Introduction

Now that the big picture is set, it is time to dive more deeply into the detailed mechanics of trading in modern financial markets. As we will see, practical aspects of market design can substantially affect the microscopic-scale behaviour of individual agents. These actions can then proliferate and cascade to the macroscopic scale.

In this part, we will embark on a detailed discussion of limit order books (LOBs), which are nowadays omnipresent in the organisation of lit markets (i.e. open markets where supply and demand are displayed publicly). We will start by describing the founding principle of LOBs, namely the interaction between limit orders, which offer trading opportunities to the rest of the world, and market orders, which take these opportunities and result in immediate transactions. LOBs are not only a place where buyers meet sellers, but also a place where patient traders (or “liquidity providers”) meet impatient traders (or “liquidity takers”). For practical reasons, LOB activity is constrained to a predefined price and volume grid, whose resolution parameters are defined by the tick size and the lot size, respectively. At any point in time, the state of an LOB is defined by the outstanding limit orders on this grid.

LOBs are an elegant and simple way to channel the trading intentions of market participants into a market price. In an LOB, any buy and sell orders whose prices cross are matched and immediately removed from the LOB. Therefore, an LOB is a collection of lower-priced buy orders and higher-priced sell orders, separated by a bid–ask spread. The persistent aspect of limit orders is key for the stability of the LOB state and the market price.

In the coming chapters, we will discuss several interesting empirical properties that emerge from the interactions of traders in an LOB. We will see that both the distribution of arriving order volumes and the distribution of outstanding volume in an LOB are fat tailed, and we will discuss the consequences of these properties in the context of market stability. We will also discuss the important role of intra-day seasonalities in understanding market dynamics. Last but not least, we will highlight how order flow presents complex conditioning that strongly affects the price-formation process. The understanding of this subtle dance, which is crucial for the modelling of price changes, will be the topic of the next part.

Introduction

Throughout the book, we have pieced together several clues that suggest that the unpredictable nature of prices emerges from a fine balance between a strongly auto-correlated order flow and a dynamic price impact. At the same time, however, we have seen that so-called surprise models can also reproduce this balance with very few assumptions. It therefore seems that there might be another side to the coin, which statistical models fail to capture. Are we missing something?

So far, we have regarded order flows as simple stochastic processes with specified statistical properties. In doing so, we have excluded the strategic behaviours implemented by real market participants. In reality, however, investors’ actions are clearly influenced by their desire to make profits. Therefore, it seems logical that strategic behaviour should play an important role in real markets.

In this part, we will take the next logical step in our journey by exploring how including strategic considerations can shed light on some otherwise surprising features of financial markets. In doing so, we will examine how markets can remain in a delicate balance, maintained by ongoing competition between rational, profit-maximising agents. We will discuss the seminal Kyle model, which provides a beautiful explanation of how impact arises from liquiditya providers’ fears of adverse selection from informed traders. The model illustrates how impact allows information to be reflected in the price, and makes clear the important role played by noise traders – as we alluded to in the very first part of this book. More generally, the Kyle model, albeit not very realistic, is a concrete example of how competition and arbitrage can produce diffusive prices, even in the presence of private information.

Economic models also provide important insights on the challenges faced by market-makers. We will discuss the work of Glosten and Milgrom, which shows how the bid–ask spread must compensate market-makers for adverse selection in a competitive market. The relationship between a metaorder's slippage and its permanent impact will appear as another manifestation of the same idea. This framework paves the way for richer models of liquidity provision, where inventory risk, P&L skewness and finite tick-size effects all contribute to the challenge. We will also discuss how the Glosten–Milgrom model teaches us an important lesson: that the apparent profit opportunities from “buying low, selling high” around the spread are completely misleading.

