---
title: "How to solve for implied volatility: Newton and bisection"
description: "How implied volatility is solved from an option price with Black 76, by Newton and bisection, with a worked Nifty call, a full chain and cases with no answer."
source_url: "https://www.rupeecase.com/learn/path-16/module-16-3-solving-for-implied-volatility"
---

[Path 16 3 of 16](/learn/path-16/)Solving for implied volatility[Next 16.4](/learn/path-16/module-16-4-iv-rank-and-iv-percentile)

Wednesday 10 Jun 2026, after the close. The Nifty 23,250 call of the 30 Jun expiry settled at Rs 321.65. The end of day file holds that price, the volume and the open interest. It holds no volatility column. The IV you see on a chain is solved from the price afterwards, and it is a calculation you can do by hand. Here it gave 15.09% for the call. The put at the same strike gave 14.65%. Same strike, same evening, two answers 0.44 points apart. I trust a number more once I know how it was made, so this lesson makes one. Every figure comes from NSE end of day files, so nothing here is live and nothing is a view on where the index goes next.

3By the end you can

1. Solve for implied volatility by hand with a guess, a price and a step.
2. Say which inputs change a solved implied volatility.
3. Spot a price that has no volatility behind it.

Watch in the terminal: which of the two alphas is this? A short tutorial on sample data.

## The idea, plainly

An option model is a machine with five inputs and one output. Put in the forward, the strike, the time to expiry, the interest rate and a volatility, and it returns a price. Implied volatility runs the machine backwards. You know the price. You search for the volatility that makes the machine return it. For Nifty options the machine is Black 76, which prices off the forward. The [first volatility lesson](/learn/path-16/module-16-1-historical-vs-implied-volatility) framed the result: a price written in volatility units.

Solving is a loop: guess, price, compare, move

The loop stops when the model price is within a paisa of the settlement price. The two ways to move the guess are in the text. Source: Black (1976) pricing model, RupeeCase engine. As of 17 Oct 2026.

* **Bisection.** Fence the answer between a low and a high volatility. Price the middle. If the model is too high, the answer is in the lower half, otherwise the upper. Repeat. It never fails, and each step halves the fence, so thirty steps shrink it about a billion times.

* **Newton.** Take the gap between the model price and the market price and divide it by vega. That is how many volatility points to move. Near the money the price is almost a straight line in volatility, so two or three steps are enough.

1. Take the settlement price of the option, not the last trade.

2. Set the forward: the future of the same month for a monthly expiry, the parity forward for a weekly one.

3. Set the time as calendar days to expiry over 365, with expiry at 15:30.

4. Set the rate from the T bill curve.

5. Run the loop until the model price matches to a paisa.

Read 7 more paragraphs, 386 words
Why search at all? The volatility sits inside the normal curve in the formula, so it cannot be moved to one side. There is no formula for it. But one fact makes the search easy: a higher volatility always gives a higher price, for a call and for a put. The slope of that rise is [vega](/learn/glossary#vega). Because price only climbs, one price fits one volatility, never two.

There are two ways to move the guess.

Newton has a weak spot. Far out of the money, vega is close to zero, the divide blows up and the next guess can leap out of range. A sound solver keeps the answer fenced and falls back to bisection when Newton leaves the fence. RupeeCase's engine does exactly this.

**How do I calculate IV for Nifty options?** The short version, which the [question page](/learn/questions/calculate-iv-nifty-options) repeats:

Two choices matter more than the maths. Use the option that is out of the money at each strike: the put below the forward, the call above it. In the money options hold mostly intrinsic value, carry little vega and wide spreads, so a small price error becomes a big volatility error. And use the same inputs every time you compare, because the answer depends on all of them.

Each input pushes the answer in a known direction. A higher forward lowers the volatility a call needs to reach its price, and raises it for a put. More days to expiry lower the volatility needed, because time alone adds value. The rate matters least for an option of a few weeks, since it only moves the discount factor, but it grows with the time left. Get the rate or the days wrong and every strike shifts the same way. Get the forward wrong and the calls shift one way while the puts shift the other, which is why a smile built on a wrong forward shows a step where it switches from puts to calls.

Sometimes there is no answer. A call cannot be worth less than the discounted gap between the forward and the strike, and cannot be worth more than the discounted forward. A price outside those bounds has no volatility behind it. That signals a stale or wide quote, and a good solver returns nothing instead of a wrong number.

