Who sets securities1 A security is a financial instrument that represents ownership, a creditor relationship, or rights to ownership in an entity. It can take various forms, including stocks, bonds, or options, and is typically traded on financial markets. Stocks (equity securities) signify ownership in a company and a claim on a portion of its assets and earnings. Bonds (debt securities) represent a loan made by an investor to a borrower, usually corporate or governmental, with the promise of repayment with interest. prices, and how? These simple questions—and their answers, which are more complex but in some ways just as straightforward—often get lost in the reporting on financial markets. Whether the “line goes up” or “line goes down” on a stock chart, we rarely stop to ask, “Wait, what even is this ‘line’, at a fundamental level?”
When you Google the current market price of Apple or Nvidia, and it shows you an amount of currency per share of stock, what does that price mean in a literal sense? Who sets it? What causes it to change? Within the scope of financial markets, these quantities have specific meanings. Yet when they’re discussed among the broader public or in the business press, the experts’ explanations often feel like a physics professor describing particle interactions by saying an electron “wants” to be repelled when it encounters another electron – that is, in a way intended to be pedagogically useful, though clearly not the full story. So you’ll often hear arcane phrases about how “the market price of a stock is determined by the market forces of supply and demand,” about how its price was “pushed up” by there being “too much supply relative to demand,” about how it’s “overvalued” and “due for a correction,” and so on.
If you’ve ever read or heard statements like these and thought, “Okay, sure…but what exactly do you mean by ‘pushed’? What is actually happening when this occurs?” – then this essay is for you.
Frederic S. Lee, a heterodox economist known for his significant contributions to price theory for industrial firms, emphasized that, fundamentally, prices are directly administered by firms according to a cost-plus markup equation; his research drew upon many foundational surveys of business owners who were asked how they set their prices.2 See John Michael Colón, “Wobbly Economics – PaaI” in Strange Matters Issue Two (Spring 2023), as well as my essay “Notes Towards a Theory of Inflation” in Strange Matters Issue One (Summer 2022) He noted that these firms are generally hesitant to raise prices for fear of losing customer goodwill, and as a result, markets for their goods exhibit a surprising degree of pricing discipline (or stability) over time – in contradiction to standard neoclassical economic theory, which posits that a market which is operating efficiently will adjust prices significantly more readily to changes in supply and demand conditions than observed reality would suggest. Ultimately, this research led him to totally reject orthodox microeconomic theory and its concepts of equilibrium prices, marginalism, price discovery, and so on; instead, he replaced these with his own model based on the theory of administered prices.3 See Frederic S. Lee, Post-Keynesian Price Theory (1997) and Microeconomic Theory: A Heterodox Approach (2018).
During a lecture on the topic of price theory,4 See (in John Michael Colón’s nomenclature) Lecture 6 starting at 08:00 and Lecture 9 starting at 42:00. These are unfortunately a privately recorded session of Lee’s graduate economics course at University of Missouri Kansas-City. Audio available upon request. a student asked Lee if his theories on price administration extended to asset markets, such as the New York Stock Exchange (NYSE). Lee acknowledged that, in his estimation, these prices were a different beast: while their fluctuations might sometimes resemble the predictions of neoclassical economists, they were actually governed by what he called “administered rules.” What he meant by this is a bit vague, but he seemed to mean that the operational rules of securities exchanges, as institutions, acted similarly to an auctioneer setting prices. Rules of this sort, he seemed to think, would dominate or at least significantly guide the pricing procedure of the relevant markets, and perhaps account for their unusual behavior compared to the rest of the economy.
The exact nature of Lee’s auctioneer (as well as the dynamics that might result from such a construct) was left unspecified. When we examine the price dynamics of securities on exchanges like the NYSE, we encounter a far more complex and intriguing reality – one whose fluctuations demand to be understood on their own terms. Although the exchanges themselves and their operational needs as businesses play a role in some price-setting processes, for the most part they actually serve a supporting function to the market participants who use them as trading venues – individual traders, institutional traders, market makers – and it is these actors whose trades directly determine price formation.
Church and Wall Street, New York City.” Published 1909 by The American
Art Publishing Co., New York City. #R-43919. The back reads,
“The New York Stock Exchange, located on Broad Street,
with an entrance on Wall Street, is built entirely of carved white
marble. It was founded on May 17, 1792, the present building
was finished in 1903. The board room is 112 by 138 feet and
80 feet high with the ceiling in gold relief. There are 1100
members trading daily from 10 A. M. until 3 P. M.” Wikimedia
Commons, Public Domain.
However, as we will see, while traders ultimately administer prices by submitting their orders to trading venues, they do not do so entirely at their discretion. Contrary to the views of neoclassicals and, to some extent, Lee, the reality of price formation in financial markets is far stranger and more complex than most theorists have envisioned. Yet, out of this complexity, financial markets exhibit a surprising resilience and a fine structure, reminiscent of the price-administrative operations in industrial firms. All this is well worth exploring. It turns out that the relatively high degree of volatility and the clustered, often unpredictable trading activity characteristic of these financial markets give rise to important statistical regularities that offer clues about the pricing procedures underlying them at the micro level.
Starting in the late 1970s and continuing to the present day, a little-known subfield of economics known as market microstructure has focused on the microfoundations of financial markets, moving away from many mainstream financial economic models like the efficient-market hypothesis5We shall return to this concept later on. in favor of models better-grounded in observed phenomena. This empirical approach led market microstructure researchers into uncharted territory, where access to significantly better data at the turn of the twenty-first century led them to a structural break from most of the rest of mainstream economics. These dissident neoclassical economists (a phrase I never thought I’d write, by the way) essentially forced a Copernican Revolution for the field. This choice made by the sub-discipline starkly contrasts with the broader discipline of economics, which often ignores data that contradicts its theories.
