---
title: "Market Microstructure Models: Roll, Kyle, Glosten Milgrom"
description: "Three classic microstructure models, the tick as a floor on cheap Nifty options, what daily files cannot say, and the closing auction from 7 Dec 2026."
source_url: "https://www.rupeecase.com/learn/path-19/module-19-9-microstructure-models"
---

[Path 19 9 of 16](/learn/path-19/)Microstructure models: spreads, informed trading and price impact[Next 19.10](/learn/path-19/module-19-10-market-making)

On 10 Jun 2026 one lot of the near Nifty future, 65 units, traded around 23,240.10 in steps of one tenth of a point. That step was 0.043 of a basis point of the price. The same day, the Nifty 30 Jun put at the 18,000 strike settled at 1.65 rupees after 870 contracts changed hands, and one tick of Rs 0.05 was 3.03% of its price. For the future the tick is a rounding error. For that put it is a real share of the price. A quote is a price for being picked off, and how large it must be depends on who is on the other side and how far the next trade can move the market. This lesson puts three classic models side by side, then tests what a daily NSE file can and cannot tell you about them. Dated data, nothing live, nothing a view.

3By the end you can

1. State what the Roll, Glosten Milgrom and Kyle models each isolate in a spread or a price move.
2. Work out the floor that the tick puts under the spread of an option at any price.
3. Say why daily end of day files cannot estimate a spread, and what the closing auction changes.

Watch in the terminal: why do the hero, key figure and XIRR differ? A short tutorial on sample data.

## The idea, plainly

### What a quote is paying for

A market maker who quotes both sides earns the gap between the price they buy at and the price they sell at, and pays three costs out of it. The first is order processing: systems, fees, capital. The second is inventory: the stock or contracts they now hold carry risk until sold on. The third is adverse selection: some of the people who trade against a quote know more than the quote does. The Roll model reads the whole bounce, whatever causes it. The other two model the adverse selection part, one trade at a time and then by order size.

A spread pays for three things, and the models read different parts

The costs a market maker must cover and what each model reads. Roll measures the whole spread from the bounce; Glosten Milgrom and Kyle model adverse selection. An illustration of the models, with no prices. Source: RupeeCase illustration of the models. As of 17 Oct 2026.

### Roll: the bounce in the price

Suppose trades alternate at random between the bid and the ask while the true value stays put. The price then bounces between two levels, and a rise is more likely to be followed by a fall than by another rise. The negative serial correlation of price changes is the signature of the spread, and the Roll model turns it into a number: the spread is twice the square root of minus the covariance of successive price changes. Everything depends on the prices being actual trade prices, one after the other.

The maths: the Roll spread
Let the observed price be the efficient price plus half the spread times a trade sign q that is plus or minus one with equal chance.

p(t) = m(t) + (s/2) q(t)
dp = dm + (s/2) dq
cov(dp(t), dp(t-1))
= -s^2 / 4
s = 2 sqrt(-cov)

The efficient price m moves only on news, so it adds no covariance across steps. The sign changes dq contribute a negative one. If the estimated covariance comes out positive the model has no answer, which happens often in real data.

### Glosten and Milgrom: informed traders widen the spread

Now let the value be uncertain. A share is worth either a low or a high amount, equally likely. A fraction of the traders who arrive know which and trade accordingly. The rest buy or sell at random. A maker who does not know who is who must set the ask where a buy tells them the value is more likely high, and the bid where a sell says low. Each informed trade costs them, each uninformed one pays them, and the quotes that break even leave a spread equal to the informed share times the size of the news.

The maths: break even quotes
Let the low and high values be V_L and V_H, each with probability one half, and the informed share be mu.

P(buy, high) = mu + (1-mu)/2
P(buy, low) = (1-mu)/2
P(high, buy) = (1+mu)/2
ask = E[V, buy]
bid = E[V, sell]
spread = mu (V_H-V_L)

The ask is the value given a buy, so it sits above the midpoint by the informed share times half the jump. The bid is the mirror. Each trade also moves the maker's belief, so quotes move after trades even with no news.

### Kyle: size moves the price

The third model asks about one big order. A single informed trader and a crowd of random traders send orders to a maker, who sees only the total and sets one price. The informed trader hides in the noise by not trading too much. The result is a straight line: the price moves by a fixed amount for each unit of net order flow, and the slope falls as the noise trading gets larger. The slope, usually written lambda, is how deep the market is.