## Worked example: one call, then the whole chain

Take the 23,250 call on 10 Jun 2026. The future settled at 23,240.10, 20 calendar days remained to the 30 Jun expiry and the rate was 5.11 percent. The call settled at Rs 321.65. Three guesses at the volatility price it as follows: Rs 211.56 at 10%, Rs 319.77 at 15% and Rs 427.98 at 20%.

A guess of 15% lands within Rs 1.88 of the market price

Price rises with volatility, so the market price of Rs 321.65 sits between the 15% and 20% guesses, much nearer 15%. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.
Solved strike by strike, low strikes solve highest and the curve bottoms above the future

Implied volatility of the out of the money option at each strike that traded, Nifty 30 Jun 2026 expiry. Each point is one solve, as above. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.
At one strike the call and the put solve to different volatilities

Show all columnsShow fewer columns
| Calls | Calls | Strike | Puts | Puts |
| --- | --- | --- | --- | --- |
| Settle | IV % | IV % | Settle |
| 405.90 | 15.4 | 23,100 | 15.0 | 258.10 |
| 374.55 | 15.2 | 23,150 | 14.9 | 278.95 |
| 347.70 | 15.1 | 23,200 | 14.8 | 300.60 |
| Spot 23,214.95 | Spot 23,214.95 |
| 321.65 | 15.1 | 23,250ATM | 14.6 | 322.05 |
| 294.60 | 14.9 | 23,300 | 14.6 | 347.65 |
| 272.55 | 14.9 | 23,350 | 14.5 | 371.80 |
| 248.10 | 14.8 | 23,400 | 14.4 | 398.75 |

Shaded cells are in the money. Settle is the settlement price in rupees per unit. IV is solved from it by RupeeCase.

Nifty 30 Jun 2026 chain of 10 Jun 2026. The row tagged ATM is nearest the future. Calls are on the left. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.
The solved at the money IV follows India VIX but sits under it on most days

Percent a year. The at the money series is computed by RupeeCase from settlement prices. India VIX is NSE's index, built from a strip of out of the money options, so the two differ by construction. Over the whole file the average at the money IV is 12.42 against 13.49 for India VIX. Source: NSE end of day data, computed by RupeeCase. As of 15 Sep 2026.
Read 8 more paragraphs, 342 words
Now Newton, starting from 20%. The model gives Rs 427.98, which is Rs 106.33 too high. Vega at that point is Rs 21.64 a unit for each volatility point. Divide: 106.33 over 21.64 is 4.91 points. The next guess is 15.09%. Price it again and the model returns Rs 321.645 against Rs 321.65. One step brought it within a paisa. The solved value is 15.09%.

Do the same for every strike and you get the smile of the chain.

The 21,400 put solves to 19.72%, the curve bottoms near 24,000 at 14.38%, and the 25,050 call solves to 16.27%. The shape has its own lesson in the [smile and skew module](/learn/path-16/module-16-7-volatility-smile-and-skew). Here the point is that each dot is a separate solve.

Back to the strike where the call and put disagreed. Here are both sides.

At 23,250 the call gives 15.09% and the put 14.65%, a gap of 0.44 points. With a vega of Rs 21.64 a unit, that gap is worth about Rs 9.52 of premium. Settlement prices are not trades, so a few rupees of disagreement between a call and a put is ordinary. Put call parity ties the two prices together, and the [parity module](/learn/path-14/module-14-10-put-call-parity) shows how the leftover is measured. It is also why the smile uses one option per strike.

And the edge case. The 24,800 put settled at Rs 1,553.20 on 146 contracts. The least a put that deep in the money can be worth is the discounted gap to the forward, Rs 1,555.54. The settlement price sits Rs 2.34 below that floor, so no volatility reproduces it. The solver returns nothing, and a screen that shows a number there has done something extra.

Over a longer stretch, the same solve run daily on the nearest monthly expiries gives a constant 30 day at the money series.

Both lines come from option prices, and both rise and fall together. They differ because they read different strikes. The [India VIX lesson](/learn/path-16/module-16-2-india-vix-explained) takes the index apart.

## The common mistake

The claim: Implied volatility is one fixed number for an option, so if two screens show different values, one of them is wrong. Implied volatility is an answer to a question, and the answer depends on what you ask. Change the forward, the number of days, the rate, the price used or the side of the strike, and the solved number changes. Here the call and the put at one strike gave 15.09% and 14.65% from the same day's settlement prices. Before you compare two IV figures, compare their inputs. The [next lesson](/learn/path-16/module-16-4-iv-rank-and-iv-percentile) asks where an IV sits against its own past, which only works if every day was solved the same way.

