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arXiv2009

Scale Invariance, Bounded Rationality and Non-Equilibrium Economics

We study a class of heterogeneous agent-based models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and product transformations. A basic guiding principle is scale invariance, which means that the dynamics of the economy should not depend on the units used to measure the different products. We develop the idea of a "near-equilibrium" expansion which allow us to study the dynamics of fluctuations around economic equilibrium. This is similar to the familiar "perturbation theory" studied in many areas of physics. We study some simple models of both centralized and decentralized markets. We show the relaxation to equilibrium when appropriate. More interestingly, we study a simple model of a decentralized market that shows a spontaneous transition into a monetary phase. We use mean field theory analysis to provide a statistical interpretation of the monetary phase. Furthermore, we show that such phase can be dynamically unstable. Finally, we study some simple centralized financial markets, one of which shows a speculative bubble and a crash.

q-fin.TR↗

arXiv2026

Pragmatic Information Rates, Generalizations of the Kelly Criterion, and Financial Market Efficiency

This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger (2002) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy Coding Theorems, two of the most important results of Shannon's theory, we begin the paper by defining a pragmatic information rate, showing that all of the relevant limits make sense, and interpreting them as the improvement in compression obtained from using the correct distribution of transmitted symbols. The first of two applications of the theory extends the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some stationary process, including, but not limited to the history of previous races. If the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings is bounded by the pragmatic information of the messages. A second application is to the question of market efficiency. An efficient market is, by definition, a market in which the pragmatic information of the "tradable past" with respect to current prices is zero. Under this definition, markets whose returns are characterized by a GARCH(1,1) process cannot be efficient. Finally, a pragmatic informational analogue to Shannon's Noisy Coding Theorem suggests that a cause of market inefficiency is that the underlying fundamentals are changing so fast that the price discovery mechanism simply cannot keep up. This may happen most readily in the run-up to a financial bubble, where investors' willful ignorance degrade the information processing capabilities of the market.

cs.IT↗

arXiv2009

Price Impact

We define what "Price Impact" means, and how it is measured and modelled in the recent literature. Although this notion seems to convey the idea of a forceful and intuitive mechanism, we discuss why things might not be that simple. Empirical studies show that while the correlation between signed order flow and price changes is strong, the impact of trades on prices is neither linear in volume nor permanent. Impact allows private information to be reflected in prices, but by the same token, random fluctuations in order flow must also contribute to the volatility of markets.

q-fin.TR↗

arXiv2009

Introducing Chaos in Economic Gas-like Models

This paper considers ideal gas-like models of trading markets, where each agent is identified as a gas molecule that interacts with others trading in elastic or money-conservative collisions. Traditionally, these models introduce different rules of random selection and exchange between pair agents. Unlike these traditional models, this work introduces a chaotic procedure able of breaking the pairing symmetry of agents (i,j)->(j,i). Its results show that, the asymptotic money distributions of a market under chaotic evolution can exhibit a transition from Gibbs to Pareto distributions, as the pairing symmetry is progressively broken.

q-fin.TR↗

arXiv2010

The price impact of order book events: market orders, limit orders and cancellations

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective impact on future price changes. We define and extract from the data the "bare" impact these events would have, if they were to happen in isolation. For large tick stocks, we show that a model where the bare impact of all events is permanent and non-fluctuating is in good agreement with the data. For small tick stocks, however, bare impacts must contain a history dependent part, reflecting the internal fluctuations of the order book. We show that this effect can be accurately described by an autoregressive model on the past order flow. This framework allows us to decompose the impact of an event into three parts: an instantaneous jump component, the modification of the future rates of the different events, and the modification of the future gaps behind the best quotes. We compare in detail the present formalism with the temporary impact model that was proposed earlier to describe the impact of market orders when other types of events are not observed. Finally, we extend the model to describe the dynamics of the bid-ask spread.

q-fin.TR↗

arXiv2009

Minimizing the expected market time to reach a certain wealth level

In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level. In an Ito market, we employ the concept of market time, which is a clock that runs according to the underlying market growth. We show the optimality of the growth-optimal portfolio for minimizing the expected market time to reach any wealth level. This reveals a general definition of market time which can be useful from an investor's point of view. We utilize this last definition to extend the previous results in a general semimartingale setting.

q-fin.PM↗

arXiv2011

Local Risk Decomposition for High-frequency Trading Systems

In the present work we address the problem of evaluating the historical performance of a trading strategy or a certain portfolio of assets. Common indicators such as the Sharpe ratio and the risk adjusted return have significant drawbacks. In particular, they are global indices, that is they do not preserve any 'local' information about the performance dynamics either in time or for a particular investment horizon. This information could be fundamental for practitioners as the past performance can be affected by the non-stationarity of financial market. In order to highlight this feature, we introduce the 'local risk decomposition' (LRD) formalism, where dynamical information about a strategy's performance is retained. This framework, motivated by the multi-scaling techniques used in complex system theory, is particularly suitable for high-frequency trading systems and can be applied into problems of strategy optimization.

