BOUCHAUD Jean Philippe

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Abstract The ability to learn from others (social learning) is often deemed a cause of human species success. But if social learning is indeed more efficient (whether less costly or more accurate) than individual learning, it raises the question of why would anyone engage in individual information seeking, which is a necessary condition for social learning’s efficacy. We propose an evolutionary model solving this paradox, provided agents (i) aim not only at information quality but also vie for audience and prestige, and (ii) do not only value accuracy but also reward originality—allowing them to alleviate herding effects. We find that under some conditions (large enough success rate of informed agents and intermediate taste for popularity), both social learning’s higher accuracy and the taste for original opinions are evolutionarily-stable, within a mutually beneficial division of labour -like equilibrium. When such conditions are not met, the system most often converges towards mutually detrimental equilibria.

We propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events on future events but also, crucially, the influence of past price changes on such events. We show that the empirically calibrated quadratic kernel is well described by a diagonal contribution (that captures past realised volatility), plus a rank-one "Zumbach" contribution (that captures the effect of past trends). We find that the Zumbach kernel is a power-law of time, as are all other feedback kernels. As in many previous studies, the rate of truly exogenous events is found to be a small fraction of the total event rate. These two features suggest that the system is close to a critical point -- in the sense that stronger feedback kernels would lead to instabilities.

We discuss the impact of a Covid-19-like shock on a simple model economy, described by the previously developed Mark-0 Agent-Based Model. We consider a mixed supply and demand shock, and show that depending on the shock parameters (amplitude and duration), our model economy can display V-shaped, U-shaped or W-shaped recoveries, and even an L-shaped output curve with permanent output loss. This is due to the economy getting trapped in a self-sustained "bad" state. We then discuss two policies that attempt to moderate the impact of the shock: giving easy credit to firms, and the so-called helicopter money, i.e. injecting new money into the households savings. We find that both policies are effective if strong enough. We highlight the potential danger of terminating these policies too early, although inflation is substantially increased by lax access to credit. Finally, we consider the impact of a second lockdown. While we only discuss a limited number of scenarios, our model is flexible and versatile enough to accommodate a wide variety of situations, thus serving as a useful exploratory tool for a qualitative, scenario-based understanding of post-Covid recovery. The corresponding code is available on-line.

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We study a self-reflexive DSGE model with heterogeneous households, aimed at characterising the impact of economic recessions on the different strata of the society. Our framework allows to analyse the combined effect of income inequalities and confidence feedback mediated by heterogeneous social networks. By varying the parameters of the model, we find different crisis typologies: loss of confidence may propagate mostly within high income households, or mostly within low income households, with a rather sharp crossover between the two. We find that crises are more severe for segregated networks (where confidence feedback is essentially mediated between agents of the same social class), for which cascading contagion effects are stronger. For the same reason, larger income inequalities tend to reduce, in our model, the probability of global crises. Finally, we are able to reproduce a perhaps counter-intuitive empirical finding: in countries with higher Gini coefficients, the consumption of the lowest income households tends to drop less than that of the highest incomes in crisis times.

"The 1987 crash and the 2008 financial crisis are events that are incomprehensible within the framework of neo-classical economics. Their occurrence showed the limits, even the harmful character of this theory. A specialist in statistical physics, Jean-Philippe Bouchaud is one of the pioneers of econophysics, which applies the concepts and methods of statistical physics to economic systems and financial markets, considered as complex systems, the seat of phenomena such as imitation, contagion and collective panic. Just as interactions between molecules can lead to unexpected emergent behaviors, the transubstantiation of the individual in the collective is a fundamental ingredient for understanding certain socio-economic or financial crises".

We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed, or equivalently the valid equilibria of multispecies Lotka-Volterra equations, in the special case where the interaction matrix is of unit rank, corresponding to a single-resource MacArthur model. We compute the average number of solutions and show that its logarithm grows as N α , where N is the number of assets or species and α ≤ 2 3 depends on the interaction matrix distribution. We conjecture that the most likely number of solutions is much smaller and related to the typical sparsity m(N) of the solutions, which we compute explicitly. We also find that the solution landscape is similar to that of spin-glasses, i.e. very different configurations are quasi-degenerate. Correspondingly, "disorder chaos" is also present in our problem. We discuss the consequence of such a property for portfolio construction and ecologies, and question the meaning of rational decisions when there is a very large number "satisficing" solutions.

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Classical statistical tools that handled real-life data have become inadequate upon the emergence of Big Data. Random matrix theory and free calculus introduced here present valuable solutions to the complex challenges posed by large datasets. Real world applications make it an essential tool for physicists, engineers, data analysts and economists.

We show how the approach to equilibrium in Kirman's ants model can be fully characterized in terms of the spectrum of a Schrödinger equation with a Pöschl-Teller (tan 2) potential. Among other interesting properties, we have found that in the bimodal phase where ants visit mostly one food site at a time, the switch time between the two sources only depends on the "spontaneous conversion" rate and not on the recruitment rate. More complicated correlation functions can be computed exactly, and involve higher and higher eigenvalues and eigenfunctions of the Schrödinger operator, which can be expressed in terms of hypergeometric functions.

We propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events on future events but also, crucially, the influence of past price changes on such events. We show that the empirically calibrated quadratic kernel is well described by a diagonal contribution (that captures past realised volatility), plus a rank-one "Zumbach" contribution (that captures the effect of past trends). We find that the Zumbach kernel is a power-law of time, as are all other feedback kernels. As in many previous studies, the rate of truly exogenous events is found to be a small fraction of the total event rate. These two features suggest that the system is close to a critical point -- in the sense that stronger feedback kernels would lead to instabilities.

No summary available.

No summary available.

We investigate a multi-household DSGE model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich, and leads to a variety of realistic output dynamics: high output with no crises. high output with increased volatility and deep, short lived recessions. alternation of high and low output states where relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, narratives become an important monetary policy tool, that can help steering the economy back on track.

Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past volatility and price trends. Such a feedback mechanism inturn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects withina stylized order book model, we demonstrate numerically that there exists a second order phasetransition between a stable regime for weak feedback to an unstable regime for strong feedback,in which liquidity crises arise with probability one. We characterize the critical exponents, whichappear to belong to a new universality class. We then propose a simpler model for spread dynamicsthat maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for thereal markets, such a phase transition scenario requires the system to sit below, but very close tothe instability threshold (self-organised criticality), or else that the feedback intensity is itself timedependent and occasionally visits the unstable region. An alternative scenario is provided by a classof non-linear Hawkes process that show occasional "activated" liquidity crises, without having to bepoised at the edge of instability.

We revisit the trading invariance hypothesis recently proposed by Kyle and Obizhaeva [1] by empirically investigating a large dataset of bets, or metaorders, provided by ANcerno. The hypothesis predicts that the quantity I := R/N 3/2 , where R is the exchanged risk (volatility × volume × price) and N is the number of bets, is invariant. We find that the 3/2 scaling between R and N works well and is robust against changes of year, market capitalisation and economic sector. However our analysis clearly shows that I is not invariant. We find a very high correlation R 2 > 0.8 between I and the total trading cost (spread and market impact) of the bet. We propose new invariants defined as a ratio of I and costs and find a large decrease in variance. We show that the small dispersion of the new invariants is mainly driven by (i) the scaling of the spread with the volatility per transaction, (ii) the near invariance of the distribution of metaorder size and of the volume and number fractions of bets across stocks.

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory e↵ects and habit formation may dominate over utility maximisation. We propose a stylized model with a history-dependent utility function where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing e↵ects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find in particular that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behaviour.

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Crowding is most likely an important factor in the deterioration of strategy performance, the increase of trading costs and the development of systemic risk. We study the imprints of crowding on both anonymous market data and a large database of metaorders from institutional investors in the U.S. equity market. We propose direct metrics of crowding that capture the presence of investors contemporaneously trading the same stock in the same direction by looking at fluctuations of the imbalances of trades executed on the market. We identify significant signs of crowding in well known equity signals, such as Fama-French factors and especially Momentum. We show that the rebalancing of a Momentum portfolio can explain between 1-2% of order flow, and that this percentage has been significantly increasing in recent years.

