--- title: "Forward volatility between two Nifty expiries" description: "How to read the volatility priced between two Nifty expiries from their implied vols and days, with the total variance check, on dated NSE chains." source_url: "https://www.rupeecase.com/learn/path-16/module-16-10-forward-volatility" --- [Path 16 10 of 16](/learn/path-16/)Forward volatility from two expiries[Next 16.11](/learn/path-16/module-16-11-india-vix-rebuilt) 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 1. Compute the forward volatility between two expiries from their implied vols and days to expiry. 2. Check that total variance rises with the expiry, and say what a failed check means. 3. Explain why forward volatility is a price for the days between, and not a forecast or an average. Watch in the terminal: why do the hero, key figure and XIRR differ? A short tutorial on sample data. ## 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 A sketch of the arithmetic, not a market number. Source: NSE end of day data, computed by RupeeCase. As of 11 Jun 2025. 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](/learn/path-16/module-16-9-term-structure-and-event-variance) 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 At the money implied volatility by expiry, Nifty, close of 11 Jun 2025. Dashed steps are the forward volatility between neighbouring expiries. At the money is the parity forward for weeklies and the future for monthlies. Source: NSE end of day data, computed by RupeeCase. As of 11 Jun 2025. 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 Near and far expiries are the monthlies with two to three and about seven weeks left. Implied volatility computed by RupeeCase from NSE settlement prices. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026. 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. Watch in the terminal: Sortino, Calmar, VaR, beta and more A short tutorial on sample data. ### 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](/learn/path-17/module-17-9-option-calendar-spreads) 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](/learn/path-16/module-16-13-variance-risk-premium) 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 From the module glossary; every term is in the Learn glossary too. Source: Module 16.10, Forward volatility from two expiries. ### 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 Average of the near and far at the money implied volatilities against the forward volatility between them, the same three pairs as above. Computed by RupeeCase from NSE settlement prices. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026. ## 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 From the module glossary. Source: Module 16.10, Forward volatility from two expiries. **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](https://www.sebi.gov.in/reports-and-statistics/research/aug-2026/study-profitability-of-individual-traders-in-the-equity-derivatives-segment-fy25-fy26-_103835.html) What does Forward volatility from two expiries cover?Two expiries give two vols. The volatility between them is not their average. It follows from total variance, and it is the number a calendar spread leans on. It works through The idea, plainly, Worked example: three shapes, three forwards, The common mistake, Key takeaways. It is module 16.10 of Path 16, Volatility, about 10 minutes of reading, free. TTry it ## Forward vol and event move, on the same example. The volatility between two expiries and the move an event prices in. Dated NSE end of day data, nothing live, no orders. **Forward vol and event move**, Nifty, 11 Jun 2025, 26 Jun 2025 expiry. [Open the forward vol and event move](/learn/tools/forward-vol?chain=NIFTY_2025-06-11_2025-06-26) AF&O on RupeeCase ## Hedging only, in development F&O at RupeeCase will do one job: protect a portfolio you already own, by a rule published before it runs. No speculation, no naked option selling, no leveraged bets. It is not available yet. [How hedging will work](/hedging)[Sign up for RupeeCase](https://invest.rupeecase.com/signup) [No hedgeFalls with the marketWith a putA floor, for a premiumIllustration with made up numbers, not a product and not a recommendation.](/hedging) QQuick check ## 10 questions, 7 to pass. Each attempt draws 10 of the 15 questions in this module's bank, and a retake draws a fresh set. A pass gives this module's Certificate of Completion. Your result stays on this device and counts towards the Path 16 certificate. 7 of 10 correct passes module 16.10 Every answer is explained when you check; a retake is always free. Source: RupeeCase Learn quiz rules (70% to pass). Passed ### Certificate ID Download PNGPrint or save as PDF[Check the ID](/learn/certificates/verify) Self paced and unproctored. A record of completing free education by RupeeCase; not a NISM certificate and not endorsed by NISM, NSE, BSE or SEBI. It qualifies no one to deal, advise or publish research. CCheck yourself ## Path 16 so far. Your quick check results on this device, stop by stop. Stop 10 of 16 on Path 16 Volatility: every live stop, this module ringed. Source: RupeeCase Learn, Path 16. 