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# 5.53 Where Is Bitcoin's Price Actually Set? Unregulated Venues Win
- URL: https://aligrithm.com/where-is-bitcoins-price-actually-set-unregulated-venues-win/
- Published: 2026-10-18T11:57:00.000Z
- Updated: 2026-10-18T11:57:00.000Z
- Description: Bitcoin price discovery squares the ratio of the Hasbrouck share to the component share, in a 10-millisecond error-correction model. The cheapest book takes the permanent move.
- Author: ali askar
- Tags: 5. Microstructure Alpha

Cosenza and Stalder line up trade prices from eight Bitcoin books, three regulated dollar spot markets and five USDT markets, two of those perpetual futures, and ask which book's last trade enters the move that does not die out. The tool is one error-correction model per hour on Tardis trades from 1 November 2022 through 31 March 2024\. At a one-second clock the Hasbrouck bounds on a single book cover almost the whole range from 0 to 1, and the leader is whichever book you ordered first in the Cholesky factor. At 10 milliseconds the bounds separate. What separates with them is a commission: put the spot fee back on and the permanent move leaves that book.

## Seven gaps, one common trend

Eight prices share one permanent move only when seven gaps between them are stationary. The paper builds each gap against the first price. USDT books sit in the same system as the dollar books, so Tether and the dollar have to be close enough, hour by hour, that one random walk can run through both.

$$ e\_{j,t} = p\_{1,t} - p\_{j,t}, \\qquad j = 2,\\ldots,8 $$ $$ \\Delta\_d p\_t = \\gamma e\_{t-d} + \\text{lagged price changes} + \\varepsilon\_t $$

The first line is the gap vector inside the error correction. Price 1 minus price j, in dollars, for each of the other seven books. The second line is the vector error-correction step over a clock of length d. Gamma is 8 by 7\. It multiplies the lagged gaps and says how many dollars each book moves to close them. The lagged price changes soak up short-run autocorrelation. Epsilon is the innovation, with covariance Omega. They demean every series first, so the model has no intercept and the average gap is zero by construction. The printed array they give for the cointegrating matrix does not multiply out to these gaps. The gaps are the objects named in the sentence above that array. Compute the gaps.

Worked gap. Coinbase prints 42,010 and Binance prints 42,000\. The gap against Binance is 10 dollars. That 10 dollars is what gamma is allowed to chew on next step. A gap that sat at 10 dollars forever would mean two random walks, and the model would be the wrong model.

They check the one-walk assumption with a Johansen test on each hour, at the 10-millisecond sampling they settle on. In the example hour, midnight to 1:00 UTC on 2 December 2022, the trace statistic at rank 6 is 39.46 against a critical value of 23.52, so six or fewer relations are rejected, and at rank 7 the trace is 4.71 against 11.65, so seven relations are not rejected. Eight prices, seven stationary gaps, one common trend. That pattern holds in 87% of hours at the 1% level, and in 91% at the 5% level. They drop the rest. The shares below are conditional on the books already being glued together.

Perpetual futures carry a funding payment that can push them off spot. They leave it out. Their bound is that the hourly funding is often under 0.01% of notional. On a 42,000 dollar bitcoin that ceiling is 4.20 dollars an hour. The 10 dollar gap above is already larger than that ceiling. Into the funding timestamp itself the perp can jump by the whole payment at once. If you are hedging across that minute, put the funding print back in. The paper follows earlier Bitcoin studies and omits it.

## A one-second clock cannot name the leader

The Hasbrouck information share of book i is that book's fraction of the variance of the permanent move. Take any row of the long-run impact matrix, call it psi. Because the eight prices are cointegrated, every row is the same row: an innovation's permanent effect is the same whichever book you read it off. Omega is the covariance of the innovations.

$$ HIS\_i = \\frac{(\[\\psi F\]\_i)^2}{\\psi \\Omega \\psi'}, \\qquad FF' = \\Omega $$

F is the lower-triangular Cholesky factor of Omega. Psi times F turns the correlated innovations into a set of uncorrelated shocks, and the squared i-th entry is the piece of the permanent variance blamed on book i. The denominator is the permanent variance itself, psi Omega psi-transpose. When the innovations are uncorrelated, F is diagonal and the numerator collapses to the square of that book's psi times that book's innovation variance. The ordering inside the Cholesky sets the upper and lower bound: put a book first and it absorbs the contemporaneous covariance. The width is the gap between those orderings.