This thesis is organized in three parts. The first part examines the relationship between microscopic and macroscopic market dynamics by focusing on the properties of volatility. In the second part, we focus on the stochastic optimal control of point processes. Finally, in the third part, we study two market design problems. We start this thesis by studying the links between the no-arbitrage principle and the volatility irregularity. Using a scaling method, we show that we can effectively connect these two notions by analyzing the market impact of metaorders. More precisely, we model the market order flow using linear Hawkes processes. We then show that the no-arbitrage principle and the existence of a non-trivial market impact imply that volatility is rough and more precisely that it follows a rough Heston model. We then examine a class of microscopic models where the order flow is a quadratic Hawkes process. The objective is to extend the rough Heston model to continuous models allowing to reproduce the Zumbach effect. Finally, we use one of these models, the quadratic rough Heston model, for the joint calibration of the SPX and VIX volatility slicks. Motivated by the intensive use of point processes in the first part, we are interested in the stochastic control of point processes in the second part. Our objective is to provide theoretical results for applications in finance. We start by considering the case of Hawkes process control. We prove the existence of a solution and then propose a method to apply this control in practice. We then examine the scaling limits of stochastic control problems in the context of population dynamics models. More precisely, we consider a sequence of models of discrete population dynamics which converge to a model for a continuous population. For each model we consider a control problem. We prove that the sequence of optimal controls associated to the discrete models converges to the optimal control associated to the continuous model. This result is based on the continuity, with respect to different parameters, of the solution of a backward-looking schostatic differential equation.In the last part we consider two market design problems. First, we examine the question of the organization of a liquid derivatives market. Focusing on an options market, we propose a two-step method that can be easily applied in practice. The first step is to select the options that will be listed on the market. For this purpose, we use a quantization algorithm that allows us to select the options most in demand by investors. We then propose a pricing incentive method to encourage market makers to offer attractive prices. We formalize this problem as a principal-agent problem that we solve explicitly. Finally, we find the optimal duration of an auction for markets organized in sequential auctions, the case of zero duration corresponding to the case of a continuous double auction. We use a model where the market takers are in competition and we consider that the optimal duration is the one corresponding to the most efficient price discovery process. After proving the existence of a Nash equilibrium for the competition between market takers, we apply our results on market data. For most assets, the optimal duration is between 2 and 10 minutes.

We propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events on future events but also, crucially, the influence of past price changes on such events. We show that the empirically calibrated quadratic kernel is well described by a diagonal contribution (that captures past realised volatility), plus a rank-one "Zumbach" contribution (that captures the effect of past trends). We find that the Zumbach kernel is a power-law of time, as are all other feedback kernels. As in many previous studies, the rate of truly exogenous events is found to be a small fraction of the total event rate. These two features suggest that the system is close to a critical point -- in the sense that stronger feedback kernels would lead to instabilities.

No summary available.

No summary available.

We show how the approach to equilibrium in Kirman's ants model can be fully characterized in terms of the spectrum of a Schrödinger equation with a Pöschl-Teller (tan 2) potential. Among other interesting properties, we have found that in the bimodal phase where ants visit mostly one food site at a time, the switch time between the two sources only depends on the "spontaneous conversion" rate and not on the recruitment rate. More complicated correlation functions can be computed exactly, and involve higher and higher eigenvalues and eigenfunctions of the Schrödinger operator, which can be expressed in terms of hypergeometric functions.

We revisit the long-standing question of the relation between image appreciation and its statistical properties. We generate two different sets of random images well distributed along three measures of entropic complexity. We run a large-scale survey in which people are asked to sort the images by preference, which reveals maximum appreciation at intermediate entropic complexity. We show that the algorithmic complexity of the coarse-grained images, expected to capture structural complexity while abstracting from high frequency noise, is a good predictor of preferences. Our analysis suggests that there might exist some universal quantitative criteria for aesthetic judgement.

We explore the effect of past market movements on the instantaneous correlations between assets within the futures market. Quantifying this effect is of interest to estimate and manage the risk associated to portfolios of futures in a non-stationary context. We apply and extend a previously reported method called the Principal Regression Analysis (PRA) to a universe of 84 futures contracts between 2009 and 2019. We show that the past up (resp. down) 10 day trends of a novel predictor-the eigen-factor-tend to reduce (resp. increase) instantaneous correlations. We then carry out a multifactor PRA on sectorial predictors corresponding to the four futures sectors (indexes, commodities, bonds and currencies), and show that the effect of past market movements on the future variations of the instantaneous correlations can be decomposed into two significant components. The first component is due to the market movements within the index sector, while the second component is due to the market movements within the bonds sector.

No summary available.

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory e↵ects and habit formation may dominate over utility maximisation. We propose a stylized model with a history-dependent utility function where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing e↵ects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find in particular that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behaviour.

No summary available.

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory e↵ects and habit formation may dominate over utility maximisation. We propose a stylized model with a history-dependent utility function where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing e↵ects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find in particular that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behaviour.

How can disturbances at the level of the individual become large fluctuations at the level of the economy? This question, despite being studied for decades, is still open. In this book, I investigate this puzzle using methods from statistical physics. Starting from an in-depth analysis of power-law distributions, I show that a clear understanding of their origin and properties allows us to better understand their socio-economic consequences. I then propose a model of a network economy, where firms depend on each other to produce, so that the very nature of their interactions can make them susceptible to amplify fluctuations. I then provide an empirical study of the statistical properties of growth rates and a framework for studying their dynamics. In the final part I focus on models that exhibit non-trivial collective phenomena because they consider imitation or memory effects in the decisions taken by individuals, showing the need to take into account the possible complexity of the different constituent parts of economic models.

This thesis consists of two interrelated parts. In the first part, we empirically study the behavior of high-frequency traders on European financial markets. In the second part, we use the results obtained to build new multi-agent models. The main objective of these models is to provide regulators and trading platforms with innovative tools to implement microstructure relevant rules and to quantify the impact of various participants on market quality.In the first part, we perform two empirical studies on unique data provided by the French regulator. We have access to all orders and trades of CAC 40 assets, at the microsecond scale, with the identities of the actors involved. We begin by comparing the behavior of high-frequency traders to that of other players, particularly during periods of stress, in terms of liquidity provision and trading activity. We then deepen our analysis by focusing on liquidity consuming orders. We study their impact on the price formation process and their information content according to the different categories of flows: high-frequency traders, participants acting as clients and participants acting as principal.In the second part, we propose three multi-agent models. Using a Glosten-Milgrom approach, our first model constructs the entire order book (spread and volume available at each price) from the interactions between three types of agents: an informed agent, an uninformed agent and market makers. This model also allows us to develop a methodology for predicting the spread in case of a change in the price step and to quantify the value of the priority in the queue. In order to focus on an individual scale, we propose a second approach where the specific dynamics of the agents are modeled by nonlinear Hawkes-type processes that depend on the state of the order book. In this framework, we are able to compute several relevant microstructure indicators based on individual flows. In particular, it is possible to classify market makers according to their own contribution to volatility. Finally, we introduce a model where liquidity providers optimize their best bid and offer prices according to the profit they can generate and the inventory risk they face. We then theoretically and empirically highlight an important new relationship between inventory and volatility.

We explore the effect of past market movements on the instantaneous correlations between assets within the futures market. Quantifying this effect is of interest to estimate and manage the risk associated to portfolios of futures in a non-stationary context. We apply and extend a previously reported method called the Principal Regression Analysis (PRA) to a universe of 84 futures contracts between 2009 and 2019. We show that the past up (resp. down) 10 day trends of a novel predictor-the eigen-factor-tend to reduce (resp. increase) instantaneous correlations. We then carry out a multifactor PRA on sectorial predictors corresponding to the four futures sectors (indexes, commodities, bonds and currencies), and show that the effect of past market movements on the future variations of the instantaneous correlations can be decomposed into two significant components. The first component is due to the market movements within the index sector, while the second component is due to the market movements within the bonds sector.