In this chapter, we address the seemingly obvious notion of price impact (which we first discussed in Section 1.3.2): buy trades tend to push the price up and sell trades tend to push the price down. Expressed in the notation and language that we have subsequently developed, we might also express this notion by saying that price impact refers to the positive correlation between the sign (+1 for a buy order and –1 for a sell order) of an incoming market order and the subsequent price change that occurs upon or after its arrival. As we discuss in Section 11.3, these seemingly obvious statements are indeed verified by empirical data.

Price impact is an all-too-familiar reality for traders who need to buy or sell large quantities of an asset. To these traders, price impact is tantamount to a cost, because the impact of their earlier trades makes the price of their subsequent trades worse on average. Therefore, monitoring and controlling impact costs is one of the most active and rapidly expanding domains of research in both academic circles and trading firms.

Understanding and assessing price impact entails considering two different but related topics. The first is how volume creates impact: how much more impact does a larger trade cause? The second is the temporal behaviour of impact: how much of a trade's impact is permanent, how much decays over time, and how does this transient behaviour unfold? We will consider both of these topics in detail throughout this chapter. As we will discuss, both of these aspects of price impact are far from trivial. Is a transaction not a fair deal between a buyer and a seller? If so, which of the two is really impacting the price?

What Is Price Impact?

In much of the existing literature, there are two strands of interpretation for price impact, which reflect the great divide between efficient-market enthusiasts (who believe that the price is always close to its fundamental value) and sceptics (who believe that the dynamics of financial markets is primarily governed by order flow).

Introduction

At this point in our journey into financial markets, we have discussed a large number of major empirical facts, developed microscopic models of the LOB, and proposed several different paths for explaining impact. We have also seen how statistical models of order flow can capture some intricacies of the price-formation process, and how economic models can shed light on some of the effects induced by strategic behaviour. However, none of the tools or approaches that we have considered so far can properly account for a crucial empirical fact: the square-root impact of traded volumes on prices. This suggests that a piece of the puzzle is still missing.

The square-root impact law has been found in many different markets, with completely different micro-structural organisations. This suggests that the explanation should not be sought within the strict framework of an LOB, but relies on a more general – perhaps more fundamental – underlying mechanism.

In this part, we will introduce a very general framework designed for understanding the behaviour of supply and demand in a complex and dynamic environment. At the core of this approach lies the following observation, which has arisen at many points throughout the book: the liquidity shortage common to all markets suggests that the visible LOB is only the tip of the iceberg, beneath which lies a large amount of latent liquidity. In the coming chapters, we will argue that understanding and modelling directly this latent liquidity is key for understanding how markets behave – and how best to act in them.

The starting point of this discussion will be the free evolution of supply and demand: how do they behave, irrespective of any transactions that might occur, and thus also of the clearing mechanism in place? To address this question, we will introduce a model that provides insight into the vanishing nature of liquidity around the market price. In contrast to the models that we have studied so far, this model successfully reproduces the square-root law of impact, while still resembling the propagator models that we have discussed in the previous parts.

Of the puzzles that we evoked at the beginning of this book, many answers may now be found. The flat signature plot can be explained by the actions of market participants seeking arbitrage opportunities, irrespective of the question of market efficiency.

Introduction

In the previous parts of this book, we have addressed the empirical and conceptual aspects of the relationship between order flow and price formation. Let us recap what we have so far: a highly predictable order flow, which is a consequence of traders splitting their metaorders into small chunks due to liquidity shortage, and some observations of how trades impact prices. In this part, we will begin our modelling efforts of market dynamics at the micro-scale by introducing a class of simple models of price formation, often dubbed propagator models. When fitted on data, these models provide a route to computing many different quantities of interest, including the aggregate impact of individual orders and the impact of metaorders.

We will use propagator models to explore two interesting topics. The first topic is how to infer the reaction impact from the observed impact of real trades. By making explicit the relationship between these two types of impact, propagator models make it possible to estimate the reaction impact from the empirical response function, which we have already encountered in Chapter 11. In this view, the prediction component of impact is simply the reaction component of other (past and future) trades. Correlations in the order flow therefore play a central role. As we will discuss in this part, the outcome of such empirical calculations is quite intriguing: the reaction impact of orders is neither permanent (as it decays to zero in the long run) nor transient (as this decay is so slow that it takes an extremely long time to vanish).

