arXiv subjects

Jean-Philippe Bouchaud

Publications and source records attributed to Jean-Philippe Bouchaud.

At least 55 records · Page 3Linked to original sources

arXiv2023

Wrapping and unwrapping multifractal fields

We develop a powerful yet simple method that generates multifractal fields with fully controlled scaling properties. Adopting the Multifractal Random Walk (MRW) model of Bacry et al. (2001), synthetic multifractal fields are obtained from the fractional integration of non-Gaussian fluctuations, built by a non-linear transformation of log-correlated Gaussian fields. The resulting fields are parameterized by their roughness exponent $H$, intermittency $λ$ and multifractal range $ξ_ω$. We retrieve all the salient features of the MRW, namely a quadratic scaling exponent spectrum $ζ_q$, fat-tail statistics of fluctuations, and spatial correlations of local volatility. Such features can be finely tuned, allowing for the generation of ideal multifractals mimicking real multi-affine fields. The construction procedure is then used the other way around to unwrap experimental data -- here the roughness map of a fractured metallic alloy. Our analysis evidences subtle differences with synthetic fields, namely anisotropic filamental clusters reminiscent of dissipation structures found in fluid turbulence.

cond-mat.stat-mech↗

arXiv2023

From Statistical Physics to Social Sciences: The Pitfalls of Multi-disciplinarity

This is the English version of my inaugural lecture at Collège de France in 2021, available at https://www.youtube.com/watch?v=bxktplKMhKU. I reflect on the difficulty of multi-disciplinary research, which often hinges of unexpected epistemological and methodological differences, for example about the scientific status of models. What is the purpose of a model? What are we ultimately trying to establish: rigorous theorems or ad-hoc calculation recipes; absolute truth, or heuristic representations of the world? I argue that the main contribution of statistical physics to social and economic sciences is to make us realise that unexpected behaviour can emerge at the aggregate level, that isolated individuals would never experience. Crises, panics, opinion reversals, the spread of rumours or beliefs, fashion effects and the zeitgeist, but also the existence of money, lasting institutions, social norms and stable societies, must be understood in terms of collective belief and/or trust, self-sustained by interactions, or on the contrary, the rapid collapse of this belief or trust. The Appendix contains my opening remarks to the workshop ``More is Different'', as a tribute to Phil Anderson.

physics.soc-ph↗

arXiv2023

Path Shadowing Monte-Carlo

We introduce a Path Shadowing Monte-Carlo method, which provides prediction of future paths, given any generative model. At any given date, it averages future quantities over generated price paths whose past history matches, or `shadows', the actual (observed) history. We test our approach using paths generated from a maximum entropy model of financial prices, based on a recently proposed multi-scale analogue of the standard skewness and kurtosis called `Scattering Spectra'. This model promotes diversity of generated paths while reproducing the main statistical properties of financial prices, including stylized facts on volatility roughness. Our method yields state-of-the-art predictions for future realized volatility and allows one to determine conditional option smiles for the S\&P500 that outperform both the current version of the Path-Dependent Volatility model and the option market itself.

q-fin.MF↗

arXiv2023

Application of spin glass ideas in social sciences, economics and finance

Classical economics has developed an arsenal of methods, based on the idea of representative agents, to come up with precise numbers for next year's GDP, inflation and exchange rates, among (many) other things. Few, however, will disagree with the fact that the economy is a complex system, with a large number of strongly heterogeneous, interacting units of different types (firms, banks, households, public institutions) and different sizes. Now, the main issue in economics is precisely the emergent organization, cooperation and coordination of such a motley crowd of micro-units. Treating them as a unique ``representative'' firm or household clearly risks throwing the baby with the bathwater. As we have learnt from statistical physics, understanding and characterizing such emergent properties can be difficult. Because of feedback loops of different signs, heterogeneities and non-linearities, the macro-properties are often hard to anticipate. In particular, these situations generically lead to a very large number of possible equilibria, or even the lack thereof. Spin-glasses and other disordered systems give a concrete example of such difficulties. In order to tackle these complex situations, new theoretical and numerical tools have been invented in the last 50 years, including of course the replica method and replica symmetry breaking, and the cavity method, both static and dynamic. In this chapter we review the application of such ideas and methods in economics and social sciences. Of particular interest are the proliferation (and fragility) of equilibria, the analogue of satisfiability phase transitions in games and random economies, and condensation (or concentration) effects in opinion, wealth, etc

physics.soc-ph↗

arXiv2023

Scale Dependencies and Self-Similar Models with Wavelet Scattering Spectra

We introduce the wavelet scattering spectra which provide non-Gaussian models of time-series having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the joint correlation across time and scales of wavelet coefficients and their modulus. This correlation matrix is nearly diagonalized by a second wavelet transform, which defines the scattering spectra. We show that this vector of moments characterizes a wide range of non-Gaussian properties of multi-scale processes. We prove that self-similar processes have scattering spectra which are scale invariant. This property can be tested statistically on a single realization and defines a class of wide-sense self-similar processes. We build maximum entropy models conditioned by scattering spectra coefficients, and generate new time-series with a microcanonical sampling algorithm. Applications are shown for highly non-Gaussian financial and turbulence time-series.