My goal in what follows is to cut through the jargon and focus on the concrete, measurable realities of how prices are set and evolve in financial markets, to reformulate the vague and often misleading notion of equilibrating supply and demand curves yielding some market price into a more accurate and precisely defined price-administration process driven by trading activity itself. By the end of this exploration, I aim to develop a theory of price formation that not only respects but is firmly grounded in the well established empirical facts of financial markets – in keeping with the laudable empirical turn of the market microstructure economists.
So, grab a cup of coffee, settle in, and grab a microscope, because we’re about to take a close look at how the formation and evolution of security prices depend primarily on the price-setting actions of individual market participants – and how out of this complex process, securities prices are administered.
Part I:
Limit Order Books:
Their Mechanics and Basic Dynamics
In order to prepare you conceptually for the theoretical argument that follows, we need to take a trip through the basic elements of financial markets.6 In the section that follows, my description of financial market operations is a synthesis for laymen of various technical sources. The most important of these, and the best introduction for anyone who wants to dig deeper, is Jean-Philippe Bouchaud, Julius Bonart, Jonathan Donier, & Martin Gould, Trades, Quotes and Prices: Financial Markets Under the Microscope (2018). Another good source is Daniel Spulber, Market Microstructure: Intermediaries and the Theory of the Firm (1999). Where I felt it would help readers to have sources for the definition of specific terms, I’ve added additional footnotes with page reference to Bouchaud et al and Spulber, or with references to articles from common authorities like Investopedia. Although you’ve likely heard of each of these terms at least in passing when a bit of financial news flashes across the screen or appears in your social media feed, it’s important to understand each of the terms and how they fit together in the real operations of financial markets. Please note that while I’m going to be using stock markets for our examples, these concepts apply broadly across markets for all types of securities (including commodities, cryptocurrencies, bonds, forex, derivatives, and much more).
Basics of the Book Itself
Orders, limit orders, and market orders
Let’s start with the most elemental building block of any financial market: the order. What is an order? It is a commitment to buy or sell a given quantity of an asset at some given price. There are four required attributes for an order: its sign (is it a buy or a sell – often denoted with a + or -, respectively), its price (quantity of a currency to be paid), its volume (a quantity of the chosen security), and its submission time (when the order was successfully submitted into a queue at a trading venue).7 This could be an exchange like the New Stock Stock Exchange (the type of trading venue we’ll be discussing most in this essay). But there are other types of venues as well, with one major type being alternative trading systems (ATSes). To help you remember the attributes, please refer to this succinct notation:
x := (s, p, v, t)8 Bouchaud et al, p. 45.
Where the order x has its sign ‘s’ (+ or -), a price ‘p’, a volume ‘v’, and a submission time ‘t’. There are many different types of orders one could make, but all of them need at least these four attributes in order to be accepted into an order queuing system. The two most common types of orders (and the ones we will be referring to most frequently in this piece) are limit orders and market orders.
Limit orders at their most basic level are orders submitted with a specified price that is the worst price (the maximum for buyers, the minimum for sellers) the trader who set it is willing to accept. These orders signal a specific price intention, and the traders who submit these orders are essentially saying they’re willing to wait if they have to in order to get their preferred price (or better). Market orders, on the other hand, are orders that are submitted with no specified price – traders who submit these orders are signaling that they favor speed of execution over price. For all practical purposes, you can think of it this way: limit orders have prices set by market participants, whereas market orders do not initially have prices because participants who place them care more about speed.
You might be asking yourself: if market orders don’t have prices, isn’t that a violation of the basic conceptual order attributes that were just mentioned? The answer is no, as they are still technically submitted with a price – it’s just set to null. That said, a market order does eventually acquire an actual price – when it is matched by the financial market’s algorithm to a limit order of the opposite sign. This is called order execution, or filling an order.9 Investopedia. “Execution.” Investopedia. Last modified August 17, 2023. https://www.investopedia.com/terms/e/execution.asp. The price that any market order ultimately gets executed at is always a price that had been set not by “the market” but by some other market participant, a counterparty whose limit order has been matched to this market order – and so the market order (which had a price of null) is ultimately executed at the price of the limit order to which it was matched. Hence, the answer to the question, “who sets prices on financial markets” is always, eventually, “market participants who set limit orders to buy or sell at a particular price” – though it takes matching with a market order for that command to be carried out.
When an order executes on the market, what it means is that a market order (say, to buy) at the null price has been matched with a limit order (say, to sell) at some particular price, so that the seller gets the buyer’s cash and the buyer gets ownership of the security (say, a stock). The relationship between this operation and the price of the security is relatively straightforward. When you see a price for a particular stock, option, currency, etc. quoted (e.g., “TESLA is at 
x/share. Let’s walk through a few examples where orders of each sign are executed, resulting in fluctuating market prices for the stock and an evolving limit order book.
We begin with a simple example of a LOB where a market order interacts with limit orders. This example will illustrate how a market order affects the order book and influences price dynamics.
The market price (the last-executed price) starts at 
50” instead of “
100” if executed nets the seller 300 x 100 = 
51.00
50.50
50.25
51 will never be executed unless a market order to sell comes in. Similarly, a limit Ask order to sell 50 shares at 
51.00
50.50
52
52.10The buy order for 200 shares moves down the Ask column from top to bottom. It first fills the 50 shares at 
52. There were originally 200 shares in the 
52 price. Meanwhile, the stock’s new market price is 
52 is the limit price of the last filled component of the trade we just executed.10 And now comes the answer to my quiz question in the previous footnote. Did you figure it out? Part of the trick is that each limit order is (probably) placed by a different seller. So the first seller, whose 50 shares were all consumed by the order at 
2,575 from the transaction. The second seller, who sold only 150 of the 200 shares they wished to sell for 
7,800 and still has 50 shares to sell. This means the buyer, to acquire their 200 desired shares, spent a total of 2,575 + 7,800 = ![10,375. This is a good exercise to repeat for each of the transactions below! Also note that the very same single large order can experience execution at very different prices as it chews through the order book. When a single order is executed at multiple price levels, market practitioners often take an average of these different levels, weighted by the number of shares at each price level, to gauge their performance. Basically, you take the money total and divide it by the number of shares ordered. This is called the <strong>average execution price</strong>. In this case, the average execution price was [ (51.5 x 50) + (52 x 150) ] / 200 =](https://i0.wp.com/strangematters.coop/wp-content/ql-cache/quicklatex.com-ed820eb6922ea4ccf5678c075cdd075e_l3.png?resize=1070%2C18&ssl=1 "Rendered by QuickLaTeX.com")
51.88. The average execution price for the same security can vary significantly depending on the composition of the limit order book.