The paper prints the numerator as psi-transpose times F. Psi is a row, so that product does not conform with the variance formula in the same section. The product that conforms is psi times F. I use that one. The printed transpose may be a typesetting slip.

Worked numbers, two books, uncorrelated residuals. Psi is 0.75 and 0.25\. The innovation variances are 2 and 8\. The permanent variance is 0.75 squared times 2, plus 0.25 squared times 8, which is 1.125 plus 0.5, so 1.625\. The first book's share is 1.125 / 1.625 = 69.23%. The second book's share is 0.5 / 1.625 = 30.77%. The noisy book has one third the long-run weight and four times the innovation variance, and its variance share, 30.77%, sits above its weight of 25%. Noise inflates the wide, jumpy book. Bitstamp's tick is 1 dollar. Coinbase and Binance tick at 0.01\. At a 42,000 dollar price the Bitstamp tick is 0.24 basis points, next to a 2.83 basis point effective spread in the hourly table. The spread gap is the larger of the two. Different ticks, different spreads, and different update rates are why a raw variance share can rank a book for the wrong reason.

The light-blue band in the figure is the one-second Hasbrouck bound for OKX through November 2022\. The red band is the same book at 10 milliseconds.

![Hasbrouck information share for OKX in November 2022. The wide light-blue band is the one-second upper and lower bound. The narrow red band is the ten-millisecond bound.](https://storage.ghost.io/c/27/cb/27cb0fc8-2c77-4434-af9e-d5d32a916994/content/images/2026/10/article_462-his_bounds_okx_nov2022.png)

The one-second band covers most of the unit interval. The 10-millisecond band is a thin ribbon around its mean. At one second you can report a midpoint of two useless bounds, which is what a lot of the earlier Bitcoin papers did. At 10 milliseconds the contemporaneous correlation has shrunk enough that the bounds stop overlapping and a share becomes a number.

They buy that resolution with a restriction on the lags. The maximum lag is 10 seconds at every sampling rate. At 10 milliseconds that is 1,000 lags per pair of books, and an unrestricted model is not something you estimate once an hour for seventeen months. They tie the lags the way a heterogeneous autoregression does. The first lag is free, lags 2 through 10 share one coefficient, lags 11 through 100 share another, and lags 101 through 1,000 share a fourth. Four coefficients per ordered pair instead of 1,000\. One model per hour, eight series in the model. Permuting the Cholesky order for Hasbrouck's bounds gets ugly past about six names, and the paper says so in the same paragraph in which it estimates eight. The tables below have eight columns. The 10-millisecond clock is doing the identification work that a full permutation would have done.

## The book that does not adjust holds the common factor

The component share hands the common trend to the book that does not correct the gap. Gamma's columns are the adjustment speeds. The component weights are a vector orthogonal to every column of gamma, normalized to sum to one. The source prints the normalization and tells you the vector is orthogonal. It does not print the two-book solution. The two-book arithmetic below is that orthogonality, applied to one column.

$$ CS\_i = \\frac{\\gamma\_{\\perp,i}}{\\sum\_{j=1}^{n} \\gamma\_{\\perp,j}} $$

Gamma-perp is orthogonal to gamma, and the share is that vector scaled by its sum. A large share means the other books do the correcting.

Same 10 dollar gap as above, now with speeds. Let the gap be Coinbase minus Binance, Coinbase's speed be -0.40, and Binance's speed be +0.05\. Next step, Coinbase moves -0.40 times 10, which is -4 dollars. Binance moves +0.05 times 10, which is +0.50 dollars. Coinbase was the rich print and Coinbase gives up 4 of the 10 dollars. Binance gives up 0.50 by ticking up. The follower closes the gap.