Watch in the terminal: how do I send a rejected order again? A short tutorial on sample data.
The maths: the one auction solution
Let the value have standard deviation s_v and the random orders have standard deviation s_u.

x = b (v-p0)
b = s_u / s_v
p = p0 + L (x + u)
L = s_v / (2 s_u)
profit = s_u s_v / 2

The informed trader trades in proportion to what they know. The maker sets the price from the total order flow, and the slope L comes from asking that the price equal the expected value. Half of what the informed trader knows gets into the price. Real impact is often found to rise more slowly than size for large orders, which the [optimal execution lesson](/learn/path-19/module-19-11-optimal-execution) takes up.

## Worked example: the tick, the bounce and the close

### The tick as a floor

No quote can be tighter than one tick. On the Nifty future the tick was one tenth of a point at an index level above fifteen thousand, and on the index options five paise. Look at what five paise means across the strikes of the 30 Jun chain, with ATM taken as the strike nearest the future.

Five paise is nothing at the money and a few percent of the price far out

Nifty puts of the 30 Jun 2026 expiry, 10 Jun 2026, each with traded volume. The percent is the smallest possible quoted gap, one tick, over the settlement price. The real gap is at least this wide. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.
Read one more paragraph, 92 words
At the money the floor is under two hundredths of a percent of the premium. Ten percent below the future, a put at 8.60 rupees has a floor of 0.58%. At the 18,000 strike, 1.65 rupees, it is 3.03%. I left out a few thin strikes whose settlement price in the file sat far below their own closing trade: a settlement field alone is not a quote. An option that cheap cannot be quoted tightly, however many market makers there are. That is a rule effect, not a liquidity one.

### What a daily file says about the bounce

Now try the Roll idea on what an end of day file has: one close a day. For each future of the file I took the close of the near contract, dropped the change across each monthly roll, and computed the Roll spread. For the high and low of the day I used the high low estimator, which turns the range of two days into a spread. Roll is built for prices that follow one another trade by trade. The high low estimator is built for daily ranges, but it needs the spread to be a visible part of the range.

Daily files put the spread at hundreds of times the tick, so they measure news, not the quote

Near month futures, daily close and range. Roll is undefined for about two in five of the stock futures, where the covariance came out positive, and the medians use the rest. The first bar is the smallest possible gap for the Nifty future on 10 Jun 2026. Source: NSE end of day data, computed by RupeeCase. As of 15 Sep 2026.
Read one more paragraph, 147 words
The Roll figures are tens of basis points, and the tick floor is a few hundredths of one. A spread of tens of basis points on the Nifty future is not plausible for a contract that size, and nothing in the file says it is real. What the estimators picked up was the day's news and the swing of the close. A daily close carries one trade out of tens of thousands, and next to a day's range a spread of a few hundredths of a basis point is invisible. The lesson I keep is that for a contract this tight, a spread needs the quotes or the trades themselves, and an end of day file has neither. Any use of recent prices in education also sits under the thirty day rule of SEBI's circular of 8 May 2026, which is why every example here is dated.

### The informed share, on the model's own numbers

Back to the model. Pick a share priced at a thousand rupees, and let an informed trader know a one percent jump. The Glosten Milgrom spread is then the informed share of orders times one percent of the price.

A spread is the informed share times the size of the news

Model, not market data. A share priced at one thousand rupees, informed traders who know a one percent jump, and the rest trading at random. The spread is linear in the informed share. Source: RupeeCase model of Glosten and Milgrom, inputs assumed. As of 17 Oct 2026.
Read one more paragraph, 98 words
With one order in a hundred informed the break even spread is a single basis point, which at that price is ten paise: two ticks. At one in five it is twenty basis points. Turn it round and the model gives a reading of a quote. A spread of one tick says that, per order, informed money is a small fraction of the flow or the news it carries is tiny. In the Nifty future the tick is so small next to the price that the model says almost nothing about who is trading from the spread alone.

### A market design that answers the model

Kyle's maker sees all orders at once and sets one price. A call auction does the same thing on purpose. SEBI's circular of 15 Oct 2026 revises the closing auction session of the cash market, which began on 3 Aug 2026, and the way expiring contracts are settled. It takes effect on 7 Dec 2026, apart from the carry over of unexecuted orders into the auction, which follows on 8 Feb 2027. The chart lays out the sequence of a day under it.

The close becomes a batch auction with a random end

1. 3:00 pm**Last 30 minutes begin**The volume weighted prices of continuous trading up to 3:30 pm set the settlement of expiring index and stock contracts.

2. 3:15 pm**Reference price window**Trades of the last 15 minutes of continuous trading give the volume weighted reference price for the closing auction.

3. 3:30 pm**Closing auction opens**Expiring index contracts stop trading on expiry day. Reference price computed in the first minute.