We revisit the trading invariance hypothesis recently proposed by Kyle and Obizhaeva [1] by empirically investigating a large dataset of bets, or metaorders, provided by ANcerno. The hypothesis predicts that the quantity I := R/N 3/2 , where R is the exchanged risk (volatility × volume × price) and N is the number of bets, is invariant. We find that the 3/2 scaling between R and N works well and is robust against changes of year, market capitalisation and economic sector. However our analysis clearly shows that I is not invariant. We find a very high correlation R 2 > 0.8 between I and the total trading cost (spread and market impact) of the bet. We propose new invariants defined as a ratio of I and costs and find a large decrease in variance. We show that the small dispersion of the new invariants is mainly driven by (i) the scaling of the spread with the volatility per transaction, (ii) the near invariance of the distribution of metaorder size and of the volume and number fractions of bets across stocks.

We investigate a multi-household DSGE model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich, and leads to a variety of realistic output dynamics: high output with no crises. high output with increased volatility and deep, short lived recessions. alternation of high and low output states where relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, narratives become an important monetary policy tool, that can help steering the economy back on track.

This thesis consists of two independent parts. The first part concerns the study of the eigenvectors of random Wigner matrices. First, we study the distribution of the eigenvectors of deformed Wigner matrices, which consist in a perturbation of a Wigner matrix by a deterministic diagonal matrix. If the two matrices are of the same order of magnitude, it has been proved that the eigenvectors delocalize completely and the eigenvalues enter the Wigner-Dyson-Mehta universality class. We study here an intermediate phase where the deterministic perturbation dominates the randomness: the eigenvectors are not completely delocalized while the eigenvalues remain universal. The eigenvector entries are asymptotically Gaussian with a variance that localizes them in an explicit part of the spectrum. Moreover, their mass is concentrated around this variance in the sense of a unique quantum ergodicity. Then, we study correlations of different eigenvectors. To do so, a new observable on the eigenvector moments of the Dyson Brownian motion is studied. It follows a closed parabolic equation which is a fermionic counterpart of the Bourgade-Yau eigenmomentum flow. By combining the study of these two observables, it is possible to analyze some correlations.The second part concerns the study of the distribution of eigenvalues of nonlinear models of random matrices. These models appear in the study of random neural networks and correspond to a non-linear version of covariance matrix in the sense that a non-linear function, called activation function, is applied input by input on the matrix. The eigenvalue distribution converges to a deterministic distribution characterized by a self-consistent equation of degree 4 on its Stieltjes transform. The distribution depends on the function on only two explicit parameters and for some choices of parameters we find the Marchenko-Pastur distribution which remains stable after passing under several layers of the neural network.

No summary available.

Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past volatility and price trends. Such a feedback mechanism inturn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects withina stylized order book model, we demonstrate numerically that there exists a second order phasetransition between a stable regime for weak feedback to an unstable regime for strong feedback,in which liquidity crises arise with probability one. We characterize the critical exponents, whichappear to belong to a new universality class. We then propose a simpler model for spread dynamicsthat maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for thereal markets, such a phase transition scenario requires the system to sit below, but very close tothe instability threshold (self-organised criticality), or else that the feedback intensity is itself timedependent and occasionally visits the unstable region. An alternative scenario is provided by a classof non-linear Hawkes process that show occasional "activated" liquidity crises, without having to bepoised at the edge of instability.

The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called "square-root impact law", which states that impact grows as the square-root of traded volume, has nothing to do with price diffusion, i.e. that typical price changes grow as the square-root of time. We rationalise empirical findings on impact and volatility by introducing a simple scaling argument and confronting it to data.

We revisit the long-standing question of the relation between image appreciation and its statistical properties. We generate two different sets of random images well distributed along three measures of entropic complexity. We run a large-scale survey in which people are asked to sort the images by preference, which reveals maximum appreciation at intermediate entropic complexity. We show that the algorithmic complexity of the coarse-grained images, expected to capture structural complexity while abstracting from high frequency noise, is a good predictor of preferences. Our analysis suggests that there might exist some universal quantitative criteria for aesthetic judgement.

It was recently discovered that SWAP, a Monte Carlo algorithm that involves the exchange of pairs of particles of differing diameters, can dramatically accelerate the equilibration of simulated supercooled liquids in regimes where the normal dynamics is glassy. This spectacular effect was subsequently interpreted as direct evidence against a static, cooperative explanation of the glass transition such as the one offered by the random first-order transition (RFOT) theory. We review several empirical facts that support the opposite view, namely, that a local mechanism cannot explain the glass transition phenomenology. We explain the speedup induced by SWAP within the framework of the RFOT theory. We suggest that the efficiency of SWAP stems from a postponed onset of glassy dynamics, which allows the efficient exploration of configuration space even in the regime where the physical dynamics is dominated by activated events across free-energy barriers. We describe this effect in terms of `crumbling metastability' and use the example of nucleation to illustrate the possibility of circumventing free-energy barriers of thermodynamic origin by a change of the local dynamical rules.

No summary available.

No summary available.

No summary available.

No summary available.

The main objective of this thesis is to understand the interactions between financial agents and the order book. We consider in the first chapter the control problem of an agent trying to take into account the available liquidity in the order book in order to optimize the placement of a unit order. Our strategy reduces the risk of adverse selection. Nevertheless, the added value of this approach is weakened in the presence of latency: predicting future price movements is of little use if agents' reaction time is slow.In the next chapter, we extend our study to a more general execution problem where agents trade non-unitary quantities in order to limit their impact on the price. In the third chapter, we build on the previous approach to solve this time market making problems rather than execution problems. This allows us to propose relevant strategies compatible with the typical actions of market makers. Then, we model the behavior of directional high frequency traders and institutional brokers in order to simulate a market where our three types of agents interact optimally with each other.We propose in the fourth chapter an agent model where the flow dynamics depend not only on the state of the order book but also on the market history. To do so, we use generalizations of nonlinear Hawkes processes. In this framework, we are able to compute several relevant indicators based on individual flows. In particular, it is possible to classify market makers according to their contribution to volatility.To solve the control problems raised in the first part of the thesis, we have developed numerical schemes. Such an approach is possible when the dynamics of the model are known. When the environment is unknown, stochastic iterative algorithms are usually used. In the fifth chapter, we propose a method to accelerate the convergence of such algorithms.The approaches considered in the previous chapters are suitable for liquid markets using the order book mechanism. However, this methodology is not necessarily relevant for markets governed by specific operating rules. To address this issue, we propose, first, to study the behavior of prices in the very specific electricity market.

We investigate a multi-household DSGE model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich, and leads to a variety of realistic output dynamics: high output with no crises. high output with increased volatility and deep, short lived recessions. alternation of high and low output states where relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, narratives become an important monetary policy tool, that can help steering the economy back on track.

Latent order book models have allowed for significant progress in our understanding of price formation in financial markets. In particular they are able to reproduce a number of stylized facts, such as the square-root impact law. An important question that is raised-if one is to bring such models closer to real market data-is that of the connection between the latent (unobservable) order book and the real (observable) order book. Here we suggest a simple, consistent mechanism for the revelation of latent liquidity that allows for quantitative estimation of the latent order book from real market data. We successfully confront our results to real order book data for over a hundred assets and discuss market stability. One of our key theoretical results is the existence of a market instability threshold, where the conversion of latent order becomes too slow, inducing liquidity crises. Finally we compute the price impact of a metaorder in different parameter regimes.

Using a large database of 8 million institutional trades executed in the U.S. equity market, we establish a clear crossover between a linear market impact regime and a square-root regime as a function of the volume of the order. Our empirical results are remarkably well explained by a recently proposed dynamical theory of liquidity that makes specific predictions about the scaling function describing this crossover. Allowing at least two characteristic timescales for the liquidity ("fast" and "slow") enables one to reach quantitative agreement with the data.