The orthogonal vector for a single column gamma = (-0.40, +0.05) is (+0.05, +0.40): the dot product is -0.40 times 0.05, plus 0.05 times 0.40, which is -0.02 plus 0.02, which is zero. The sum of the weights is 0.45\. Coinbase's component share is 0.05 / 0.45 = 11.11%. Binance's is 0.40 / 0.45 = 88.89%. The book that moved 0.50 dollars owns 88.89% of the common factor. The book that moved 4 dollars owns 11.11%. Flip the orthogonal vector's sign and the weights go negative, so you keep the direction whose entries sum to a positive number. This is a component-share toy. The 88.89 and the earlier 69.23 come from different inputs.

In the eight-book system the same division applies to an 8-vector in the null space of an 8-by-7 gamma, which is a numerical object. A big component share means the other books are the ones walking back toward this one.

## Square the ratio when the two shares disagree

The source treats the information leadership share as the ranking, on the argument that noise pushes the Hasbrouck share and the component share in opposite directions. A book can look informative on one metric and like a satellite on the other. The leadership share divides one by the other and squares the ratio, which is the normalization they use for more than two books. The source calls the ratio beta. That letter is already the cointegrating matrix. I call the ratio lambda.

$$ \\lambda\_i = \\frac{HIS\_i}{CS\_i}, \\qquad ILS\_i = \\frac{\\lambda\_i^2}{\\sum\_{j=1}^{n} \\lambda\_j^2} $$

Lambda is large when a book's variance share is high relative to its component share. Squaring and dividing by the sum of squares forces the leadership shares to add to one. The Hasbrouck share and the component share sit in the appendix, because the tick sizes and the spreads differ across books.

Worked ratio, a third toy. Book L has a Hasbrouck share of 0.55 and a component share of 0.40\. Book N has 0.45 and 0.60\. Lambda-L is 0.55 / 0.40 = 1.375, and 1.375 squared is 1.890625\. Lambda-N is 0.45 / 0.60 = 0.75, and 0.75 squared is 0.5625\. The sum of squares is 2.453125\. Book L's leadership share is 1.890625 / 2.453125 = 77.07%. Book N's is 0.5625 / 2.453125 = 22.93%. The variance split said 55 against 45, almost a tie, with the noisy book flattered. The component split said the noisy book was the common factor. The squared ratio hands three quarters of the leadership to the book whose variance share was high relative to how much correcting it does.

That 77.07 is a hand example so the algebra is checkable. The paper's numbers, next, are eight-book averages of this same share, estimated every hour.

## A point of relative volume moves the share

They regress the hourly leadership share, in percent, on the hour's return, the book's share of the eight-book volume, the effective spread, realized volatility, and one lag of the share. Relative volume is that book's dollars divided by the eight books' dollars, in percent. The spread is in basis points. Volatility is annualized percent. One regression per book, Newey-West standard errors with 24 hourly lags, split on the fee date so each regime has its own slopes.

$$ ILS\_{i,t} = \\beta\_0 + \\beta\_1 R\_{i,t} + \\beta\_2 RTV\_{i,t} + \\beta\_3 S\_{i,t} + \\beta\_4 V\_{i,t} + \\rho\\, ILS\_{i,t-1} + \\epsilon\_{i,t} $$

The slope on relative volume is the one that shows up on every book. After 22 March 2023, 7,749 hours, Kraken's slope is 2.899: one extra percentage point of the hour's volume on Kraken raises Kraken's leadership share by 2.90 points, holding the spread, the volatility, the return, and last hour's share fixed. Coinbase's slope is 1.591\. Bitstamp's is 0.974\. Binance futures' is 0.538\. The paper's prose pairs a 0.7 point Bitstamp slope with a 2.9 point Kraken slope. The 0.706 is Bitstamp before the fee, in the other regression. The 2.899 is Kraken after. Same sign, different samples. Do not quote them as one fit.

Kraken's average hourly volume is 4.24 million dollars against 849.31 million across the eight books in the hourly summary, about half a percent of the dollars. A one-point move in relative volume is a large change in Kraken's own size. The slope is steep because the book is small, and the level of the share stays small: Kraken's post-fee average leadership share is 1.90\. Add the 2.90 points and you are still at a satellite. Binance futures average 511.15 million dollars an hour against Coinbase's 21.27 million, about 24 times the dollars, and the futures book is where the level of the share sits.