physics.data-an↗

arXiv2023

Income Inequalities Increase with City Size: Evidence from French Data

We analyse the income distributions of cities in France and the scaling of the income of different deciles as a function of the population. We find a significant difference in the scaling exponents for the richer and poorer parts of the population, implying an unequivocal rise in inequalities in larger cities, made worse by living costs that are disproportionately higher for the poor. We find that the distribution of revenues of cities in France has a universal, Gumbel-like form, with mean and variance growing with the logarithm of population. We show how this result directly implies different income scaling exponents as a function of decile. We also study the spatial correlations of income and population, which decay exponentially with distance. We find that large cities are not more income-segregated than small cities. Finally, we search for couplings between social and economic factors, like age and income, and propose a toy model that reproduces some of our observations.

physics.soc-ph↗

arXiv2023

The Cost of Misspecifying Price Impact

Portfolio managers' orders trade off return and trading cost predictions. Return predictions rely on alpha models, whereas price impact models quantify trading costs. This paper studies what happens when trades are based on an incorrect price impact model, so that the portfolio either over- or under-trades its alpha signal. We derive tractable formulas for these misspecification costs and illustrate them on proprietary trading data. The misspecification costs are naturally asymmetric: underestimating impact concavity or impact decay shrinks profits, but overestimating concavity or impact decay can even turn profits into losses.

q-fin.TR↗

arXiv2023

Multivariate Quadratic Hawkes Processes -- Part I: Theoretical Analysis

Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous co-jumps (simultaneous price jumps of several assets) we extend QHawkes to a multivariate framework (MQHawkes), that is considering several financial assets and their interactions. Assuming that quadratic kernels write as the sum of a time-diagonal component and a rank one (trend) contribution, we investigate endogeneity ratios and the resulting stationarity conditions. We then derive the so-called Yule-Walker equations relating covariances and feedback kernels, which are essential to calibrate the MQHawkes process on empirical data. Finally, we investigate the volatility distribution of the process and find that, as in the univariate case, it exhibits power-law behavior, with an exponent that can be exactly computed in some limiting cases.

q-fin.TR↗

arXiv2023

On Hawkes Processes with Infinite Mean Intensity

The stability condition for Hawkes processes and their non-linear extensions usually relies on the condition that the mean intensity is a finite constant. It follows that the total endogeneity ratio needs to be strictly smaller than unity. In the present note we argue that it is possible to have a total endogeneity ratio greater than unity without rendering the process unstable. In particular, we show that, provided the endogeneity ratio of the linear Hawkes component is smaller than unity, Quadratic Hawkes processes are always stationary, although with infinite mean intensity when the total endogenity ratio exceeds one. This results from a subtle compensation between the inhibiting realisations (mean-reversion) and their exciting counterparts (trends).

q-fin.TR↗

arXiv2022

The RFOT Theory of Glasses: Recent Progress and Open Issues

The Random First Order Transition (RFOT) theory started with the pioneering work of Kirkpatrick, Thirumalai and Wolynes. It leverages the methods and advances of the theory of disordered systems. It fares remarkably well at reproducing the salient experimental facts of super-cooled liquids. Yet, direct and indisputable experimental validations are missing. In this short survey, we will review recent investigations that broadly support all static aspects of RFOT, but also those for which the standard dynamical extension of the theory appears to be struggling, in particular in relation with facilitation effects. We discuss possible solutions and open issues.

cond-mat.dis-nn↗

arXiv2022

Exploration of the Parameter Space in Macroeconomic Agent-Based Models

Agent-Based Models (ABM) are computational scenario-generators, which can be used to predict the possible future outcomes of the complex system they represent. To better understand the robustness of these predictions, it is necessary to understand the full scope of the possible phenomena the model can generate. Most often, due to high-dimensional parameter spaces, this is a computationally expensive task. Inspired by ideas coming from systems biology, we show that for multiple macroeconomic models, including an agent-based model and several Dynamic Stochastic General Equilibrium (DSGE) models, there are only a few stiff parameter combinations that have strong effects, while the other sloppy directions are irrelevant. This suggest an algorithm that efficiently explores the space of parameters by primarily moving along the stiff directions. We apply our algorithm to a medium-sized agent-based model, and show that it recovers all possible dynamics of the unemployment rate. The application of this method to Agent-based Models may lead to a more thorough and robust understanding of their features, and provide enhanced parameter sensitivity analyses. Several promising paths for future research are discussed.