No summary available.

This thesis aims at understanding several aspects of the roughness of volatility observed universally on financial assets. This is done in six steps. In the first part, we explain this property from the typical behaviors of agents in the market. More precisely, we build a microscopic price model based on Hawkes processes reproducing the important stylized facts of the market microstructure. By studying the long-run price behavior, we show the emergence of a rough version of the Heston model (called rough Heston model) with leverage. Using this original link between Hawkes processes and Heston models, we compute in the second part of this thesis the characteristic function of the log-price of the rough Heston model. This characteristic function is given in terms of a solution of a Riccati equation in the case of the classical Heston model. We show the validity of a similar formula in the case of the rough Heston model, where the Riccati equation is replaced by its fractional version. This formula allows us to overcome the technical difficulties due to the non-Markovian character of the model in order to value derivatives. In the third part, we address the issue of risk management of derivatives in the rough Heston model. We present hedging strategies using the underlying asset and the forward variance curve as instruments. This is done by specifying the infinite-dimensional Markovian structure of the model. Being able to value and hedge derivatives in the rough Heston model, we confront this model with the reality of financial markets in the fourth part. More precisely, we show that it reproduces the behavior of implied and historical volatility. We also show that it generates the Zumbach effect, which is a time-reversal asymmetry observed empirically on financial data. In the fifth part, we study the limiting behavior of the implied volatility at low maturity in the framework of a general stochastic volatility model (including the rough Bergomi model), by applying a density development of the asset price. While the approximation based on Hawkes processes has addressed several questions related to the rough Heston model, in Part 6 we consider a Markovian approximation applying to a more general class of rough volatility models. Using this approximation in the particular case of the rough Heston model, we obtain a numerical method for solving the fractional Riccati equations. Finally, we conclude this thesis by studying a problem not related to the rough volatility literature. We consider the case of a platform seeking the best make-take fee scheme to attract liquidity. Using the principal-agent framework, we describe the best contract to offer to the market maker as well as the optimal quotes displayed by the latter. We also show that this policy leads to better liquidity and lower transaction costs for investors.

Which level of inflation should Central Banks be targeting? The authors investigate this issue in the context of a simplified Agent Based Model of the economy. Depending on the value of the parameters that describe the behaviour of agents (in particular inflation anticipations), they find a rich variety of behaviour at the macro-level. Without any active monetary policy, our ABM economy can be in a high inflation/high output state, or in a low inflation/low output state. Hyper-inflation, deflation and " business cycles " between coexisting states are also found. The authors then introduce a Central Bank with a Taylor rule-based inflation target, and study the resulting aggregate variables. The main result is that too-low inflation targets are in general detrimental to a CB-monitored economy. One symptom is a persistent under-realization of inflation, perhaps similar to the current macroeconomic situation. Higher inflation targets are found to improve both unemployment and negative interest rate episodes. The results are compared with the predictions of the standard DSGE model.

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We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t −β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested.

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We present an empirical study of price reversion after the executed metaorders. We use a data set with more than 8 million metaorders executed by institutional investors in the US equity market. We show that relaxation takes place as soon as the metaorder ends:while at the end of the same day it is on average ≈ 2/3 of the peak impact, the decay continues the next days, following a power-law function at short time scales, and converges to a non-zero asymptotic value at long time scales (∼ 50 days) equal to ≈ 1/2 of the impact at the end of the first day. Due to a significant, multiday correlation of the sign of executed metaorders, a careful deconvolution of the observed impact must be performed to extract the estimate of the impact decay of isolated metaorders.

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We first review empirical evidence that asset prices have had episodes of large fluctuations and been inefficient for at least 200 years. We briefly review recent theoretical results as well as the neurological basis of trend following and finally argue that these asset price properties can be attributed to two fundamental mechanisms that have not changed for many centuries: an innate preference for trend following and the collective tendency to exploit as much as possible detectable price arbitrage, which leads to destabilizing feedback loops.

The field of stochastic processes and random matrix theory (RMT) has been a rapidly evolving subject during the past fifteen years where the continuous development and discovery of new tools, connections, and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar–Parisi–Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the past twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensemble of random matrices. These chapters not only cover this topic in detail but also present more recent developments that have emerged from these discoveries, for instance in the context of low-dimensional heat transport (on the physics side) or in the context of integrable probability (on the mathematical side).

We introduce and study a new class of Banded Random Matrix model describing sparse, long range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and mappings to statistical physics models, we establish the phase diagram of the model. A genuine localisation transition, with well defined mobility edges, appears as the hopping rate decreases slower than $\ell^{-2}$, where $\ell$ is the distance. Correspondingly, the decay of the localised states evolves from a standard exponential shape to a stretched exponential and finally to a novel $\exp(-C\ln^\kappa \ell)$ behaviour, with $\kappa > 1$.

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The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all intra-day scales [1]. Here we investigate how well these curves, their scaling, and the underlying return dynamics are captured by linear "propagator" models. We find that the classification of trades as price-changing versus non-price-changing can explain the price impact nonlinearities and short-term return dynamics to a very high degree. The explanatory power provided by the change indicator in addition to the order sign history increases with increasing tick size. To obtain these results, several long-standing technical issues for model calibration and -testing are addressed. We present new spectral estimators for two- and three-point cross-correlations, removing the need for previously used approximations. We also show when calibration is unbiased and how to accurately reveal previously overlooked biases. Therefore, our results contribute significantly to understanding both recent empirical results and the properties of a popular class of impact models.Comment: Companion paper to [1]: arXiv:1706.0416.

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This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.Comment: 165 pages, article submitted to Physics Report.

We run an experiment to investigate the emergence of excess and synchronised trading activity leading to market crashes. Although the environment clearly favours a buy-and-hold strategy, we observe that subjects trade too much, which is detrimental to their wealth given the implemented market impact (known to them). We find that preference for risk leads to higher activity rates and that price expectations are fully consistent with subjects’ actions. In particular, trading subjects try to make profits by playing a buy low, sell high strategy. Finally, we do not detect crashes driven by collective panic, but rather a weak but significant synchronisation of buy activity.

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This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.

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The purpose of this thesis is to link the valuation of derivatives to the scenario analysis that is the reference in bank management. The valuation of options is an area that has given rise to a very large literature with a well-defined mathematical framework, developed rather for market finance practitioners with a view to replication hedging. The risk management of these products is therefore analyzed from the perspective of the famous principle of no arbitrage opportunity. According to this principle, the estimate for a future rate becomes the one anticipated by the markets today thanks to the presence of hedging instruments. On the other hand, corporate financial management is based on a so-called "scenario approach", in which different scenarios that seem insightful and make economic sense to the bank's management are selected, and a projection for each scenario is studied. These scenarios are generally not probabilized. We are in a model of the uncertain where the notion of probability and expectation does not intervene. The bank, which has complex products related to its activity, does not hedge its risks in the same way as a service related to market activities. The study of this framework of analysis is part of the thesis. We analyze this need for projection by scenario on the perimeter of complex products.

We propose a theory of one of the most economically significant stock market anomalies, i.e. the "profitability" anomaly. In our model, investors forecast future profits using a signal and sticky belief dynamics. In this model, past profits forecast future returns (the profitability anomaly). Using analyst forecast data, we measure expectation stickiness at the firm level and find strong support for three additional predictions of the model: (1) analysts are on average too pessimistic regarding the future profits of high profit firms, (2) the profitability anomaly is stronger for stocks which are followed by stickier analysts, and (3) it is also stronger for stocks with more persistent profits.

This thesis is devoted to the study of price formation in financial markets, especially when these markets are composed of a large number of agents. We begin with an empirical study of an emerging market -- bitcoin -- in order to better understand how individual actions affect prices -- the so-called "market impact". We then develop a theoretical model of impact based on the concept of the heterogeneous agent, which manages to replicate empirical observations of a concave impact in a non-manipulable market. The heterogeneous agent framework allows us to revisit the concepts of supply and demand in a dynamic framework, to better understand the impact of the market mechanism on liquidity, and to lay the foundations of a realistic market simulator. Finally, we show, through the empirical study of several bubbles and crashes on the bitcoin market, the crucial role of the micro-structure in the understanding of extreme phenomena.