The spread slope is real and smaller. After the fee, one extra basis point of effective spread cuts Coinbase's share by 0.815 points and Binance futures' share by 3.269 points. Binance futures' full-sample estimated spread averages 0.33 basis points, so a doubling of that estimate is 3.269 times 0.33, about 1.08 leadership points. That is a nudge next to a regime shift of several dozen points. The intercept is the fitted share when return, relative volume, spread, volatility, and the lag are all zero. Before the fee, Binance spot's intercept is 53.40, the fitted value on a zero row the sample never visits. The average leadership share on that book, from the venue table, is 84.13 before the fee and 7.31 after.

Read the spread coefficient in the units of the estimator they fed the regression. They had no full quote history, so the spread is the EDGE estimator, sampled at five minutes. In the one month they compare estimators to quote-based effective spreads, November 2022, Binance futures' quote-based effective spread averages 1.992 basis points and EDGE averages 0.544, 3.66 times smaller. Coinbase the same month is 1.462 quote-based against 1.860 EDGE. EDGE is close on the dollar book and low on the perpetual, and it flips the ranking: the quote-based month has the perpetual wider than Coinbase, while the EDGE column has it much tighter. The source calls EDGE the best fit in that table because it beats the other estimator on the level. On the perpetual, that "best" still sits 1.45 basis points below the quote-based spread. The slope of -3.27 is per basis point of EDGE. A quoted-spread basis point on the perpetual is about 3.66 of those EDGE units. The fee schedule is the cost fact that stands without this estimator. Binance spot was free until 22 March 2023 and 2.4 to 10 basis points for a taker after that. Binance futures takers pay 1.53 to 4.5\. Coinbase takers pay 5 to 60\. The explicit fee is what changed on the break date.

Volatility loads positive on the unregulated futures and negative on the regulated spot books. After the fee, one point of annualized volatility raises Binance futures' share by 0.125 and cuts Coinbase's by 0.166\. A 10-point vol move, against a full-sample average near 28 and a standard deviation near 28, is 1.25 points on the perpetual and 1.66 points off Coinbase, in two separate regressions. Do not add them and call it a transfer. The sign says the permanent move leans toward the leveraged book in the volatile hour.

## The fee date is the comparison

The red line is Binance spot. The pink line is Binance futures. Both are 7-day averages of the information leadership share.

![Seven-day average information leadership share by venue, November 2022 to March 2024. Binance spot falls from around 85 percent to under 10 percent at the end of March 2023. Binance futures rise from under 10 percent to around 50 to 60 percent and stay there.](https://storage.ghost.io/c/27/cb/27cb0fc8-2c77-4434-af9e-d5d32a916994/content/images/2026/10/article_462-ils_binance_fee_break.png)

Before 22 March 2023, Binance spot's average information leadership share is 84.13%. After the fee it is 7.31%, and Binance futures' average over that later window is 55.63%.

Across the full sample the unregulated futures take a leadership share of 50.80 on 79.01% of volume, unregulated spot takes 33.51 on 17.58%, and the three regulated dollar books take 15.68 on 3.41%, which is 15.68 / 3.41 = 4.60 times their volume share, while the futures' 50.80 is 0.64 times their 79.01% volume share. Kraken, Bitstamp, and Kucoin stay under 2 in both subperiods, and the brown Kucoin line that opens the chart dies within the first weeks, in line with Kucoin's own zero-fee window ending on 16 November 2022\. The full-sample futures share of 50.80 carries a standard deviation of 30.94 across hours. The old article "Price Discovery Across Venues: Polymarket Leads Kalshi (When Liquid)" finds the same tilt on a different product: the liquid book leads, and the other venue follows with the gap still open on a tradable clock.