Here’s how the new LOB will end up looking:
| Bid (Buy) | Ask (Sell) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
100 shares,  52 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
50 shares,  52.10 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
200 shares,  51.00* | 50 shares,  50.50* | 100 shares,  50.25*150 shares,  50.25 (the price of the last batch used to fill the order – i.e., the third box down the left column of the LOB). The new LOB looks like this:
In this rather extreme example, the entire Bid side of the LOB is filled, leaving no liquidity on the Bid side. And yet 50 shares from the market sell order remain unfilled. Hence the rest of the market sell order sits in queue, awaiting new limit buy orders (Bids) to match with. Let’s say that buyers who had been sitting on the sidelines observing the past 10 minutes of trading take notice and sense an opportunity to buy at a good (read: low) price.11 That is, they believe that despite the fact there’s a selloff currently underway, the security’s market price will soon appreciate, meaning that now is a good time to get a cheap deal since they expect it to increase in price soon enough to yield a nice profit. This practice is called buying the dip. That said, like all trades it carries risk – in this case, that you aren’t actually at or near the bottom of the dip, and that the security’s market price will only continue to decline and not actually increase anytime soon. Presumably the participants who initiated the selloff in the first place are under just such an impression and wanted to cut their losses, getting out of their position while they still could. Who’s right? Well, who cares? (They do, since they’ve put money down on the question, but what about us?) The more important point for our purposes is that, no matter who’s right, the answer has less to do with the inherent value of the security, necessarily, than it has to do with the limit and market orders participants will place in the next day or week – since it is this which generates the interaction between the LOB and market orders that causes prices to move. Those decisions by market participants may reflect the value of the security – or merely their impressions about its values. Or, it may be decided by entirely different factors – perhaps different ones, depending on the participants and their strategies. They could, for example, just as easily be trying to predict each others’ behavior, something I’ll be discussing later in the essay. These buyers replenish liquidity by placing limit buy orders, refilling the Bid side of the limit order book with three new limit buy orders:
Next, a new market buy order for 200 shares comes in. The buy order is matched with the best-available Ask, which happens to be the new limit sell order that arrived only a moment ago. Let’s see how the order book handles this one:
The result is a commonplace one: despite a rather large market order, the stock’s new market price ends up completely unchanged after the transaction, remaining at Once again we can see that the market price of a security is generated by the interaction of the limit prices set by some participants in the LOB with unpriced market orders set by others outside of it, which are matched by the algorithm according to its (usually price-time) priorities. This system does not particularly lend itself to notions of these prices tending towards any equilibrium whatsoever. However, it does suggest the possibility – indeed, the commonality – of nonlinear and stochastic dynamics in price movements that could suddenly, after a period of stasis, launch them in unexpected new directions. LiquidityHaving explored the concept of order flow and examined some practical examples of how trades are directed and executed in financial markets, we can now turn our attention to the fundamental notion of liquidity. In order-driven markets, liquidity is intricately tied to the depth of priced orders available at various price levels in the LOB, which (as we’ve seen) directly influences the ease with which trades can be executed without significantly impacting prices. At first glance, the section header above might feel like an overly basic one. It’s just the amount of money in a system, right? Well, liquidity in financial markets as conceived by market microstructure theorists means something a little different than, say, liquidity in the banking system, or elsewhere. Remember, financial market operations run on orders, and those need to be supplied by market participants at some price chosen by the participants. Liquidity in market microstructure research refers to the ability of a market to absorb large orders without a significant impact on the price of the asset being traded. It is a crucial concept, as it affects the ease with which participants can execute trades, especially in financial markets where large volumes of assets are exchanged daily. High liquidity implies that there are enough priced orders in the LOB on both sides of the book, allowing transactions to occur quickly and with minimal price fluctuations. Conversely, low liquidity can lead to greater price volatility, as large trades can move prices significantly, making it more difficult for participants to execute their orders at desired prices. In the context of an LOB, liquidity is often understood as the depth of priced orders – which, you’ll recall, means the number and size of buy and sell orders at various price levels. The depth of the order book indicates how much volume is available at each price point, and thus, how much the price might move in response to a large order. A deep order book, with substantial volume at many price levels, suggests high liquidity because it can accommodate larger trades without causing significant price changes. This depth is critical for traders, particularly those executing large orders, as it reduces the likelihood of slippage – where the final execution price deviates from the intended price due to insufficient liquidity.12 To elaborate: in the context of trading, slippage refers to the difference between the expected price of a trade and the actual price at which the trade is executed. It typically occurs in fast-moving markets or when a large order is executed in a relatively illiquid market, causing the order to be filled at different price levels. Slippage can be positive (better execution price than expected) or negative (worse execution price than expected), though it is more commonly associated with negative impacts on the trader’s strategy. Slippage is particularly significant in high-frequency trading, algorithmic strategies, and during volatile market conditions, where rapid price fluctuations make it difficult to execute trades at desired prices. Liquidity is not static and can fluctuate based on market conditions, the actions of large market participants, and other phenomena endogenous to financial markets that we will explore more deeply further down. Various measures are used to quantify liquidity in the LOB, including bid-ask spreads, market depth, and the price impact13 Price impact in market microstructure literature refers to the apparent impact that an individual trade, or trades, have on the market price of the asset being traded. As we’ve already seen, and will continue to investigate, modeling price impact is highly non-trivial. of trades.14 Widely cited works in market microstructure research that discuss liquidity and its implications include Maureen O’Hara, Market Microstructure Theory (1995), which offers a comprehensive overview of how market structures impact trading and liquidity; and “Continuous Auctions and Insider Trading” by Albert S. Kyle (1985). Another important work is Jón