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We generalise the stylised macroeconomic Agent-Based model introduced in our previous paper [1], with the aim of investigating the role and efficacy of monetary policy of a 'Central Bank', that sets the interest rate such as to steer the economy towards a prescribed inflation and employment level. Our major finding is that provided its policy is not too aggressive (in a sense detailed in the paper) the Central Bank is successful in achieving its goals. However, the existence of different equilibrium states of the economy, separated by phase boundaries (or " dark corners "), can cause the monetary policy itself to trigger instabilities and be counter-productive. In other words, the Central Bank must navigate in a narrow window: too little is not enough, too much leads to instabilities and wildly oscillating economies. This conclusion strongly contrasts with the prediction of DSGE models.

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Mean-field game theory is a powerful formalism recently introduced to study stochastic optimization problems with a large number of agents. After recalling the basic principles of this theory and presenting some typical applications, we study in detail a stylized model of a seminar, of the mean field type. We derive an exact equation that allows us to predict the start time of the seminar and analyze different limit regimes, in which we arrive at approximate expressions of the solution. Thus we obtain a "phase diagram" of the problem. We then turn to a more complex population model with attractive group effects. Thanks to a formal analogy with the nonlinear Schrödinger equation, we show general evolution laws for the mean values of the problem, that the system verifies certain conservation laws and we develop approximations of variational type. This allows us to understand the qualitative behavior of the problem in the regime of strong interactions.

Glasses are ubiquitous in daily life and technology. However the microscopic mechanisms generating this state of matter remain subject to debate: Glasses are considered either as merely hyper-viscous liquids or as resulting from a genuine thermodynamic phase transition towards a rigid state. We show that third and fifth order susceptibilities provide a definite answer to this longstanding controversy. Performing the corresponding high-precision nonlinear dielec-tric experiments for supercooled glycerol and propylene carbonate, we find strong support for theories based upon thermodynamic amorphous order. Moreover, when lowering temperature, we find that the growing transient domains are compact – that is their fractal dimension d f = 3. The glass transition may thus represent a class of critical phenomena different from canonical second-order phase transitions for which d f < 3.

We revisit the Hébraud–Lequeux (HL) model for the rheology of jammed materials and argue that a possibly important time scale is missing from HL's initial specification. We show that our generalization of the HL model undergoes interesting oscillating instabilities for a wide range of parameters, which lead to intermittent, stick-slip flows under constant shear rate. The instability we find is akin to the synchronization transition of coupled elements that arises in many different contexts (neurons, fireflies, financial bankruptcies, etc.). We hope that our scenario could shed light on the commonly observed intermittent, serrated flows of glassy materials under shear.

Major ecological and climatic transformations are currently underway. They are a source of environmental instability, as extreme climatic events have become more frequent, more intense, and affecting new regions of the globe. If we cannot prevent these changes, how can human societies adapt to them? For many researchers and decision-makers, resilience is the key to success. This concept seems to contain new solutions, adapted to a turbulent and uncertain world. By definition, resilient systems are able to bounce back from unexpected shocks, learn quickly and adapt to new conditions. Despite the interest in this notion, the processes that enable a society to be resilient remain poorly understood. This thesis develops a new conceptual framework that allows, through mathematical modeling, to explore the theoretical links between economic mechanisms and resilience. This framework is based on a critical analysis of resilience in ecology - the original domain of the concept - and in economics - our field of application. We apply it to economic production systems, modeled as networks of firms and analyzed through dynamic systems theory. This thesis evaluates the ability of such multi-agent models to generate bifurcation profiles, an essential step in the mathematical analysis of resilience. We study a very general prey-predator dynamic in ecology and economics. Second, this thesis addresses a major factor that hinders resilience: the strong interdependencies between economic activities, through which production delays and interruptions propagate from one firm to another. Using realistic production networks, we show how supply delays, when embedded in particular topologies, multiply these propagation phenomena. Then, thanks to an evolutionary model, we highlight the existence of a systemic risk: cascades of incidents occur even though all agents have inventories adapted to the risk level. This phenomenon is amplified when supply chains become specialized and fragmented. These theoretical results are of general value, and can be used to guide future empirical research. This thesis also advances knowledge on very recent mathematical methods and objects, such as Boolean delay equations forming a complex network, and evolutionary dynamics on graphs. The proposed models and conceptual framework open new research perspectives on resilience, in particular on the impact of environmental feedbacks on the structural evolution of production networks.

This note investigates the causes of the quality anomaly, which is one of the strongest and most scalable anomalies in equity markets. We explore two potential explanations. The "risk view", whereby investing in high quality firms is somehow riskier, so that the higher returns of a quality portfolio are a compensation for risk exposure. This view is consistent with the Efficient Market Hypothesis. The other view is the "behavioral view", which states that some investors persistently underestimate the true value of high quality firms. We find no evidence in favor of the "risk view": The returns from investing in quality firms are abnormally high on a risk-adjusted basis, and are not prone to crashes. We provide novel evidence in favor of the "behavioral view": In their forecasts of future prices, and while being overall overoptimistic, analysts systematically underestimate the future return of high quality firms, compared to low quality firms.

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This note investigates the causes of the quality anomaly, which is one of the strongest and most scalable anomalies in equity markets. We explore two potential explanations. The "risk view", whereby investing in high quality firms is somehow riskier, so that the higher returns of a quality portfolio are a compensation for risk exposure. This view is consistent with the Efficient Market Hypothesis. The other view is the "behavioral view", which states that some investors persistently underestimate the true value of high quality firms. We find no evidence in favor of the "risk view": The returns from investing in quality firms are abnormally high on a risk-adjusted basis, and are not prone to crashes. We provide novel evidence in favor of the "behavioral view": In their forecasts of future prices, and while being overall overoptimistic, analysts systematically underestimate the future return of high quality firms, compared to low quality firms.

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We extend in a minimal way the stylized model introduced in in "Tipping Points in Macroeconomic Agent Based Models" [JEDC 50, 29-61 (2015)], with the aim of investigating the role and efficacy of monetary policy of a `Central Bank' that sets the interest rate such as to steer the economy towards a prescribed inflation and employment level. Our major finding is that provided its policy is not too aggressive (in a sense detailed in the paper) the Central Bank is successful in achieving its goals. However, the existence of different equilibrium states of the economy, separated by phase boundaries (or "dark corners"), can cause the monetary policy itself to trigger instabilities and be counter-productive. In other words, the Central Bank must navigate in a narrow window: too little is not enough, too much leads to instabilities and wildly oscillating economies. This conclusion strongly contrasts with the prediction of DSGE models.

Crashes have fascinated and baffled many canny observers of financial markets. In the strict orthodoxy of the efficient market theory, crashes must be due to sudden changes of the fundamental valuation of assets. However, detailed empirical studies suggest that large price jumps cannot be explained by news and are the result of endogenous feedback loops. Although plausible, a clear-cut empirical evidence for such a scenario is still lacking. Here we show how crashes are conditioned by the market liquidity, for which we propose a new measure inspired by recent theories of market impact and based on readily available, public information. Our results open the possibility of a dynamical evaluation of liquidity risk and early warning signs of market instabilities, and could lead to a quantitative description of the mechanisms leading to market crashes.

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We introduce a highly stylized, yet non trivial model of the economy, with a public and private sector coupled through a wealth tax and a redistribution policy. The model can be fully solved analytically, and allows one to address the question of optimal taxation and of wealth inequalities. We find that according to the assumption made on the relative performance of public and private sectors, three situations are possible. Not surprisingly, the optimal wealth tax rate is either 0% for a deeply dysfunctional government and/or highly productive private sector, or 100 % for a highly efficient public sector and/or debilitated/risk averse private investors. If the gap between the public/private performance is moderate, there is an optimal positive wealth tax rate maximizing economic growth, even -- counter-intuitively -- when the private sector generates more growth. The compromise between profitable private investments and taxation however leads to a residual level of inequalities. The mechanism leading to an optimal growth rate is related the well-known explore/exploit trade-off.