## Key takeaways

* Implied volatility is found by search, because the formula cannot be turned around.
* Price only rises with volatility, so one price gives one answer.
* Newton is fast near the money and needs a fence far from it.
* Use the settlement price, the right forward and the out of the money side.
* A price below its lower bound has no implied volatility.
* Compare the inputs before you compare two implied volatility figures.

3 terms this section turns on

From the module glossary; every term is in the Learn glossary too. Source: Module 16.3, Solving for implied volatility.
**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 Solving for implied volatility cover?The option price is known and the volatility is the unknown. How a solver finds it, where it fails, and why two screens can differ. It works through The idea, plainly, Worked example: one call, then the whole chain, The common mistake, Key takeaways. It is module 16.3 of Path 16, Volatility, about 9 minutes of reading, free.

TTry it

## IV solver, on the same example.
The implied volatility behind a dated settlement price. Dated NSE end of day data, nothing live, no orders.

**IV solver**, Nifty, 10 Jun 2026, 30 Jun 2026 expiry.

[Open the iv solver](/learn/tools/iv-solver?chain=NIFTY_2026-06-10_2026-06-30)

  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 16.3

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 3 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#quiz)
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)
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 16.1Volatility: historical against implied7 min read](/learn/path-16/module-16-1-historical-vs-implied-volatility)
* [Free module 16.4IV rank and IV percentile, done properly9 min read](/learn/path-16/module-16-4-iv-rank-and-iv-percentile)
* [Free module 16.7Smile and skew: a first look at Nifty and stocks8 min read](/learn/path-16/module-16-7-volatility-smile-and-skew)
* [Free module 14.10Put call parity and synthetic positions9 min read](/learn/path-14/module-14-10-put-call-parity)
* [QuestionWhat is implied volatility?A short answer with a dated chart](/learn/questions/what-is-implied-volatility)

      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.
7 sources, NSE the most cited

The publisher of each source listed below. Source: Module 16.3 source list.
1. [NSE, option chain (Nifty 50 index options)](https://www.nseindia.com/option-chain) NSE
2. [NSE, derivatives end of day reports: F&O bhavcopy and participant wise open interest](https://www.nseindia.com/all-reports-derivatives) NSE
3. [NSE, equity derivatives contract specifications](https://www.nseindia.com/static/products-services/equity-derivatives-contract-specifications) NSE
4. [NSE Clearing, settlement price of futures and options](https://www.nseclearing.in/clearing-settlement/equity-derivatives/settlement-price) NSE
5. [NISM, Series VIII Equity Derivatives certification examination: test objectives](https://www.nism.ac.in/revamp-nism/test-objectives-revised-nism-series-viii-equity-derivatives-certification-examination/) NISM
6. [Black, F. (1976), The pricing of commodity contracts, Journal of Financial Economics](https://doi.org/10.1016/0304-405X(76)90024-6) Paper
7. Hull, J., Options, Futures, and Other Derivatives, Pearson (implied volatility) Book

GTerms

## 5 terms from this module.
Implied volatilityThe volatility that, put into an option pricing model, returns the option's market price. A price in volatility units.
[Vega](/learn/glossary#vega)The change in an option's price for a one point rise in volatility. It is the slope a Newton step divides by.
BisectionA search that fences the answer between a low and a high guess and halves the fence each step. It always converges.
Newton's methodA search that moves the guess by the price gap divided by vega. Fast near the money, unstable where vega is close to zero.
Lower boundThe least an option can be worth without an arbitrage: the discounted gap between the forward and the strike, or zero. A price below it has no implied volatility.
[All 230 terms in the glossary](/learn/glossary)

[Question people askWhat is implied volatility?A short answer with a dated chart](/learn/questions/what-is-implied-volatility)[Question people askHow do I calculate IV for Nifty options?A short answer with a dated chart](/learn/questions/calculate-iv-nifty-options)[Related module16.1 Volatility: historical against implied7 min, Beginner](/learn/path-16/module-16-1-historical-vs-implied-volatility)[Related module16.4 IV rank and IV percentile, done properly9 min, Intermediate](/learn/path-16/module-16-4-iv-rank-and-iv-percentile)[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.