Daníelsson and Richard Payne, “Measuring and Explaining Liquidity on an Electronic Limit Order Book: Evidence from Reuters D2000-2,” Bank of International Settlements website (https://www.bis.org) (3 October 2001), which explores the specifics of liquidity measurement in LOBs. Market microstructure research has developed several specific measurement statistics to quantify market liquidity, which are essential for understanding the ease with which trades can be executed without significantly impacting asset prices. It’s easy to get the terms mixed up, so let’s review them and trace their relationship to one another. Among the most commonly used measures is the bid-ask spread, which as we’ve seen represents the difference between the best available bid price (the highest price a buyer is willing to pay) and the best available ask price (the lowest price a seller is willing to accept). A narrower bid-ask spread indicates higher liquidity, as it suggests that buyers and sellers are willing to trade at prices close to each other, reflecting a more competitive market. Another critical measure is market depth, which you will recall assesses the volume of buy and sell orders available at different price levels in the LOB. Market depth indicates how much of an asset can be traded without causing significant price changes; greater market depth signifies higher liquidity, as large trades can be executed with minimal impact on prices. Depth is often analyzed at specific price intervals away from the best bid and ask, providing a more detailed view of how liquidity is distributed across the order book. Additionally, price impact measures the extent to which large trades affect the asset’s price. This impact is typically evaluated by observing the price movement resulting from a trade of a certain size, where a lower price impact implies higher liquidity, indicating that the market can absorb large orders with minimal price disruption. Price impact functions and Kyle’s lambda (introduced by Albert S. Kyle in 1985 – a model which we will explore more shortly) are tools used to quantify this effect, with Kyle’s lambda specifically measuring the linear relationship between trade size and price changes. Furthermore, the Amihud illiquidity measure, proposed by Yakov Amihud in 2002, captures the daily price impact relative to trading volume, calculated as the absolute price change per unit of trading volume, averaged over a period. A higher Amihud ratio indicates lower liquidity, as it suggests that price changes are more sensitive to trading volume. Lastly, the turnover ratio reflects trading activity in relation to the size of the market, calculated as the trading volume divided by the number of shares outstanding, where a higher turnover ratio suggests higher liquidity because it indicates that a large proportion of the asset is being traded frequently. These statistics offer various perspectives on liquidity, enabling researchers and market participants to assess the ease of trading and the resilience of the market to large orders. Finally, let’s make sure to connect this concept of liquidity back to our knowledge of the limit order book. If you think back to the LOB examples, you will probably recall instances where a large market order came in and “chewed through” multiple price levels in the book, causing the market price to change. The term of art for this is walking the book – a concept long known intuitively to traders, but only recently examined empirically by market microstructure researchers. A LOB with high liquidity will be able to resist the ability of any one market order to walk the book, leading to fewer price changes; the bigger and more numerous the market orders that come in, the faster the LOB’s liquidity will be depleted. As you also saw in the examples, a liquidity refill refers to the process by which new limit orders may be added to the LOB, restoring liquidity at specific price levels. Just as new market orders potentially deplete liquidity and reduce the depth of the book, refills potentially restore liquidity and increase the depth of the book. Liquidity refills – whether done manually or with automated trading algorithms – stabilize the market by ensuring that there is always some level of liquidity available, which can reduce the volatility caused by large trades and maintain more orderly market conditions. It is this one-two operation of book-walking followed by liquidity refills (with eventual reversals in the directionality of the trades – from buy to sell, or vice versa) that constitutes a good deal of the liquidity shifts we see in LOBs. The Players and Their TechniquesHaving explored a simple model of price dynamics within the LOB, let’s now proceed to take a brief tour of the market participants who might make use of it. Who are they? What do they want? And how do they go about getting it? While not comprehensive, the discussion that follows will give you an overview of various important players, the moves they might make, and how these affect the order flow and hence the price determination of securities markets. TradersLet’s begin with the most simple sort of player: your typical trader. Only, no trader is really typical when you think about it. They might be a lone individual or the employee of a large firm – a retail trader looking to make money for themselves, or an institutional trader managing the assets of an investment bank, hedge fund, pension program, etc. It is very difficult to generalize about traders. They can adopt all sorts of trading strategies, from value investing that seeks to profit off the inherent value (whatever that is!) of presently undervalued securities to momentum investing that tries to buy securities that have already been moving up in price while selling off any securities that have been moving down in price over some recent period. They operate at different time scales, from day traders who buy and sell within a single trading day to position traders who hold onto securities long-term in the hopes they will continually appreciate. And indeed, different traders will play with different sorts of securities: some will deal in stocks, others in derivatives such as options and futures, yet others in the currency pairs of foreign exchange (forex) markets, and yet again others in the raw materials and agricultural products which the exchanges call commodities. There is much more to be said about the many different kinds of traders and their divergent perspectives than I can fit in this essay – stay tuned for future work on this subject – but for now it should suffice to say that the most common rule of thumb among them is one you’ve probably heard of: whatever security you deal in, buy it cheap and sell it dear, so that you can pocket the difference. If you know anything about financial markets, you probably already had at least a vague sense of the above. But now that you’ve understood the basic mechanics of the limit order book, you should have a sense of how traders in general affect market prices and why that’s so important. Because ultimately, it is the traders who are in the driver’s seat when it comes to the evolution of securities prices throughout the trading day, as we’ve already examined using simplified examples of LOBs. By submitting limit orders, traders set the prices at which orders may or may not get executed throughout the trading day. As these orders are continuously matched (or not) on the exchange’s order book, they drive price changes in real-time. Market MakersFor a more complex example of a major player, we might look at market makers, one of the key providers of liquidity. These participants help ensure the stability of financial markets by continuously quoting