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Trust is a collective, self-fulfilling phenomenon that suggests analogies with phase transitions. We introduce a stylized model for the build-up and collapse of trust in networks, which generically displays a first order transition. The basic assumption of our model is that whereas trust begets trust, panic also begets panic, in the sense that a small decrease in trust may be amplified and ultimately lead to a sudden and catastrophic drop of trust. We show, using both numerical simulations and mean-field analytic arguments, that there are extended regions of the parameter space where two equilibrium states coexist: a well-connected network where confidence is high, and a poorly connected network where confidence is low. In these coexistence regions, spontaneous jumps from the well-connected state to the poorly connected state can occur, corresponding to a sudden collapse of trust that is not caused by any major external catastrophe. In large systems, spontaneous crises are replaced by history dependence: whether the system is found in one state or in the other essentially depends on initial conditions. Finally, we document a new phase, in which agents are connected yet distrustful.

The aim of this work is to explore the possible types of phenomena that simple macroeconomic Agent-Based models (ABM) can reproduce. We propose a methodology, inspired by statistical physics, that characterizes a model through its 'phase diagram' in the space of parameters. Our first motivation is to understand the large macro-economic fluctuations observed in the 'Mark I' ABM. Our major finding is the generic existence of a phase transition between a 'good economy' where unemployment is low, and a 'bad economy' where unemployment is high. We introduce a simpler framework that allows us to show that this transition is robust against many modifications of the model, and is generically induced by an asymmetry between the rate of hiring and the rate of firing of the firms. The unemployment level remains small until a tipping point, beyond which the economy suddenly collapses. If the parameters are such that the system is close to this transition, any small fluctuation is amplified as the system jumps between the two equilibria. We have explored several natural extensions of the model. One is to introduce a bankruptcy threshold, limiting the leverage of firms. This leads to a rich phase diagram with, in particular, a region where acute endogenous crises occur, during which the unemployment rate shoots up before the economy can recover. We also introduce simple wage policies. This leads to inflation (in the 'good' phase) or deflation (in the 'bad' phase), but leaves the overall phase diagram of the model essentially unchanged. We have also started exploring the effect of simple monetary policies that attempt to contain rising unemployment and defang crises. We end the paper with general comments on the usefulness of ABMs to model macroeconomic phenomena, in particular in view of the time needed to reach a steady state that raises the issue of ergodicity in these models.

Crashes have fascinated and baffled many canny observers of financial markets. In the strict orthodoxy of the efficient market theory, crashes must be due to sudden changes of the fundamental valuation of assets. However, detailed empirical studies suggest that large price jumps cannot be explained by news and are the result of endogenous feedback loops. Although plausible, a clear-cut empirical evidence for such a scenario is still lacking. Here we show how crashes are conditioned by the market liquidity, for which we propose a new measure inspired by recent theories of market impact and based on readily available, public information. Our results open the possibility of a dynamical evaluation of liquidity risk and early warning signs of market instabilities, and could lead to a quantitative description of the mechanisms leading to market crashes.

In this mostly numerical study, we revisit the statistical properties of the ground state of a directed polymer in a $d=1+1$ "hilly" disorder landscape, i.e. when the quenched disorder has power-law tails. When disorder is Gaussian, the polymer minimizes its total energy through a collective optimization, where the energy of each visited site only weakly contributes to the total. Conversely, a hilly landscape forces the polymer to distort and explore a larger portion of space to reach some particularly deep energy sites. As soon as the fifth moment of the disorder diverges, this mechanism radically changes the standard "KPZ" scaling behaviour of the directed polymer, and new exponents prevail. After confirming again that the Flory argument accurately predicts these exponent in the tail-dominated phase, we investigate several other statistical features of the ground state that shed light on this unusual transition and on the accuracy of the Flory argument. We underline the theoretical challenge posed by this situation, which paradoxically becomes even more acute above the upper critical dimension.

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In this thesis, we consider two types of applications of feedback effects in finance. These effects come into play when market participants execute sequences of trades or take part in chain reactions, which generate peaks of activity. The first part presents a dynamic optimal execution model in the presence of an exogenous stochastic market order flow. We start from the benchmark model of Obizheva and Wang, which defines an optimal execution framework with a mixed price impact. We add an order flow modeled using Hawkes processes, which are jump processes with a self-excitation property. Using stochastic control theory, we determine the optimal strategy analytically. Then we determine the conditions for the existence of Price Manipulation Strategies, as introduced by Huberman and Stanzl. These strategies can be excluded if the self-excitation of the order flow exactly offsets the price resilience. In a second step, we propose a calibration method for the model, which we apply on high frequency financial data from CAC40 stock prices. On these data, we find that the model explains a non-negligible part of the price variance. An evaluation of the optimal strategy in backtesting shows that it is profitable on average, but that realistic transaction costs are sufficient to prevent price manipulation. Then, in the second part of the thesis, we focus on the modeling of intraday volatility. In the literature, most of the backward-looking volatility models focus on the daily time scale, i.e., on day-to-day price changes. The objective here is to extend this type of approach to shorter time scales. We first present an ARCH-type model with the particularity of taking into account separately the contributions of past intraday and night-time returns. A calibration method for this model is studied, as well as a qualitative interpretation of the results on US and European stock returns. In the next chapter, we further reduce the time scale considered. We study a high-frequency volatility model, the idea of which is to generalize the Hawkes process framework to better reproduce some empirical market characteristics. In particular, by introducing quadratic feedback effects inspired by the QARCH discrete time model we obtain a power law distribution for volatility as well as time skewness.

Presentation of the editor : "Technical analysis of financial markets represents today one of the best methods of forecasting stock prices. Widely used in most of the world's markets, particularly in the United States (its country of origin), its practice is growing rapidly, thanks in particular to the technological revolution represented by the Internet. Its purpose is to identify the main trends and to define specific configurations allowing to determine price objectives. Nowadays, all financial websites offer charts and technical analysis tools. All that remains is to understand them and to know how to use them. This book presents in a clear and didactic way the main methods used today by technical analysts. Suitable for all audiences, it will enable the reader to assimilate and apply the most traditional and most recent methods of technical analysis. With a wide range of techniques at his disposal, the reader will be able to establish a precise market diagnosis (determination of the price trend and the main graphic figures, technical objectives, timing of movements, calculation of turning points, risk assessment), giving him the possibility of intervening concretely on the markets with greater efficiency.

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We decompose, within an ARCH framework, the daily volatility of stocks into overnight and intra-day contributions. We find, as perhaps expected, that the overnight and intra-day returns behave completely differently. For example, while past intra-day returns affect equally the future intra-day and overnight volatilities, past overnight returns have a weak effect on future intra-day volatilities (except for the very next one) but impact substantially future overnight volatilities. The exogenous component of overnight volatilities is found to be close to zero, which means that the lion's share of overnight volatility comes from feedback effects. The residual kurtosis of returns is small for intra-day returns but infinite for overnight returns. We provide a plausible interpretation for these findings, and show that our Intra-day/Overnight model significantly outperforms the standard ARCH framework based on daily returns for Out-of-Sample predictions.

We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.

We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance epsilon from continuous second-order glass transitions. We find that the dynamical correlation length xi behaves generically as epsilon^{-1/3} and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where xi grows with time as [ln(t)]^2 exactly at criticality. All these results suggest a deep analogy between the glassy behaviour of attractive colloids or randomly pinned supercooled liquids and that of the Random Field Ising Model.

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We propose a minimal theory of non-linear price impact based on the fact that the (latent) order book is locally linear, as suggested by reaction-diffusion models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order that consistently generalizes previously proposed propagator models. We account for the universally observed square-root impact law, and predict non-trivial trajectories when trading is interrupted or reversed. We prove that our framework is free of price manipulation and that prices can be made diffusive (albeit with a generic short-term mean-reverting contribution). Our model suggests that prices can be decomposed into a transient 'mechanical' impact component and a permanent 'informational' component.