4. 3:31 pm**Limit and market orders**Five minutes of order entry, then four minutes of limit orders only.

5. 3:38 to 3:40 pm**Random close**The order entry period ends at a random moment in the last two minutes. Orders then match at one price.

6. 3:45 pm**Other derivatives stop**Index derivatives that are not expiring and all stock derivatives trade until 3:45 pm.

The times are those of SEBI's circular of 15 Oct 2026 from 7 Dec 2026. The random close removes a known last moment to aim at. Rules, not prices. Source: SEBI circular of 15 Oct 2026, layout by RupeeCase. As of 15 Oct 2026.
The term this section turns on: Closing auction session

From the module glossary; every term is in the Learn glossary too. Source: Module 19.9, Microstructure models: spreads, informed trading and price impact.
Read one more paragraph, 100 words
Under SEBI's circular of 16 Jan 2026, expiry day settlement had moved to the closing prices that the auction sets. The circular of 15 Oct 2026 takes it back to the volume weighted prices of the last 30 minutes of continuous trading from 7 Dec 2026, so the dates matter. The auction collects orders and clears them at one price, as Kyle's maker does. The random end takes away a last second to aim at. Whether it narrows the information gap is for the data of the months to come to show, and I have not seen that data yet.

### Where this meets India

Futures on NSE have an operating range of ten percent of the base price, and each option has a contract specific range from its delta, so a model that assumes any price can print does not fit the book near a limit. The tick for stock options depends on the price of the stock, and NSE has set it by rule, not by the market. A trader who buys at the offer and sells at the bid pays one full spread on a round trip, on top of the statutory charges. For the big index contracts the floor on that is a few hundredths of a basis point. For a far out of the money option it can be several percent of the price.

## The common mistake

The claim: The spread is the whole cost of trading, so a tight spread means a cheap trade. The spread is the cost of one small order at the best quote. A bigger order uses up the quotes and moves the price, as the Kyle model shows, and a spread can widen when informed flow arrives. On the cheap far out of the money puts the one tick floor was about three percent of the price, so a trade could be costly even when the quote was as tight as the rules allowed. Before judging a cost, ask what size it is for, which price it uses and whether the number came from quotes or from daily closes.

## Key takeaways

* A spread pays for order processing, inventory risk and adverse selection.
* In the Glosten Milgrom model the spread is the informed share times the jump.
* In the Kyle model the price moves in a line with net order flow.
* One tick is a few percent of a far out of the money option's price.
* Daily files cannot estimate a tight spread, because the news swamps the bounce.

Two terms to hold on to from 19.9

From the module glossary. Source: Module 19.9, Microstructure models: spreads, informed trading and price impact.

Where this section sits in module 19.9

Sections 1 to 4 of 4; the highlighted one is next. Source: Module 19.9, Microstructure models: spreads, informed trading and price impact.
**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 Microstructure models: spreads, informed trading and price impact cover?A quote pays for three things. Three models pull them apart, and one daily file cannot. It works through The idea, plainly, Worked example: the tick, the bounce and the close, The common mistake, Key takeaways. It is module 19.9 of Path 19, Algo, HFT and Backtesting, about 11 minutes of reading, free.

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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 19 certificate.

7 of 10 correct passes module 19.9

Every answer is explained when you check; a retake is always free. Source: RupeeCase Learn quiz rules (70% to pass).

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CCheck yourself

## Path 19 so far.
Your quick check results on this device, stop by stop.

Stop 9 of 16 on Path 19

Algo, HFT and Backtesting: every live stop, this module ringed. Source: RupeeCase Learn, Path 19.