buy (Bid) and sell (Ask) prices for various securities. They stand ready to buy or sell these securities from their own inventories, thereby facilitating trades and stabilizing prices through the liquidity this adds to the system.15 The role of market makers has evolved significantly from the early days of financial markets, where individual traders at exchanges specialized in providing liquidity for specific securities. These individuals, often known as specialists or floor traders, would stand ready to buy and sell particular stocks, ensuring that there was always someone willing to trade, thereby maintaining an orderly market. Over time, as markets grew in size and complexity, the role of market maker transitioned from one performed by individuals on the trading floor to one managed by large corporations equipped with the most advanced technology. These corporations now act as designated market makers (DMMs) for exchanges, managing liquidity across thousands of securities. Despite the shift from individual traders to sophisticated algorithms run by large firms, the basic business model of market making has remained largely the same: market makers earn profits by capturing the bid-ask spread. They also provide critical services to the market by ensuring continuous liquidity, facilitating smooth trading, and reducing price volatility. The evolution has been driven by the need for greater efficiency and the ability to handle larger volumes, but the fundamental principles of maintaining liquidity and earning profits from spreads have persisted throughout. Examples of market makers include investment banks, brokerage firms, and specialized trading firms. For instance, firms like Goldman Sachs and Morgan Stanley act as market makers in equities, bonds, and derivatives, while proprietary trading firms such as Citadel Securities and Virtu Financial focus on high-frequency trading strategies to provide liquidity. Additionally, stock exchanges like the New York Stock Exchange (NYSE) designate certain firms as designated market makers (DMMs) to manage the trading of specific stocks, ensuring an orderly market. By bridging the gap between buyers and sellers, market makers play a vital role in enhancing market efficiency and price formation. When the market makers update their bid and ask prices in the LOB, as they do continually based on market conditions and their own inventory levels, this is called a quote. These quotes facilitate liquidity and act as reference points in the market; they help to ensure that there are always buyers and sellers available as well as to maintain a stable and efficient trading environment. Generally, market makers aim to maintain a neutral inventory position – that is, they want to begin and end the trading day with as close to 0 of their particular asset on their books as possible. So how, then, do these people make money? The market makers’ revenue structure is too complex to go into here, but an oversimplified version for our purposes is that they have two sources of income: (1.) they’re paid a commission by the exchange, for the service of providing liquidity; and (2.) they try to make money on the round trip trade of all the operations they undertake on a trading day, which basically amounts to whatever money they make on orders16 The most obvious way the market makers could make money is off their sell orders. However, buy orders aren’t just costs – they can make money, too, under certain conditions. For example, if the market maker is in a short position – if they’ve sold some quantity of a borrowed security – and the market price of that asset decreases, then when they buy as much of the asset as they’d sold to close the position they’ll have made more money overall (because they sold when it was high and bought when it was low). Market makers do this all the time since they want to end the day in a neutral inventory position. But any trader can make money the same way, if they think some asset will depreciate for whatever reason. Market makers are often juggling such typical trading considerations alongside their duty to provide liquidity to the market in general. They might do a short in order to pocket some money for themselves – or they might do it because they see an imbalance in the LOB and want to provide more liquidity on (say) the Ask side. minus their operating costs. An aside on the transition from quote-driven to order-driven marketsThe historical transition of financial markets from quote-driven to order-driven systems marks a significant evolution in trading mechanisms. In quote-driven systems, market makers or dealers play a central role by continuously providing buy and sell quotes for securities, thereby ensuring liquidity. These market makers profit from the spread between the bid and ask prices, and their willingness to trade at quoted prices stabilizes the market. This system was prevalent in many major exchanges, including the New York Stock Exchange (NYSE) and the London Stock Exchange (LSE), where human intermediaries facilitated most trades. With advancements in technology and the rise of electronic trading, financial markets gradually transitioned to order-driven systems. In these markets, all participants can submit buy and sell orders directly into a central order book, where trades are matched based on price and time priority. This democratization of trading access led to increased transparency, as all market participants could view the same order book and the associated prices. The move to order-driven markets has reduced reliance on intermediaries, which has lowered transaction costs. Exchanges like NASDAQ and electronic communication networks (ECNs) spearheaded this transition, ultimately transforming the landscape of global financial trading. While the shift to order-driven markets has transformed the landscape of financial trading, market makers continue to play a crucial role in providing quotes for securities prices, ensuring liquidity and stability. In contemporary order-driven markets, market makers are not just traditional intermediaries but sophisticated entities employing advanced algorithms to manage their inventory and mitigate risks. Their presence in the order book helps bridge gaps during periods of low trading activity, offering buy and sell quotes that enable other participants to execute trades efficiently. By continuously updating their quotes based on market conditions, they help maintain a balanced and orderly market. Thus, while the dynamics of their role have evolved, market makers remain vital to the smooth functioning of modern financial markets, complementing the decentralized nature of order-driven trading systems.17 The transition in securities markets from a quote-driven to an order-driven system parallels similar shifts in physical production industries, moving from a “push” to a “pull” model. In the former, firms would maintain large inventories and sell from stock, absorbing storage costs and restocking as needed. In the latter, technological advances enabled firms to scale production more efficiently, producing goods only as orders came in, thereby minimizing inventory. Likewise, in securities markets, the shift was facilitated by advancements in telecommunications and computing technologies, which enabled real-time tracking of orders and improved coordination between buyers and sellers. This allowed for more nimble price formation and liquidity provision without the need for market makers to hold large inventories of securities. For more on the transition in securities markets, see Hung-Neng Lai (2007). “The Market Quality of Dealer Versus Hybrid Markets: The Case of Moderately Liquid Securities,” Journal of Business Finance & Accounting 