We argue that when a social convergence mechanism exists and is strong enough, one should expect the emergence of a well-defined ?field?, i.e. a slowly evolving, local quantity around which individual attributes fluctuate in a finite range. This condensation phenomenon is well illustrated by the Deffuant?Weisbuch opinion model for which we provide a natural extension to allow for spatial heterogeneities. We show analytically and numerically that the resulting dynamics of the emergent field is a noisy diffusion equation that has a slow dynamics. This random diffusion equation reproduces the long-ranged, logarithmic decrease of the correlation of spatial voting patterns empirically found in Borghesi and Bouchaud (2010 Eur. Phys. J. B?75 395) and Borghesi et?al (2012 PLoS One?7 e36289). Interestingly enough, we find that when the social cohesion mechanism becomes too weak, cultural cohesion breaks down completely, in the sense that the distribution of intentions/opinions becomes infinitely broad. No emerging field exists in this case. All these analytical findings are confirmed by numerical simulations of an agent-based model.

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This thesis presents several aspects of the stochastic growth of interfaces, through its most studied model, the Kardar-Parisi-Zhang (KPZ) equation. Although very simple in expression, this equation conceals a great phenomenological richness and has been the object of intensive research for decades. This has led to the emergence of a new class of universals, containing some of the most common growth models, such as the Eden model or the Polynuclear Growth Model. The KPZ equation is also related to optimization problems in the presence of disorder (the Directed Polymer), or to the turbulence of fluids (Burger equation), reinforcing its interest. However, the limits of this class of universalities are still poorly understood. The purpose of this thesis is, after presenting the most recent progress in the field, to test the limits of this class of universality. The thesis is articulated in four parts:i) First, we present theoretical tools that allow us to finely characterize the evolution of the interface. These tools show a great flexibility, which we illustrate by considering the case of a confined geometry (an interface growing along a wall).ii) We then focus on the influence of disorder, and more particularly the importance of extreme events in the growth mechanics. Large fluctuations in disorder deform the interface and lead to a noticeable modification of the scaling exponents. We pay particular attention to the consequences of such disorder on optimization strategies in disordered media.iii) The presence of correlations in disorder is of immediate experimental interest. Although they do not modify the universality class, they greatly influence the average growth rate of the interface. This part is dedicated to the study of this average speed, often neglected because it is difficult to define, and to the existence of a growth optimum closely linked to the competition between exploration and exploitation.iv) Finally, we consider an experimental example of stochastic growth (which does not belong to the KPZ class) and develop a phenomenological formalism to model the propagation of a chemical interface in a disordered porous medium. Throughout the manuscript, the consequences of the observed phenomena in various fields, such as optimization strategies, population dynamics, turbulence or finance, are detailed.

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We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered when the quadratic kernel is diagonal. The calibration of these models on US stock returns reveals several unexpected features. The off-diagonal (non ARCH) coefficients of the quadratic kernel are found to be highly significant both In-Sample and Out-of-Sample, although all these coefficients turn out to be one order of magnitude smaller than the diagonal elements. This confirms that daily returns play a special role in the volatility feedback mechanism, as postulated by ARCH models. The feedback kernel exhibits a surprisingly complex structure, incompatible with all models proposed so far in the literature. Its spectral properties suggest the existence of volatility-neutral patterns of past returns. The diagonal part of the quadratic kernel is found to decay as a power-law of the lag, in line with the long-memory of volatility. Finally, QARCH models suggest some violations of Time Reversal Symmetry in financial time series, which are indeed observed empirically, although of much smaller amplitude than predicted. We speculate that a faithful volatility model should include both ARCH feedback effects and a stochastic component.

Many problems in finance are related to first passage times. Among all of them, we chose three on which we contributed personally. Our first example relates Kolmogorov-Smirnov like goodness-of-fit tests, modified in such a way that tail events and core events contribute equally to the test (in the standard Kolmogorov-Smirnov, the tails contribute very little to the measure of goodness-of-fit). We show that this problem can be mapped onto that of a random walk inside moving walls. The second example is the optimal time to sell an asset (modelled as a random walk with drift) such that the sell time is as close as possible to the time at which the asset reaches its maximum value. The last example concerns optimal trading in the presence of transaction costs. In this case, the optimal strategy is to wait until the predictor reaches (plus or minus) a threshold value before buying or selling. The value of this threshold is found by mapping the problem onto that of a random walk between two walls.

We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance epsilon from continuous second-order glass transitions. We find that the dynamical correlation length xi behaves generically as epsilon^{-1/3} and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where xi grows with time as [ln(t)]^2 exactly at criticality. All these results suggest a deep analogy between the glassy behaviour of attractive colloids or randomly pinned supercooled liquids and that of the Random Field Ising Model.

The authors study a dynamical model of interconnected firms which allows for certain market imperfections and frictions, restricted here to be myopic price forecasts and slow adjustment of production. Whereas the standard rational equilibrium is still formally a stationary solution of the dynamics, the authors show that this equilibrium becomes linearly unstable in a whole region of parameter space. When agents attempt to reach the optimal production target too quickly, coordination breaks down and the dynamics becomes chaotic. In the unstable, "turbulent", phase the aggregate volatility of the total output remains substantial even when the amplitude of idiosyncratic shocks goes to zero or when the size of the economy becomes large. In other words, crises become endogenous. This suggests an interesting resolution of the "small shocks, large business cycles" puzzle.

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The backbone of the modeling of stock market variations, the random walk model has known different mathematical forms during its eventful history. This book presents this model in a systematic way, from its intuition in the mid-19th century to its most recent transformations. It describes the origins of the idea of random walk in finance, the statistical validation and intellectual domination of this model in professional practices, and provides an overview of the scientific controversies that have accompanied it since its birth. Several specific aspects are discussed: the interaction between the random walk model and the hypothesis of market efficiency, the relationship between the normal law and modern portfolio management, the influence of the Brownian representation on the notion of perfect hedging of options, and the change in time frame with the introduction of intrinsic stock market time. The persistence of this model, while many problems remain, is analyzed in the context of contemporary debates around techno-sciences. [4th cover].

We construct a diffusive matrix model for the $\beta$-Wishart (or Laguerre) ensemble for general continuous $\beta\in [0,2]$, which preserves invariance under the orthogonal/unitary group transformation. Scaling the Dyson index $\beta$ with the largest size $M$ of the data matrix as $\beta=2c/M$ (with $c$ a fixed positive constant), we obtain a family of spectral densities parametrized by $c$. As $c$ is varied, this density interpolates continuously between the Mar\vcenko-Pastur ($c\to \infty$ limit) and the Gamma law ($c\to 0$ limit). Analyzing the full Stieltjes transform (resolvent) equation, we obtain as a byproduct the correction to the Mar\vcenko-Pastur density in the bulk up to order 1/M for all $\beta$ and up to order $1/M^2$ for the particular cases $\beta=1,2$.

The aim of our work is to propose a natural framework to account for all the empirically known properties of the multivariate distribution of stock returns. We define and study a "nested factor model", where the linear factors part is standard, but where the log-volatility of the linear factors and of the residuals are themselves endowed with a factor structure and residuals. We propose a calibration procedure to estimate these log-vol factors and the residuals. We find that whereas the number of relevant linear factors is relatively large (10 or more), only two or three log-vol factors emerge in our analysis of the data. In fact, a minimal model where only one log-vol factor is considered is already very satisfactory, as it accurately reproduces the properties of bivariate copulas, in particular the dependence of the medial-point on the linear correlation coefficient, as reported in Chicheportiche and Bouchaud (2012). We have tested the ability of the model to predict Out-of-Sample the risk of non-linear portfolios, and found that it performs significantly better than other schemes.