1. [19.1What a backtest is, and five biases that ruin itNot yet](/learn/path-19/module-19-1-backtest-biases)
2. [19.2Strategy metrics: CAGR, Sharpe, Sortino, drawdown and expectancyNot yet](/learn/path-19/module-19-2-strategy-metrics)
3. [19.3HFT, MFT and LFT comparedNot yet](/learn/path-19/module-19-3-hft-mft-lft)
4. [19.4Colocation, latency and fairness: NSE's historyNot yet](/learn/path-19/module-19-4-colocation-and-latency)
5. [19.5Building a compliant retail algoNot yet](/learn/path-19/module-19-5-building-a-compliant-algo)
6. [19.6Backtesting options on Indian dataNot yet](/learn/path-19/module-19-6-backtesting-options)
7. [19.7Walk forward and out of sample testingNot yet](/learn/path-19/module-19-7-walk-forward-testing)
8. [19.8Monte Carlo and bootstrap of trade resultsNot yet](/learn/path-19/module-19-8-monte-carlo-and-bootstrap)
9. [19.9Microstructure models: spreads, informed trading and price impactNot yet](/learn/path-19/module-19-9-microstructure-models#quiz)
10. [19.10Market making: inventory and quotingNot yet](/learn/path-19/module-19-10-market-making)
11. [19.11Optimal execution and market impactNot yet](/learn/path-19/module-19-11-optimal-execution)
12. [19.12HFT economics and the latency raceNot yet](/learn/path-19/module-19-12-hft-economics)
13. [19.13Backtest overfitting: deflated Sharpe, PBO and multiple testingNot yet](/learn/path-19/module-19-13-backtest-overfitting)
14. [19.14Financial machine learning done carefullyNot yet](/learn/path-19/module-19-14-financial-machine-learning)
15. [19.15Expiry day market integrity: a SEBI interim order, FutEq limits and surveillanceNot yet](/learn/path-19/module-19-15-expiry-day-market-integrity)
16. [19.16Capstone: a research note on an Indian derivatives questionNot yet](/learn/path-19/module-19-16-capstone-research-note)
17. [TPath test, 30 questionsNot yet](/learn/path-19/module-19-16-capstone-research-note#pathTestSection)

Path 19 in reading time: 172 minutes over 16 modules

Minutes of reading per module, this one in amber. Source: RupeeCase Learn, Path 19.

    Explore next

## Put the module to work.

* [Free module 15.5Liquidity in the chain: spreads, volume and tradable strikes9 min read](/learn/path-15/module-15-5-option-chain-liquidity)
* [ToolOption payoff builderLegs on a dated Nifty chain, breakevens and charges](/learn/tools/payoff-builder)
* [Free module 19.3HFT, MFT and LFT compared10 min read](/learn/path-19/module-19-3-hft-mft-lft)
* [Free module 19.4Colocation, latency and fairness: NSE's history11 min read](/learn/path-19/module-19-4-colocation-and-latency)
* [Free module 19.10Market making: inventory and quoting11 min read](/learn/path-19/module-19-10-market-making)
* [Free module 19.11Optimal execution and market impact12 min read](/learn/path-19/module-19-11-optimal-execution)

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SSources

## Go to the source.
5 sources, Paper the most cited

The publisher of each source listed below. Source: Module 19.9 source list.
1. [NSE, equity derivatives contract specifications (tick sizes, price bands, lots, European exercise)](https://www.nseindia.com/static/products-services/equity-derivatives-contract-specifications) NSE
2. [SEBI circular of 15 Oct 2026, review of the closing auction session, market timings and settlement methodology for derivatives contracts](https://www.sebi.gov.in/legal/circulars/oct-2026/review-of-certain-aspects-of-the-closing-auction-session-market-timings-and-settlement-methodology-for-derivatives-contracts_105293.html) SEBI
3. [SEBI circular of 8 May 2026, norms for sharing and usage of price data for educational purposes](https://www.sebi.gov.in/legal/circulars/may-2026/norms-for-sharing-and-usage-of-price-data-for-educational-purposes_101293.html) SEBI
4. [Glosten, L. R. and Milgrom, P. R. (1985), Bid, ask and transaction prices in a specialist market with heterogeneously informed traders, Journal of Financial Economics](https://doi.org/10.1016/0304-405X(85)90044-3) Paper
5. [Kyle, A. S. (1985), Continuous auctions and insider trading, Econometrica](https://doi.org/10.2307/1913210) Paper

GTerms

## 5 terms from this module.
Tick sizeThe smallest price step an order may use. No quoted spread can be tighter than one tick.
Adverse selectionThe cost of trading against someone who knows more than the quote. It is the reason a market maker's spread is wider than the cost of doing business.
Roll spreadA spread estimated as twice the square root of minus the covariance of successive price changes, which needs trade by trade prices.
Kyle lambdaThe slope of the price against net order flow: how much the price moves for each unit of order. A deeper market has a smaller lambda.
Closing auction sessionA short session after continuous trading in which orders are collected and matched at one closing price, with a random end.
[All 230 terms in the glossary](/learn/glossary)

[Question people askWhat are the order book, bid ask spread, impact cost and tick size?A short answer with a dated chart](/learn/questions/order-book-spread-impact-cost)[Question people askWhat is market making?A short answer with a dated chart](/learn/questions/what-is-market-making)[Related module19.3 HFT, MFT and LFT compared10 min, Advanced](/learn/path-19/module-19-3-hft-mft-lft)[Related module19.4 Colocation, latency and fairness: NSE's history11 min, Advanced](/learn/path-19/module-19-4-colocation-and-latency)[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.