.04 percent and the 52 day monthly 19.71 percent. The forward vol for the 35 days between is 16.51 percent, against an average of 22.38 percent.
The rule that falls out: when the curve rises, the forward is above the far vol, and when it falls, the forward is below it. On the stress evening the gap between the average and the forward was the widest, because the near days carried most of the nerves and the far vol averages them in.
What if total variance falls?
Then there is no forward volatility. Total variance has to rise with the expiry, and here it did, by 3.7, 2.3 and 1.9 times. If the later expiry held less total variance than the earlier, the number under the root would be negative. On a real chain that points to a stale quote, a calendar arbitrage, or two expiries read at different forwards, as a weekly and a monthly can be. Check the variance step before trusting the root.
How much does one quote move it?
The forward is built from a difference, so it is touchy. Lift the far vol on 11 Jun 2025 by one vol point and the forward vol rises to 15.11 percent, a move of 1.38 points. Lift the near vol by one point and it falls to 13.30 percent, a move of 0.42 points. The far quote enters with the larger weight, because its vol is multiplied by its 50 days and the near vol by its 15. So a small error in the far quote is magnified in the forward, and a pair with a thin or stale quote gives a forward I do not trust.
What if one of the expiries is a weekly?
The second dashed step on the 11 Jun 2025 chart joins the 8 day weekly at 12.02 percent and the 15 day monthly at 12.83 percent. The 7 days between carry a forward of 13.69 percent. The weekly is read at the parity forward and the monthly at the future, and the two forwards differ a little, so a mixed pair carries that difference into the answer. Where I can, I pair two monthlies, as the main example does.
Why do calendar spreads care?
A calendar spread sells the near option and buys the far one at one strike. Its price is the difference of two premiums, and that difference is the market's price for the days between. Take the 23,250 strike on 10 Jun 2026. The near call had a vega of Rs 1,407 a lot per vol point and the far call Rs 2,169. Selling one and buying the other leaves Rs 762 of net vega. A calendar spread is long volatility on balance, and the volatility it holds is the far one. How the near and far vols move against each other decides the rest, and the forward vol is where that shows up. The calendar spreads module draws the payoff.
Is forward volatility a forecast?
No. It is a price, and it carries the market's charge for bearing the risk. A price and a forecast can differ for good reasons: the price includes what a buyer pays to be covered against a jump, and whether that charge is larger than what follows, on average, is the variance risk premium. For the two windows the files let me look at, what followed was lower. The forward vol for the 28 days to 28 Jul 2026 was 14.58 percent, and Nifty's 20 day realised vol ending that day, close to close, was 12.07 percent. For the days to 31 Jul 2025 the forward was 13.72 percent and the realised vol over the 20 days ending then was 7.46 percent. Two windows prove nothing about whether the gap is typical. The variance risk premium module is where that question belongs. The day counts of the two numbers differ a little, which I ignore at this scale.
The term this section turns on: Forward volatility
How would I use it, and how not?
As a map. It shows between which dates the market puts its movement, which is useful beside a calendar of known events. It is a quick check on a calendar spread's price, and a check on whether two expiries are quoted consistently. It is not a forecast, it is not an average, and a pair of mixed weekly and monthly expiries can give a number that reflects the two forwards and not the days between.
The common mistake
The claim: The volatility between two expiries is just the average of their two vols.
It is not. On 11 Jun 2025 the average was 13.14 percent and the forward 13.72. On 10 Jun 2026 they were 14.90 and 14.58. On the stress evening of 7 Apr 2025 they were 22.38 and 16.51, a gap of several vol points. The average ignores that the near days are inside both numbers and ignores the time each one covers. I take the variances first and the root last, and I write the days next to the answer.
The average and the forward part ways, most on the stress evening
Key takeaways
- Forward variance is the later total variance less the earlier, over the days between.
- Forward volatility is not the average of the two implied vols.
- On an upward curve it sits above the far vol, on a falling one below.
- Total variance must rise with the expiry, or no forward vol exists.
- A calendar spread holds more far vega than near vega.
- Forward volatility prices the days between. It is not a forecast.
Two terms to hold on to from 16.10
Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study