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The aim of this work is to explore the possible types of phenomena that simple macroeconomic Agent-Based models (ABMs) can reproduce. We propose a methodology, inspired by statistical physics, that characterizes a model through its “phase diagram” in the space of parameters. Our first motivation is to understand the large macro-economic fluctuations observed in the “Mark I” ABM devised by Delli Gatti and collaborators. In this regard, our major finding is the generic existence of a phase transition between a “good economy” where unemployment is low, and a “bad economy” where unemployment is high. We then introduce a simpler framework that allows us to show that this transition is robust against many modifications of the model, and is generically induced by an asymmetry between the rate of hiring and the rate of firing of the firms. The unemployment level remains small until a tipping point, beyond which the economy suddenly collapses. If the parameters are such that the system is close to this transition, any small fluctuation is amplified as the system jumps between the two equilibria. We have explored several natural extensions of the model. One is to introduce a bankruptcy threshold, limiting the firms maximum level of debt-to-sales ratio. This leads to a rich phase diagram with, in particular, a region where acute endogenous crises occur, during which the unemployment rate shoots up before the economy can recover. We also introduce simple wage policies. This leads to inflation (in the “good” phase) or deflation (in the “bad” phase), but leaves the overall phase diagram of the model essentially unchanged. We have also explored the effect of simple monetary policies that attempt to contain rising unemployment and defang crises. We end the paper with general comments on the usefulness of ABMs to model macroeconomic phenomena, in particular in view of the time needed to reach a steady state that raises the issue of ergodicity in these models.

We model the arrival of mid-price changes in the E-Mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to -1.15 at short times, less than approximately 10^3 seconds, and crosses over to a second power-law regime with a larger decay exponent of approximately -1.45 for longer times scales in the range [10^3, 10^6] seconds. More importantly, we find that the Hawkes kernel integrates to unity independently of the analysed period, from 1998 to 2011. This suggests that markets are and have always been close to criticality, challenging a recent study which indicates that reflexivity (endogeneity) has increased in recent years as a result of increased automation of trading. However, we note that the scale over which market events are correlated has decreased steadily over time with the emergence of higher frequency trading.

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important problems in economic theory. In this paper, we review recent efforts to include heterogeneities and interactions in models of decision. We argue that the Random Field Ising model (RFIM) indeed provides a unifying framework to account for many collective socio-economic phenomena that lead to sudden ruptures and crises. We discuss different models that can capture potentially destabilising self-referential feedback loops, induced either by herding, i.e. reference to peers, or trending, i.e. reference to the past, and account for some of the phenomenology missing in the standard models. We discuss some empirically testable predictions of these models, for example robust signatures of RFIM-like herding effects, or the logarithmic decay of spatial correlations of voting patterns. One of the most striking result, inspired by statistical physics methods, is that Adam Smith's invisible hand can badly fail at solving simple coordination problems. We also insist on the issue of time-scales, that can be extremely long in some cases, and prevent socially optimal equilibria to be reached. As a theoretical challenge, the study of so-called "detailed-balance" violating decision rules is needed to decide whether conclusions based on current models (that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys. several minor improvements along reviewers' comment.

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The main objective of the thesis is to explore problems specific to the social sciences and to study them using tools from the field of statistical physics and complex systems. The work of the thesis is thus declined on three main topics whose main problem is the question of the aggregation of individual entities into a collective structure. The first topic is centered on a paradigmatic example of the emergence of an unexpected macroscopic collective behavior from simple individual rules: the Schelling segregation model. In particular, we have proposed a novel analytical resolution of this model and we have studied analytically and via simulations the impact of different forms of cooperation between individual agents on the global collective behavior. This topic has been developed both from an economic and a physical point of view. The second topic concerns the exploration of bibliometric databases. We have produced 'science maps' representing the field of complex systems (its internal structure being deciphered via an analysis of the references used by ~1,400,000 articles) or the state of research within an institution such as the ENS de Lyon. Finally, the third theme deals with the development of models based on 'hard' science tools but sociologically founded. We present the process of elaboration of a model built with a team of sociologists. Finally, we develop a model of opinion that specifically answers a question: the existence of structures that last from entities that do not last.

We study the spatio-temporal regularities present in the electoral results and the participation rates of the communes (or polling stations) of the French elections between 1992 and 2007. We then try to develop models, based on a simple imitation of agents in the same neighborhood, that are consistent with the data. A complement develops a model of an experiment, which deals with the modification of agents' choices by the knowledge of other agents' choices.

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This thesis deals with the description of the way forces propagate in granular media such as sand. This category of materials is in fact very vast, and being able to predict satisfactorily the distribution of stresses within a granular system is a real and concrete industrial issue. But this is difficult. One of the reasons is that this distribution is very inhomogeneous: the forces applied to a stack are mostly supported and carried by only a fraction of the grains, which then form real force chains - or vaults. It follows, for example, that the pressure profile under a pile of sand depends on the way it has been built. To describe these effects quantitatively, we have proposed a phenomenological relation of friction between the vaults. The resulting differential equations are of hyperbolic type. This means in particular that there are privileged lines of propagation called characteristics, which we have made coincide with these vaults. These models reproduce well the experimental data, and allow among other things to explain the presence of a depression in the center of the heap when it is built with a funnel. They also improve the predictions of the janssen model for the silo. We have also investigated the fluctuations of these stresses, and we have highlighted the brittle character - i. E. Rearrangement - of a granular stack. This has been studied in particular within a very simple scalar model which allows to visualize the variations of the internal structure of a granular system and the resulting changes in the distribution of forces.

This thesis is devoted to the study of a series of quantities that can be defined and calculated with any stochastic process. In particular, we consider the asymptotic distribution of the extreme value of the process and the statistics of persistent deviations (the probability that the process persists under atypical conditions for long times). First we were interested in the statistics of extremes applied to the study of some disordered systems. In particular, a corrosion model has been studied, looking at the statistics of extremal quantities such as the maximum depth reached by the corrosive agent in the attacked medium and the spontaneous stop time of the corrosion process. Other applications of the asymptotic statistics of extremes to the equilibrium physics of spin glasses are recalled and discussed. The statistics of persistent events is introduced and applied to domain growth dynamics in models such as the diffusion equation, the ising model. It has been recently appreciated that very subtle phenomena are present in these systems. Persistence, defined as the fraction of sites that have always been in the same phase, decreases algebraically with time with a non-trivial exponent. This definition of persistence can be extended by considering the distribution of the local time-averaged magnetization at a given site, m(t), which is a measure of the fraction of time spent in one of the possible phases: the usual persistence exponent then belongs to a continuous family (x) of exponents which describe the persistent deviations of m(t) above a given level x. In particular, minimal models that reproduce this complex phenomenology have been studied and it has been shown how the dynamics of the interfaces between the competing domains during the dynamics can influence the spectra of the generalized persistence exponents of the process.

This thesis is a multidisciplinary study of the statistical regularities in the price variations of stock market assets, with three objectives: the identification of these regularities from empirical market data, their representation in probabilistic form and finally the elaboration of theoretical models linking the existence of these regularities to underlying market mechanisms. We use techniques from stochastic process theory, econometrics, economic theory and statistical mechanics. The first part is devoted to mathematical tools such as stochastic processes, levy processes, sums of random variables, cumulants, long dependence processes. The second part deals with the study of the statistical properties of empirical data from various markets and countries, trying to identify universal statistical regularities common to all these time series. Particular attention is given to the properties of temporal aggregation (scaling laws), distribution tails and the serial dependence of price increments. We then compare the empirical regularities with the predictions of the different models proposed in the literature: random walk, diffusion processes, garch, subordinate processes and deterministic chaos. The third part attempts to develop theoretical models linking the statistical properties of aggregate variables (price, supply and demand) to economic mechanisms and to the behavior of agents. The first model shows how mimetic behavior in financial markets leads to a leptokurtic distribution of aggregate demand and returns. The second model shows how, starting from a realistic level of volatility, taking into account the feedback between the dynamics of price and excess demand can lead to the appearance of stock market crashes whose frequency and dynamic form correspond to those observed empirically.