The grouped Hasbrouck shares in the same table are 11.86, 28.52, and 59.86, and those three add to 100.24 rather than 100\. Rounding residue, or a small leak in the grouping. The component shares add to 100.00 and the leadership shares add to 99.99\. I use the leadership column, which is the one the source asked you to use, and I leave the 0.24 as printed.

## The 4 pm print leads for one hour

Coinbase's average leadership share in the hour starting at 19:00 UTC is 0.172, against a full-sample average of 0.132\. The ratio of those averages is 0.172 / 0.132 = 1.30\. That hour is 3 pm New York while the United States is on daylight time, and 2 pm New York while it is on standard time, which is why a UTC average understates the fixing hour. The orange line in the figure is the same share divided by that day's own 24-hour average, plotted on a New York clock. It peaks in the hour starting at 15:00.

$$ RPD\_t = \\frac{PD\_t}{\\frac{1}{24}\\sum\_{h \\in d} PD\_h} $$

Relative price discovery is the hour's leadership share divided by the average of the 24 hours in the same day. A value of 1.30 means that hour carries 1.30 times the day's typical Coinbase share. The figure averages this daily ratio. The 1.30 above is a ratio of full-sample averages, a close cousin of the plotted line.

![Coinbase information leadership share relative to its daily average, by hour. The orange line, on New York time, peaks in the hour starting at 15:00. The blue line, on UTC, peaks later, around 19:00 to 20:00.](https://storage.ghost.io/c/27/cb/27cb0fc8-2c77-4434-af9e-d5d32a916994/content/images/2026/10/article_462-coinbase_ils_by_hour.png)

After the fee, with return, relative volume, spread, and volatility in the regression, the dummy for 3 pm to 4 pm New York time adds 10.49 points to Coinbase's leadership share. The standard error is 2.00\. Kraken's dummy is 0.76 and Bitstamp's is 0.11, neither distinguishable from zero. Coinbase is the volume inside the CME CF Bitcoin Reference Rate, the New York variant, the volume-weighted median of eligible prints from 3 pm to 4 pm New York. Kraken and Bitstamp are on the constituent list, and their dummies sit inside the noise. The interaction of the dummy with relative volume is -1.04, so the volume slope is weaker in that hour. The 10.49 is what remains with relative volume and the spread already in the regression. During the zero-fee window the same dummy is -1.43 and insignificant. The fixing hour shows up once Binance spot is no longer free.

The daylight-saving regression is the causal claim, and the coefficient needs the design in front of it. They keep the 7 pm UTC hour and the 8 pm UTC hour. Under daylight time, 7 pm UTC is the fix. Under standard time, 8 pm UTC is the fix. The interaction of "this is the 7 pm UTC hour" with "daylight time is in force" is 0.346, standard error 0.170\. They read 0.346 as the window lifting Coinbase's relative share by 34.6%, and they multiply by 16.82 to get about 5.8 points of the whole system's share. The product is 0.346 times 16.82 = 5.82\. The 16.82 is Coinbase's post-fee average in the venue table, and the regression is post-fee, so the base matches that sample. The full-sample Coinbase average is 13.20, and 0.346 times 13.20 is 4.57\. The paper's sentence says "during our sample" while pointing at a table with three panels. The 16.82 lives in the post-fee panel.

The design problem is larger. Because the fix and the control hour swap when the clocks change, the interaction equals the sum of the two within-season contrasts you can back out of the same coefficients. The 7 pm dummy is -0.105\. Treat-minus-control in standard time is 0.105\. Treat-minus-control in daylight time is -0.105 plus 0.346, which is 0.241\. Those point estimates add to 0.346\. Reading 0.346 as the effect of a single fixing hour adds the two seasons. Neither main effect is significant on its own. I keep 0.346 and 5.82 as printed. The one-hour effect on a New York clock, already in leadership-share points, is the 10.49 dummy.

A placebo that shifts the daylight dates by three months produces an interaction of -0.28, the wrong sign, starred at the 10% level. The paper's text calls the robustness checks insignificant. The star is there. The same specification on the 5 pm UTC pair and the 9 pm UTC pair is flat, and so is the interaction on Kraken, Bitstamp, and the USDT books. A further interaction with the 8 January 2024 ETF approval is 0.414, significant only at 10%, and the sample ends in March. Leave it.