econ.GN↗

arXiv2022

Bounded Rationality and Animal Spirits: A Fluctuation-Response Approach to Slutsky Matrices

The Slutsky equation, central in consumer choice theory, is derived from the usual hypotheses underlying most standard models in Economics, such as full rationality, homogeneity, and absence of interactions. We present a statistical physics framework that allows us to relax such assumptions. We first derive a general fluctuation-response formula that relates the Slutsky matrix to spontaneous fluctuations of consumption rather than to response to changing prices and budget. We then show that, within our hypotheses, the symmetry of the Slutsky matrix remains valid even when agents are only boundedly rational but non-interacting. We then propose a model where agents are influenced by the choice of others, leading to a phase transition beyond which consumption is dominated by herding (or `"fashion") effects. In this case, the individual Slutsky matrix is no longer symmetric, even for fully rational agents. The vicinity of the transition features a peak in asymmetry.

econ.TH↗

arXiv2022

Occupation time of a renewal process coupled to a discrete Markov chain

A semi-Markov process is one that changes states in accordance with a Markov chain but takes a random amount of time between changes. We consider the generalisation to semi-Markov processes of the classical Lamperti law for the occupation time of a two-state Markov process. We provide an explicit expression in Laplace space for the distribution of an arbitrary linear combination of the occupation times in the various states of the process. We discuss several consequences of this result. In particular, we infer the limiting distribution of this quantity rescaled by time in the long-time scaling regime, as well as the finite-time corrections to its moments.

cond-mat.stat-mech↗

arXiv2022

Excess Out-of-Sample Risk and Fleeting Modes

Using Random Matrix Theory, we propose a universal and versatile tool to reveal the existence of "fleeting modes", i.e. portfolios that carry statistically significant excess risk, signalling ex-post a change in the correlation structure in the underlying asset space. Our proposed test is furthermore independent of the "true" (but unknown) underlying correlation structure. We show empirically that such fleeting modes exist both in futures markets and in equity markets. We proposed a metric to quantify the alignment between known factors and fleeting modes and identify momentum as a source of excess risk in the equity space.

q-fin.PM↗

arXiv2022

Self-Fulfilling Prophecies, Quasi Non-Ergodicity and Wealth Inequality

We construct a model of an exchange economy in which agents trade assets contingent on an observable signal, the probability of which depends on public opinion. The agents in our model are replaced occasionally and each person updates beliefs in response to observed outcomes. We show that the distribution of the observed signal is described by a quasi-non-ergodic process and that people continue to disagree with each other forever. These disagreements generate large wealth inequalities that arise from the multiplicative nature of wealth dynamics which make successful bold bets highly profitable.

econ.TH↗

arXiv2022

Will Random Cone-wise Linear Systems Be Stable?

We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with $\mathbb{A}$, $\mathbb{B}$ independently drawn a rotationally invariant ensemble of $N \times N$ matrices) depending on the sign of the first component of $\mathbf{v}$. We establish strong connections with the random diffusion persistence problem. When $N \to \infty$, we find that the Lyapounov exponent is non self-averaging, i.e. one can observe apparent stability and apparent instability for the same system, depending on time and initial conditions. Finite $N$ effects are also discussed, and lead to cone trapping phenomena.

math-ph↗

arXiv2022

The Inelastic Market Hypothesis: A Microstructural Interpretation

We attempt to reconcile Gabaix and Koijen's (GK) recent Inelastic Market Hypothesis (IMH) with the order-driven view of markets that emerged within the microstructure literature in the past 20 years. We review the most salient empirical facts and arguments that give credence to the idea that market price fluctuations are mostly due to order flow, whether informed or non-informed. We show that the Latent Liquidity Theory of price impact makes a precise prediction for GK's multiplier $M$, which measures by how many dollars, on average, the market value of a company goes up if one buys one dollar worth of its stocks. Our central result is that $M$ is of order unity, as found by GK, and increases with the volatility of the stock and decreases with the fraction of the market cap. traded daily. We discuss several empirical results suggesting that the lion's share of volatility is due to trading activity. We argue that the IMH holds for all asset classes, beyond the case of stock markets considered by GK.

econ.GN↗

arXiv2021

Optimal cleaning for singular values of cross-covariance matrices

We give a new algorithm for the estimation of the cross-covariance matrix $\mathbb{E} XY'$ of two large dimensional signals $X\in\mathbb{R}^n$, $Y\in \mathbb{R}^p$ in the context where the number $T$ of observations of the pair $(X,Y)$ is large but $n/T$ and $p/T$ are not supposed to be small. In the asymptotic regime where $n,p,T$ are large, with high probability, this algorithm is optimal for the Frobenius norm among rotationally invariant estimators, i.e. estimators derived from the empirical estimator by cleaning the singular values, while letting singular vectors unchanged.

math.ST↗