The second topic is understanding how prices can remain unpredictable when order flows exhibit strong, long-range autocorrelations. As we discussed in the first part of this book, the signature plot of market prices is nearly flat on all scales, which indicates that price returns are linearly unpredictable. How is this possible when the order flow itself is so predictable? As we will see, the answer stems from the dynamic nature of price impact. By performing detailed calculations, we will show that the slowly decaying reaction impact exactly compensates for the autocorrelation in order flow, so as to produce diffusive prices. We will also present another angle for understanding this fine balance: if the impact of an order is proportional to its surprise, and not just its direction, then by definition prices must be unpredictable.

As we discussed in Chapter 1, organising a market to ensure fair and orderly trading is by no means a trivial task. As we also discussed in Chapter 1, transactions can only take place if some market participants post binding quotes to the rest of the market, in the sense that they specify prices at which they agree to buy or sell a specified quantity of an asset. By posting these quotes, liquidity providers put themselves at risk, because liquidity takers can decide whether or not they want to accept these offers to trade – and will only do so if they believe that the price is favourable. Liquidity providers are therefore exposed to a systematic, adverse bias: while some trades are uninformed and innocuous, other trades may be informed and be followed by large price moves in the direction of the trade, to the detriment of the liquidity provider.

Given this seemingly unfavourable position, why do any market participants provide liquidity at all? The answer is that many liquidity-provision strategies, including the popular strategy of market-making, can be profitable in the long run because a large fraction of trades are in fact non-informed (or very weakly informed). As we noted in Section 1.3.2, the fundamental consideration for implementing these strategies in the long run is the balance between the mean size of the bid–ask spread and the mean strength of adverse impact.

In older financial markets, only a select few market participants were able to act as market-makers. Due to the large spreads that were typical of these markets, market-making was a highly profitable business for these individuals. In modern electronic markets, by contrast, any market participant can act as a market-maker. As we discuss in the chapter, this important change has made market-making a highly competitive business that is typically only marginally profitable.

In this chapter, we introduce and study some simple models that help to make our previous discussions of market-making and the bid–ask spread more precise.

Introduction

What are agent-based (AB) models? In a nutshell, they are models (i.e., abstract representations of the reality) in which (i) a multitude of objects interact with each other and with the environment, (ii) the objects are autonomous (i.e., there is no central, or “top-down,” control over their behavior and, more generally, on the dynamics of the system), and (iii) the outcome of their interaction is numerically computed. Since the objects are autonomous, they are called agents. The application of agent-based modeling to economics is called Agent-Based Computational Economics (ACE). As Leigh Tesfatsion – one of the leading researchers in the field and the “mother” of the ACE acronym – defines it, ACE is

In other terms, AB models are the tool traditionally employed by ACE researchers to study economies as complex evolving systems, that is systems composed by many interacting units evolving through time.

None of the features above, in isolation, define the methodology: the microperspective implied by (i) and (ii) is roughly the same as the one adopted, for instance, by game theory, where strategic interaction is investigated analytically (though in game theory the number of individuals who populate the models is generally very small). The computational approach, instead, is typical of Computational General Equilibrium or Stock-Flow Consistent models, which are, however, based on aggregate representations of the system.

In this introductory chapter we describe the features of AB models (Section 2.2), offering an overview of their historical development (Section 2.3), discussing when they can be fruitfully employed and how they can be combined with more traditional approaches (Section 2.4). As an example, we describe one of the first and most prominent AB models, Thomas Schelling's Segregation model (Section 2.5). Conclusions follow.

Features of Agent-Based Models

The basic units of AB models are the “agents.” In economics, agents can be anything from individuals to social groups – like families or firms. They may also be more complicated organizations (banks for instance), or even industries or countries. Agents can be composed by other agents: the only requirement being that they are perceived as a unit from the outside, and that they do something – that is they have the ability to act – and possibly react to external stimuli and interact with the environment and with other agents.