34, 349-373. For more on the transition from “push” to “pull” systems in industrial supply chains, see Shigeo Shingo, A Study of the Toyota Production System From an Industrial Engineering Viewpoint (1989), pp. 97-119. The ExchangesAs I’ve discussed at length, it is market participants themselves who are in charge when it comes to setting prices on securities markets. Stock exchanges, such as the New York Stock Exchange (NYSE), play a supportive role in the price-administration process by providing the algorithmic procedure by which market orders are matched to limit orders to execute a trade. Beyond this, prices are for the most part administered by traders in the pursuit of their many and sundry strategies. That said, exchanges do in certain very narrow and particular contexts take a more direct role in administering at least some securities prices – particularly during the opening and closing auctions, where they determine the reference prices for the beginning and end of the trading day. These reference prices are calculated based on the aggregation and matching of orders submitted by market participants. The exchanges have the authority to intervene in this process to ensure orderly markets, especially during times of significant imbalance, by facilitating additional liquidity or adjusting the mechanics of the auction. However, the primary function of the exchange even in these moments is to act as a facilitator that organizes and reflects the intentions of the market participants, rather than independently determining prices per se. It’s important not to exaggerate the role of the auction as a determining factor, however. The opening and closing call auctions on stock exchanges, like those at the NYSE, differ significantly from the auctions theorized by early economists such as Léon Walras (whose work we shall turn towards in more detail further down), particularly in their execution and the role of price formation. Walrasian auctions are theoretical constructs where prices adjust continuously until supply equals demand, resulting in a market-clearing equilibrium. In contrast, stock exchange call auctions are discrete events where orders are collected and matched at specific times (opening and closing), and the final price is determined by the highest volume of matched orders, rather than a continuous adjustment process. Moreover, stock exchanges allow for interventions by market makers to manage imbalances, whereas Walrasian auctions assume no such external influence. And, as of course we’ve seen, during the rest of the trading day there is no discernible equilibrating mechanism in anything that happens in the limit order book, and little reason to believe such a mechanism exists. To put the call auctions into terms of price administration, some market participants at the beginning and end of the trading day are essentially telling the exchanges that they are okay with ceding their price-setting to the exchange (and where applicable, designated market makers assisting exchanges). Similar to how those submitting market orders during continuous trading periods are essentially telling the LOB, “I’m ceding my ability to price-set to others in exchange for certainty of execution,” participants in the opening and closing call auctions are ceding their ability to price-set to the exchanges (who are arguably also “participants” in this instance – albeit a special class of them who are providing everyone with the trading venue themselves.) The reference prices that exchanges arrive at during their call opening and closing auctions are indeed functions of the priced orders previously submitted by market participants. In these call auctions, all orders for each particular security are gathered and matched at a single price that maximizes the volume of trades. This price is determined by the limit orders (i.e., priced orders) that participants have already submitted. The exchange’s algorithm considers these orders to find the price where the highest number of shares can be traded, often considering factors like minimizing order imbalance and maximizing the traded quantity. The table below summarizes six of the largest exchanges and the basic schematics of a trading day at each, along with their chosen matching algorithm for the continuous trading period.
IPOsLet’s go back to thinking about stocks, the most famous kind of security. So traders set prices as market orders are matched to limit orders; exchanges set reference prices at the start and end of the trading day to maximize executed orders at that moment, based on previous orders placed by participants in the limit order book; and at any given instant, the market price of the stock is nothing more than the price of the last executed order. That accounts for stock prices most of the time. But you may find yourself asking: wait a second, companies only start selling stocks on financial markets when they go public, which is a long and drawn-out process. Who sets the initial price of a company’s stock – known as its initial public offering (IPO) – before it becomes publicly listed on an exchange, and how? On what basis? To whose benefit? Although a complete analysis of the IPO process is beyond the scope of this essay, for the sake of completeness, allow me to give you a general description of the IPO price-setting procedure. Here, too, we can examine the process concretely using a price-administrative framework. Determining the IPO price for a company going public is a multi-step process involving both the company and corporate underwriters who typically work for investment banks. The process begins with the underwriters conducting a thorough valuation of the company, which includes analyzing financial statements, assessing market conditions, and comparing the company to similar firms that are already publicly traded. One common method used is the discounted cash flow (DCF) analysis, where future cash flows of the company are estimated and then discounted to their present value to determine an intrinsic value. Another method is the comparable company analysis (CCA), where the company’s financial metrics, like earnings and revenue, are compared to those of similar publicly traded companies to establish a valuation range.19 Yadav, Ajay, Jaya Mamta Prosad, and Sumanjeet Singh. 2023. “Pre-IPO Financial Performance and Offer Price Estimation: Evidence from India” Journal of Risk and Financial Management 16, no. 2: 135. https://doi.org/10.3390/jrfm16020135 Once the valuation is established, the underwriters gauge investor interest through a process called book building.20 Once the order book is fully built, and the underwriters have a clear picture of demand at various price points, they set the final IPO price. This price reflects a price level that satisfies both the company’s capital-raising objectives and the investors’ expectations for future returns. The final step involves allocating shares to investors, often prioritizing long-term institutional investors who are more likely to hold the stock rather than flip it for short-term gains. In market microstructure terms, book building is akin to a continuous auction process where underwriters act are essentially acting as market makers in the primary market for stocks (as opposed to in the more familiar (and much larger) secondary market of the exchanges), matching buyers and sellers while dynamically adjusting the auction parameters (i.e., price and quantity) based on real-time feedback from investors during the roadshow. During this phase, they conduct what are referred to as roadshows, where the company’s management presents its business case to potential investors, allowing the underwriters to collect feedback on the price range