1. [16.1Volatility: historical against impliedNot yet](/learn/path-16/module-16-1-historical-vs-implied-volatility) 2. [16.2India VIX for beginners: what it measures and what it does notNot yet](/learn/path-16/module-16-2-india-vix-explained) 3. [16.3Solving for implied volatilityNot yet](/learn/path-16/module-16-3-solving-for-implied-volatility) 4. [16.4IV rank and IV percentile, done properlyNot yet](/learn/path-16/module-16-4-iv-rank-and-iv-percentile) 5. [16.5Measuring realised volatility: four estimatorsNot yet](/learn/path-16/module-16-5-realised-volatility-estimators) 6. [16.6Events and IV crush: results, Budget, RBI and electionsNot yet](/learn/path-16/module-16-6-iv-crush-around-events) 7. [16.7Smile and skew: a first look at Nifty and stocksNot yet](/learn/path-16/module-16-7-volatility-smile-and-skew) 8. [16.8Skew measures: risk reversal, butterfly and slopeNot yet](/learn/path-16/module-16-8-skew-measures) 9. [16.9Term structure and event varianceNot yet](/learn/path-16/module-16-9-term-structure-and-event-variance) 10. [16.10Forward volatility from two expiriesNot yet](/learn/path-16/module-16-10-forward-volatility#quiz) 11. [16.11India VIX rebuilt step by stepNot yet](/learn/path-16/module-16-11-india-vix-rebuilt) 12. [16.12Forecasting volatility: EWMA, GARCH and HARNot yet](/learn/path-16/module-16-12-forecasting-volatility) 13. [16.13The variance risk premium in NiftyNot yet](/learn/path-16/module-16-13-variance-risk-premium) 14. [16.14Variance swaps and replicationNot yet](/learn/path-16/module-16-14-variance-swaps) 15. [16.15Volatility surface models: SVI, SABR, local and stochastic volNot yet](/learn/path-16/module-16-15-volatility-surface-models) 16. [16.16Skew dynamics: sticky strike against sticky deltaNot yet](/learn/path-16/module-16-16-skew-dynamics) 17. [TPath test, 30 questionsNot yet](/learn/path-16/module-16-16-skew-dynamics#pathTestSection) Path 16 in reading time: 159 minutes over 16 modules Minutes of reading per module, this one in amber. Source: RupeeCase Learn, Path 16. Explore next ## Put the module to work. * [ToolOption payoff builderLegs on a dated Nifty chain, breakevens and charges](/learn/tools/payoff-builder) * [Free module 17.9Option calendar spreads9 min read](/learn/path-17/module-17-9-option-calendar-spreads) * [Free module 16.6Events and IV crush: results, Budget, RBI and elections9 min read](/learn/path-16/module-16-6-iv-crush-around-events) * [Free module 16.1Volatility: historical against implied7 min read](/learn/path-16/module-16-1-historical-vs-implied-volatility) * [Free module 16.8Skew measures: risk reversal, butterfly and slope10 min read](/learn/path-16/module-16-8-skew-measures) * [Free module 16.9Term structure and event variance10 min read](/learn/path-16/module-16-9-term-structure-and-event-variance) Community ## Join my WhatsApp group. Scan the code, fillFill one short form, and join my WhatsApp group. Slides, sources, factsheets and the rebalance logs live there, and members join a daily Google Meet with me. New to RupeeCase? [Getting started](/getting-started) [See the terminal](/terminal) [Sign up for RupeeCase](https://invest.rupeecase.com/signup) [Join the WhatsApp group](https://forms.gle/C6HMtM1Z2GfeocQV7) [One form, one group](https://forms.gle/C6HMtM1Z2GfeocQV7)Scan with your phone camera SSources ## Go to the source. 6 sources, NSE the most cited The publisher of each source listed below. Source: Module 16.10 source list. 1. [NSE, equity derivatives contract specifications: expiry cycles, lot sizes and cash settlement](https://www.nseindia.com/static/products-services/equity-derivatives-contract-specifications) NSE 2. [NSE, derivatives end of day reports: the F&O bhavcopy these figures are built from](https://www.nseindia.com/all-reports-derivatives) NSE 3. [NSE, India VIX: index page and methodology](https://www.nseindia.com/static/products-services/indices-indiavix-index) NSE 4. [NISM, Series VIII Equity Derivatives, test objectives (option pricing, volatility and option strategies)](https://www.nism.ac.in/revamp-nism/test-objectives-revised-nism-series-viii-equity-derivatives-certification-examination/) NISM 5. [SEBI investor education, Understanding derivatives](https://investor.sebi.gov.in/understanding_derivatives.html) SEBI 6. Gatheral, J. (2006), The Volatility Surface: A Practitioner's Guide, Wiley Book GTerms ## 5 terms from this module. Forward volatilityThe volatility implied by two expiries for the days between them, found from the difference in their total variances. Forward varianceThe later total variance less the earlier total variance, divided by the time between the two expiries. Total varianceImplied volatility squared times time in years. It rises with the expiry in any consistent set of prices. Calendar arbitrageA set of prices in which total variance falls with the expiry. No volatility between the two expiries can match it. Calendar spreadA near option sold and a far option bought at one strike. Its value rests on the gap between the two expiries' vols. [All 230 terms in the glossary](/learn/glossary) [Question people askWhat is forward volatility and how does it relate to calendar spreads?A short answer with a dated chart](/learn/questions/what-is-forward-volatility)[Related module17.9 Option calendar spreads9 min, Intermediate](/learn/path-17/module-17-9-option-calendar-spreads)[Related module16.6 Events and IV crush: results, Budget, RBI and elections9 min, Intermediate](/learn/path-16/module-16-6-iv-crush-around-events)[Pillar guideDerivatives and Quant115 modules across paths 12 to 19](/learn/derivatives) Education only, not investment advice, a research report or a recommendation to buy, sell or hold any security. RupeeCase (QC Alpha Technologies Pvt Ltd) is not registered with SEBI as an investment adviser or research analyst. Contracts and prices shown are for illustration only, come from NSE end of day files at least 30 days old, and are not recommendatory. Derivatives trading carries a high risk of loss.