As Schumpeter pointed out long ago, conceptual frameworks, models and policy prescriptions are embedded in the economist's ‘preanalytic vision’ of the economy. And preanalytic visions have been, and still are, very different in the profession.

Nowadays the majority of the profession embraces the neoclassical approach to economic behaviour, according to which agents are endowed with substantial rationality, adopt optimal rules and interact indirectly through the price vector on markets which are continuously in equilibrium. This approach has been extraordinarily fruitful, as it has allowed economists to build models that can be solved analytically and yield clear-cut policy implications. The obvious case in point is Walras's theory of General Equilibrium, beautifully outlined in his Elements d'Economie Politique, and elegantly extended and refined by Arrow and Debreu. Moreover, the approach has been remarkably flexible. Appropriately designed variants of the neoclassical approach have been applied to economies characterised by imperfect competition, imperfect information, strategic interaction, and heterogeneous agents. The most insightful of these theoretical developments have been incorporated in microfounded macroeconomic models of the New Neoclassical Synthesis that have been all the rage during the years of the Great Moderation.

However, the capability of the neoclassical approach to encompass and explain all the complex details of economic life has reached a limit. For instance, it is now abundantly clear that the neoclassical approach is not wellsuited to describe the Global Financial Crisis and the Great Recession. In models that follow the New Neoclassical Synthesis, in fact, a great recession may be explained only by a large aggregate negative shock, whose probability is extremely low (i.e., it is an extreme and rare event). This mechanism does not clarify much of the crisis and does not help to devise appropriate remedies.

The current predicament, both in the real world and in the public debate, resembles the early 1930s. The way out of the Great Depression required a new economic theory and the Second World War.1 Luckily, in order to escape the current predicament, we can dispense at least with the latter. We still need, however, to reshape the way in which we think about the economy.

For several years now, a complexity approach has been developed which conceives the economy as a complex system of heterogeneous interacting agents characterised by limited information and bounded rationality. In this view, a ‘crisis’ is a macroscopic phenomenon which spontaneously emerges from the web of microscopic interactions.

Introduction

We are now approaching the end of a long empirical, theoretical and conceptual journey. In this last part, we will take the important step of accumulating all this knowledge about markets to illuminate some important decisions about how to best act in them. In the following chapters, we will address two practical topics of utmost importance for market participants and regulators: optimal trade execution and market fairness and stability.

For both academics and practitioners, the question of how to trade and execute optimally is central to the study of financial markets. Given an investment decision with a given direction, volume and time horizon, how should a market participant execute it in practice? Addressing this question is extremely difficult, and requires a detailed understanding of market dynamics that ranges from the microscopic scale of order flow in the LOB (e.g. for optimising the positioning of orders within a queue or for choosing between a limit order and a market order) to the mesoscopic scale of slow liquidity (e.g. for scheduling the execution of large investment decisions over several hours, days or months). Many important questions on these topics have been active areas of research in the last two decades.

The final chapter of this book will address the critical question of market fairness and stability. These topics have been at the core of many debates in recent years – especially with the rise of competition between exchanges and high-frequency trading. In this last chapter, we will discuss how some market instabilities can arise from the interplay between liquidity takers and liquidity providers, and can even be created by the very mechanisms upon which markets are built.

In this jungle, regulators bear the important responsibility of designing the rules that define the ecology in financial markets. As we will discuss, because the resulting system is so complex, sometimes these rules can have unintended consequences on both the way that individual traders behave and the resulting price-formation process. Therefore, sometimes the most obvious solutions are not necessarily the best ones!

We conclude with a discussion of an interesting hypothesis: that markets intrinsically contain – and have always contained – some element of instability. From long-range correlations to price impact, this book has evidenced a collection of phenomena that are likely inherent to financial markets, and that we argue market observers, actors and regulators need to understand and accept.