they would be willing to pay. Based on this feedback, the underwriters and the company narrow down the IPO price range. Finally, after considering factors like market demand, overall market conditions, and the company’s financial needs, the underwriters set the final IPO price. This price aims to balance the company’s desire to raise capital with the need to ensure strong post-IPO performance by leaving some potential upside for new investors. For instance, if investor demand is high, the final price may be set at the upper end of the range or even above it. Conversely, if demand is lukewarm, the price might be set at the lower end or even below the initially proposed range. MetaordersLet’s return once again to our main story of price formation in limit order books. Having established a foundational understanding of market microstructure, including the intricacies of LOBs and the role of market makers, we can now look into a somewhat more advanced (though no less foundational, as I will argue) topic: metaorders and the traders who place them. Metaorders are large trading orders that are strategically executed over a period of time, rather than all at once, to minimize market impact and achieve a more favorable average execution price.21 Viktor Bazylevych and Vitalii Ihnatiuk (2019). “Metaorder limit prices in evaluating expected market impact and assessing execution service quality.” Investment Management and Financial Innovations, 16(2), 355-369. doi:10.21511/imfi.16(2).2019.30 These orders are broken down into smaller, manageable portions to avoid sudden price movements that could result from a single, large trade walking the book – or from other traders noticing the large order and revising their orders in light of perceived urgency of whoever submitted the large order. Typically employed by institutional traders, metaorders require sophisticated algorithms and detailed market analysis to optimize execution. By carefully timing and placing these smaller orders, traders can obscure their true intentions from the market, thereby reducing the risk of adverse price changes that could be triggered by revealing the full size of their trading position. This is a very common form of strategic behavior in the LOB. As the metaorder is broken down into smaller portions, these individual trades gradually consume the liquidity available at various price levels in the order book. The hope of the trader who adopts a metaorder strategy is that this effect will happen slowly enough, and in small enough portions relative to the liquidity refills to the LOB, that the price will stay the same for the entire order, rather than changing adversely (buying becoming more expensive, selling less profitable) as the order is executed.22 Vincent Van Kervel & Albert Menkveld, “High-Frequency Trading around Large Institutional Orders,” The Journal of Finance 74:3 (June 2019), pp. 1091-1137. Now, there’s no reason to believe they’ll always succeed, of course. A metaorder can still significantly impact the price within the LOB – albeit spread out over a longer time period – due to its large size; and this will especially be the case if the metaorder execution strategy were to be prematurely discovered. If a substantial portion of the metaorder matches with existing limit orders, it can contribute toward a depletion of the best Bid or Ask prices, causing the market price to change. For example, a large buy metaorder can cause the market price to move upward as it absorbs the available priced sell orders, beginning with the best Ask, and continuing down the book. Conversely, a large sell metaorder can drive prices down by flooding walking down the price levels of the buy side of the book. A LOB without sufficient depth may find itself giving way before the metaorder despite its piecemeal arrival. Furthermore, when not properly monitored by the trader who is conducting it, a metaorder’s gradual but persistent execution can still create trends in the price movement, influencing other traders’ perceptions and actions within the market. As the metaorder slowly hits the LOB, observant traders may detect the unusual patterns of consistent buying or selling. This can lead them to infer the existence of a large underlying order, prompting strategic responses. Some traders might attempt to front-run the metaorder by placing their orders ahead of the anticipated price movement, to capitalize on the expected trend. Others might withdraw their orders, anticipating adverse price changes, thus reducing liquidity and exacerbating the metaorder’s impact. The perceived order imbalance can create a feedback loop, where the market reacts not only to the actual trades currently underway but also to expectations about the behaviors of other participants, further amplifying price movements. The concept of the metaorder first emerged formalistically in the theoretical discussions of market microstructure in the late 70s, though an intuition of its existence among traders long predates its inclusion in modeling efforts., Theory became more sophisticated as financial markets became more computerized. Early studies by economists and financial theorists began to explore the impact of large orders on market prices and liquidity. Researchers postulated that institutional investors, who typically handle significant volumes of trades, would break down their large orders into smaller ones to mitigate market impact and avoid signaling their trading intentions to the market. These early theories were grounded in the observation that executing a large order in one go could cause substantial price disruptions, making it less favorable for traders seeking optimal execution prices. The practical discovery and empirical validation of metaorders came with the advent of advanced trading technologies and the increased availability of high-frequency trading data in the late 90s and early 2000s. As algorithmic trading became more prevalent, it became possible to analyze and identify patterns consistent with the strategic execution of large orders. Researchers and market analysts began to uncover the sophisticated techniques used by institutional traders to distribute their large orders over time, confirming the earlier theoretical predictions that were based on comparatively more sparse empirical work. This period also saw the development of algorithms specifically designed for executing metaorders, such as VWAP (Volume Weighted Average Price) and TWAP (Time Weighted Average Price). (We will explore other more bespoke execution algorithms later on.) The ability to recognize and model the impact of these orders has since become a crucial aspect of market analysis and strategy development for both institutional and individual traders. The UpshotIf you’ve made it this far, congratulations! You’re already ahead of the curve compared to most economists and commentators in understanding the micro-level dynamics of LOBs, and by extension, some of the basic dynamics of security price administration. As I hinted at earlier towards the start of the essay, the question of who sets security prices (and how) is, on one level, straightforward: traders set the market price directly by submitting limit orders – priced orders – into LOBs, thereby providing the liquidity necessary to ensure a resilient order flow. But there is another, more complex side to the story. We’ve gone through what is happening at a concrete, simplified level. Now we must turn to the question how price formation perpetuates itself. We need to learn more about the resilience of order flow in the face of substantial fluctuations in trading activity, and rapid shifts in available liquidity. We also need to begin learning about past efforts to model