At the desk this chooses the fair value you quote around. If you quote Coinbase, or you mark a spot ETF to the 4 pm New York rate, the fair value for the other 23 hours is the perpetual, adjusted for the funding you can see. In the fixing hour Coinbase's leadership share steps up by 10.49 points. Coinbase's post-fee average is 16.82, and the post-fee futures group averages 67.47, so the busy hour on the reference-rate book leaves the perpetual holding the permanent move. I am against calling the 4 pm print the price that was discovered. You can mark the fund to that print, because that is the contract, and you are marking a follower that has one busy hour. The old article ["Why Retail FX Execution Is Not the Same as Interbank FX"](https://aligrithm.com/why-retail-fx-execution-is-not-the-same-as-interbank-fx/) is this split in currencies. The ticket the customer trades is downstream of the price that moved.

Two measurement holes change how hard you lean on the ranking. Exchange clocks disagree with each other. For November 2023 they recompute the shares on the vendor's receipt time. Binance futures' leadership share moves from 0.519 on exchange time to 0.484 on receipt time, and OKX futures move from 0.142 to 0.180\. Binance futures stays the leader on both clocks. "Small," their word, is 3 to 4 points on the futures books. On the hours the cointegration test fails, about 13% of hours, the model returns no share, and those are the hours a cross-venue hedge is least glued together. The quoted-mid check, which would answer the charge that trade prices favor the book that prints most often, is unreported. They say the ranking holds. There is no table behind that sentence.

The volume slopes have the same problem one level down. Relative volume is exchange-reported dollars. These venues have a wash-trading reputation, and the regression says reported relative volume is what lifts the share. A book that trades with itself can look like a price setter on this metric. The fee-date break is harder to wash away: the commission changed, the spot book died, the perpetual took the permanent move. That is the fact I would underwrite. The 50.80 is a noisy average on top of it.

![](https://storage.ghost.io/c/27/cb/27cb0fc8-2c77-4434-af9e-d5d32a916994/content/images/2026/10/article_462-visual-0.png)

## KEY POINTS

- Sample the eight trade prices at 10 milliseconds before you estimate the error-correction model. At one second the Hasbrouck bounds on one book cover almost the whole range from 0 to 1.
- Form the information leadership share by dividing the Hasbrouck share by the component share and squaring. In the hand example, shares of 0.55 and 0.40 become a leadership share of 77.07, against 22.93 for 0.45 and 0.60.
- Split the sample on 22 March 2023\. Binance spot's leadership share falls from 84.13 to 7.31 when the zero fee ends, and Binance futures average 55.63 after that date.
- Keep the full-sample weights next to the volume. Unregulated futures hold 50.80 of the leadership share on 79.01% of volume. Regulated dollar spot holds 15.68 on 3.41% of volume, 4.60 times its volume share.
- Add 10.49 points to Coinbase's leadership share in the 3 pm New York hour after the fee, and hedge the other hours off the perpetual. Read the daylight-saving interaction of 0.346 as the sum of two seasonal contrasts, 0.105 and 0.241.

## References

- [Price Discovery Across Venues: Polymarket Leads Kalshi (When Liquid)](https://aligrithm.ghost.io/price-discovery-across-venues-polymarket-leads-kalshi-when-liquid/?ref=aligrithm.com)
- [Why Retail FX Execution Is Not the Same as Interbank FX](https://aligrithm.com/why-retail-fx-execution-is-not-the-same-as-interbank-fx/)
- [Where is the Price of Bitcoin Determined? (Cosenza and Stalder)](https://papers.ssrn.com/sol3/papers.cfm?abstract%5Fid=4983566&ref=aligrithm.com)

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**A note on AI.* The ideas, research, analysis, and conclusions in this article are my own. I use AI tools to help with editing and wordsmithing, because English is not my first language, and I am not shy about that. AI-generated ideas and AI-assisted writing are not the same thing: the first is empty slop from a generic prompt, the second is a tool for communicating years of real research more clearly. Judge the work by its substance, not by whether software helped polish the prose.*