arXiv subjects
Publications and source records attributed to Damien Challet.
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
A new simple model of financial market is proposed, based on the sequential and inter-temporal nature of trader-trader interaction, and on a new simple trading strategy space. In this pattern-based speculation model, the traders open and close their positions explicitly. Information ecology is strikingly similar to that of the Minority Game which suggest to reinterpret the latter as a model of synchronisation of predictability exploitation. Naive and sophisticated agents are shown to give rise to very different phenomenology
Minority games where groups of agents remember, react or incorporate information with different timescales are investigated. We study how their respective gains depend on their timescales for standard models and games with no public information, and support our findings by analytical arguments whenever possible.
We introduce a simple microscopic description of software bug dynamics where users, programmers and a maintainer interact through a given program, with a particular emphasis on bug creation, detection and fixing. When the program is written from scratch, the first phase of development is characterized by a fast decline of the number of bugs, followed by a slow phase where most bugs have been fixed, hence, are hard to find. Releasing immediately bug fixes speeds up the debugging process, which substantiates bazaar open-source methodology. We provide a mathematical analysis that supports our numerical simulations. Finally, we apply our model to Linux history and determine the existence of a lower bound to the quality of its programmers.
We demonstrate that minority mechanisms arise in the dynamics of markets because of effects of price impact; accordingly the relative importance of minority and delayed majority mechanisms depends on the frequency of trading. We then use minority games to illustrate that a vanishing price return auto-correlation function does not necessarily imply market efficiency. On the contrary, we stress the difference between correlations measured conditionally and unconditionally on external patterns.
The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular, the region in the parameter space where there is almost surely at least one fully-working subset. Dynamic recycling of a flux of imperfect binary components leads to zero wastage.
We analyze grand-canonical minority games with infinite and finite score memory and different updating timescales (from `on-line' games to `batch' games) in detail with various complementary methods, both analytical and numerical. We focus on the emergence of `stylized facts' and on the production of exploitable information, as well as on the dynamic behaviour of the models. We find that with finite score memory no agent can be frozen, and that all the current analytical methods fail to provide satisfactory explanation of the observed behaviours.
A finite memory is introduced in the score dynamics of Minority Games. As expected, this removes the dependence of the stationary state on the initial conditions. However, it also causes an unexpected increase of fluctuations in grand-canonical models for very large times. Current analytical methods are inadequate to solve this simple and natural extension.
Starting from the Minority Game and building more and more sophisticated models of adaptive agents, we show that minority mechanisms underly any model where agents learn collectively a resource level that can be either obvious and constant in time, obvious and time-varying, or hidden.
Software dependence networks are shown to be scale-free and asymmetric. We then study how software components are affected by the failure of one of them, and the inverse problem of locating the faulty component. Software at all levels is fragile with respect to the failure of a random single component. Locating a faulty component is easy if the failures only affect their nearest neighbors, while it is hard if the failures propagate further.
We use the Minority Game and some of its variants to show how efficiency depends on learning in models of agents competing for limited resources. Exact results from statistical physics give a clear understanding of the phenomenology, and opens the way to the study of reverse problems. What agents can optimize and how well is discussed in details.
We mathematize El Farol bar problem and transform it into a workable model. In general, the average convergence to optimality at the collective level is trivial and does not even require any intelligence on the side of agents. Secondly, specializing to a particular ensemble of continuous strategies yields a model similar to the Minority Game. Statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model, on the basis of its phase diagram.
Using simple particle models of limit order markets, we argue that mid-term over-diffusive price behaviour is inherent to the very nature of these markets. Several rules for rate changes are considered. We obtain analytical results for bid-ask spread properties, Hurst plots and price increment correlation functions.
We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise only close to a line of critical points with non-trivial properties. By a simple argument, we show that, in Minority Games, the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets as critical systems.
We briefly review data analysis of the Island order book, part of NASDAQ, which suggests a framework to which all limit order markets should comply. Using a simple exclusion particle model, we argue that short-time price over-diffusion in limit order markets is due to the non-equilibrium of order placement, cancellation and execution rates, which is an inherent feature of real limit order markets.
We report a statistical analysis of the Island ECN (NASDAQ) order book. We determine the static and dynamic properties of this system, and then analyze them from a physicist's viewpoint using an equivalent particle system obtained by treating orders as massive particles and price as position. We identify the fundamental dynamical processes, test existing particles models of such markets against our findings, and introduce a new model of limit order markets.
We present and study a Minority Game based model of a financial market where adaptive agents -- the speculators -- interact with deterministic agents -- called producers. Speculators trade only if they detect predictable patterns which grant them a positive gain. Indeed the average number of active speculators grows with the amount of information that producers inject into the market. Transitions between equilibrium and out of equilibrium behavior are observed when the relative number of speculators to the complexity of information or to the number of producers are changed. When the system is out of equilibrium, stylized facts arise, such as fat tailed distribution of returns and volatility clustering. Without speculators, the price follows a random walk; this implies that stylized facts arise because of the presence of speculators. Furthermore, if speculators abandon price taking behavior, stylized facts disappear.
By considering diffusion on De Bruijn graphs, we study in details the dynamics of the histories in the Minority Game, a model of competition between adaptative agents. Such graphs describe the structure of temporal evolution of $M$ bits strings, each node standing for a given string, i.e. a history in the Minority Game. We show that the frequency of visit of each history is not given by $1/2^M$ in the limit of large $M$ when the transition probabilities are biased. Consequently all quantities of the model do significantly depend on whether the histories are real, or uniformly and randomly sampled. We expose a self-consistent theory of the case of real histories, which turns out to be in very good agreement with numerical simulations.