these complex dynamics. The LOB serves as the central mechanism through which liquidity is managed and prices are formed for a given security in modern financial markets. By analyzing its basic operations and dynamics, we gain a clearer understanding of how orders interact to determine market prices, how liquidity is both provided and consumed, and the critical role that limit orders play in maintaining an orderly market. Liquidity, as defined in market microstructure, is not just the availability of buyers and sellers, but the depth, resiliency, and tightness of the LOB, which together influence the ease and cost of trading. This foundational understanding of the limit order book sets the stage for a deeper exploration of market microstructure theory. I will now trace the intellectual history that has shaped our best current views on how markets function, how prices are formed, and the ongoing evolution of trading mechanisms and market participants. As we transition into this next section, we will dive into the key theories and models that have been developed to explain the complexities of financial markets, starting with the seminal ideas that have driven market microstructure research.  Part II:An Intellectual History of Market MicrostructureHaving established an understanding of the mechanisms of LOBs, the role of market makers, and the complexities of metaorders—we now turn our attention to the intellectual history of market microstructure theory. This field, which emerged formally in the latter half of the 20th century, has provided insights into the micro-level workings of financial markets, particularly regarding how prices are formed and the dynamics of trading. By examining the evolution of market microstructure theory, we can appreciate the foundational ideas that underpin modern trading practices and the models used by market participants today. A key focus within this intellectual journey has been the theorization of metaorders and their impact on price. Early theorists sought to understand how large, strategically executed orders influence market prices and liquidity. Over time, their models have evolved to capture the nuanced behaviors of institutional traders and the resulting market effects. This section will explore the intellectual contributions of a range of thinkers from varying theoretical (and ideological) frameworks. Early ModelsLéon Walras (1874)The so-called Walrasian Auctioneer23See Bouchaud et. al., p. 6-9 model is a theoretical construct, first proposed by Léon Walras in the late 19th century, which describes an idealized market mechanism for setting prices in financial markets. Under this model, an auctioneer hypothetically calls out prices for goods and services, and then buyers and sellers submit quantities demanded and supplied at those prices. There is a strict functional relationship between the auctioneer’s price and the buyers’ and sellers’ quantities; when the former changes, so too do the latter in exact proportion. The auctioneer adjusts the prices iteratively, causing the quantities supplied and demanded to adjust in turn, until a market equilibrium is reached where the total quantity demanded equals the total quantity supplied. This process ensures efficiency in the allocation of resources and that the market can clear without excess supply or demand. One of the strong points of the Walrasian Auctioneer model is that it has a very straightforward mathematical formulation, which allows for the derivation of equilibrium prices and quantities under the assumption of perfect competition. It provides a basic building block for general equilibrium theory by showing how decentralized markets can yield fundamentally efficient outcomes. The model assumes – somewhat breathtakingly, this author thinks – that all participants have perfect information and that there are no transaction costs or frictions. This simplifies the analysis and makes the model a powerful tool for theoretical exploration, though not particularly useful for real-world modeling. The Walrasian Auctioneer model has several notable shortcomings. First, the assumption of an auctioneer who continuously adjusts prices until equilibrium is reached is unrealistic, as no such central figure exists in real markets. Presumably this is a metaphor for some emergent process that markets undertake in a more piecemeal and decentralized fashion, but if you try to observe it happening in the wild it will prove frustratingly elusive. Additionally, the model assumes that all trades occur only at equilibrium prices, ignoring the dynamics of real-world trading processes where prices are constantly in flux due to any number of potential issues – several of which we’ve already explored, and a few more that we shall visit further along (information asymmetry, market impact, order flow, liquidity constraints, and strategic behavior by market participants all being potential candidates). Consequently, however important the Walrasian Auctioneer model was to the development of neoclassical models, it falls short in providing a comprehensive understanding of the actual mechanisms, strategic behaviors, and really-existing decentralized price-administration that is driving market behavior, and with it, price formation. To give you an idea of the absurdity (sorry) of Walras’ idea for the general equilibrium, consider the following brief worked numerical example. Suppose we have a simple market for apples. There are three buyers and three sellers. Let’s say we have a market for apples, where multiple buyers and sellers exist. The auctioneer’s job is to find the equilibrium price where the quantity of apples demanded by buyers equals the quantity supplied by sellers: Initial Prices and Quantities
Adjusting the Price
Concluding the Auction
|
52
52 to 
2, while the market sell order (which ate up 2½ boxes) only decreased the stock’s market price by 
50 to 
52 to 
50.25*![52</td></tr><tr><td class="has-text-align-center" data-align="center"><em>[</em><em>NOTE</em><em>: </em><strong><em>50 shares</em></strong><em> of the market order remain to be filled!]</em></td><td class="has-text-align-center" data-align="center">100 shares,](https://i0.wp.com/strangematters.coop/wp-content/ql-cache/quicklatex.com-94bc5722652a8899db4ef21c156c4356_l3.png?resize=582%2C106&ssl=1 "Rendered by QuickLaTeX.com")
52.10
52
52.10
52
52.10
49.50
49.00
49.75.
49.50
49.00
52.10
49.75*
49.00
2! But here, the same market buy order left the stock price exactly where it was. 
2): At this price, buyers are willing to purchase 50 apples.
2, there is an excess supply of 20 apples (70 supplied – 50 demanded).
1.50): At the new price, buyers now want to buy 60 apples.
1.50, the quantity demanded equals the quantity supplied (60 apples each).
1 change in the price of the underlying asset, the price of the option would change by $0.50. Delta hedging involves balancing your position in the option with an opposite position in the underlying asset to reduce risk. If you own a call option (which benefits from the asset price going up) and you want to hedge against the possibility that the price might go down, you could sell some of the underlying asset. The amount you sell would be based on the delta. If the delta is 0.5, you might sell half as much of the asset as the option controls. This way, if the asset price moves, the losses on one side (the option) are offset by gains on the other side (the asset), keeping your overall position more stable. In essence, delta hedging helps you manage the risk of price movements by creating a balanced position that minimizes the impact of those movements on your portfolio. You can think of it like purchasing a temporary insurance policy against your underlying position.