q-fin.RM↗

arXiv2010

Executing large orders in a microscopic market model

In a recent paper, Alfonsi, Fruth and Schied (AFS) propose a simple order book based model for the impact of large orders on stock prices. They use this model to derive optimal strategies for the execution of large orders. We apply these strategies to an agent-based stochastic order book model that was recently proposed by Bovier, Černý and Hryniv, but already the calibration fails. In particular, from our simulations the recovery speed of the market after a large order is clearly dependent on the order size, whereas the AFS model assumes a constant speed. For this reason, we propose a generalization of the AFS model, the GAFS model, that incorporates this dependency, and prove the optimal investment strategies. As a corollary, we find that we can derive the ``correct'' constant resilience speed for the AFS model from the GAFS model such that the optimal strategies of the AFS and the GAFS model coincide. Finally, we show that the costs of applying the optimal strategies of the GAFS model to the artificial market environment still differ significantly from the model predictions, indicating that even the improved model does not capture all of the relevant details of a real market.

q-fin.TR↗

arXiv2009

Emergence of Price Divergence in a Model Short-Term Electric Power Market

A minimal model of a market of myopic non-cooperative agents who trade bilaterally with random bids reproduces qualitative features of short-term electric power markets, such as those in California and New England. Each agent knows its own budget and preferences but not those of any other agent. The near-equilibrium price established mid-way through the trading session diverges to both much higher and much lower prices towards the end of the trading session. This price divergence emerges in the model without any possibility that the agents could have conspired to "game" the market. The results were weakly sensitive to the endowments but strongly sensitive to the nature of the agent's preferences and budget constraints.

q-fin.TR↗

arXiv2010

Class formation in a social network with asset exchange

We study two kinds of economic exchange, additive and multiplicative, in a system of N agents. The work is divided in two parts, in the first one, the agents are free to interact with each other. The system evolves to a Boltzmann-Gibbs distribution with additive exchange and condenses with a multiplicative one. If bankruptcy is introduced, both types of exchange lead to condensation. Condensation times have been studied. In the second part, the agents are placed in a social network. We analyze the behavior of wealth distributions in time, and the formation of economic classes was observed for certain values of network connectivity.

q-fin.TR↗

arXiv2009

Trading leads to scale-free self-organization

Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free behavior of the distribution of returns of different financial assets have been confirmed in a series of works. The existence of a Pareto-like distribution of the wealth of market participants has been connected with the scale-free distribution of trading volumes and price-returns. The origin of the Pareto-like wealth distribution, however, remained obscure. Here we show that it is the process of trading itself that under two mild assumptions spontaneously leads to a self-organization of the market with a Pareto-like wealth distribution for the market participants and at the same time to a scale-free behavior of return fluctuations. These assumptions are (i) everybody trades proportional to his current capacity and (ii) supply and demand determine the relative value of the goods.

q-fin.TR↗

arXiv2010

Dynamical Clustering of Exchange Rates

We use techniques from network science to study correlations in the foreign exchange (FX) market over the period 1991--2008. We consider an FX market network in which each node represents an exchange rate and each weighted edge represents a time-dependent correlation between the rates. To provide insights into the clustering of the exchange rate time series, we investigate dynamic communities in the network. We show that there is a relationship between an exchange rate's functional role within the market and its position within its community and use a node-centric community analysis to track the time dynamics of this role. This reveals which exchange rates dominate the market at particular times and also identifies exchange rates that experienced significant changes in market role. We also use the community dynamics to uncover major structural changes that occurred in the FX market. Our techniques are general and will be similarly useful for investigating correlations in other markets.

q-fin.TR↗

arXiv2009

Housing Market Microstructure

In this article, we develop a model for the evolution of real estate prices. A wide range of inputs, including stochastic interest rates and changing demands for the asset, are considered. Maximizing their expected utility, home owners make optimal sale decisions given these changing market conditions. Using these optimal sale decisions, we simulate the implied evolution of housing prices providing insights into the recent subprime lending crisis.

q-fin.TR↗

arXiv2010

Leverage Causes Fat Tails and Clustered Volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing", i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior", such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.

q-fin.ST↗

arXiv2009

The International-Trade Network: Gravity Equations and Topological Properties

This paper begins to explore the determinants of the topological properties of the international - trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a "residual" ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and so on. We then compare the topological properties of the original and residual ITNs. We find that the residual ITN displays, unlike the original one, marked signatures of a complex system, and is characterized by a very different topological architecture. Whereas the original ITN is geographically clustered and organized around a few large-sized hubs, the residual ITN displays many small-sized but trade-oriented countries that, independently of their geographical position, either play the role of local hubs or attract large and rich countries in relatively complex trade-interaction patterns.

q-fin.GN↗

arXiv2009

A Computational View of Market Efficiency

We propose to study market efficiency from a computational viewpoint. Borrowing from theoretical computer science, we define a market to be \emph{efficient with respect to resources $S$} (e.g., time, memory) if no strategy using resources $S$ can make a profit. As a first step, we consider memory-$m$ strategies whose action at time $t$ depends only on the $m$ previous observations at times $t-m,...,t-1$. We introduce and study a simple model of market evolution, where strategies impact the market by their decision to buy or sell. We show that the effect of optimal strategies using memory $m$ can lead to "market conditions" that were not present initially, such as (1) market bubbles and (2) the possibility for a strategy using memory $m' > m$ to make a bigger profit than was initially possible. We suggest ours as a framework to rationalize the technological arms race of quantitative trading firms.

cs.CE↗

arXiv2009

The scale of market quakes

We define a methodology to quantify market activity on a 24 hour basis by defining a scale, the so-called scale of market quakes (SMQ). The SMQ is designed within a framework where we analyse the dynamics of excess price moves from one directional change of price to the next. We use the SMQ to quantify the FX market and evaluate the performance of the proposed methodology at major news announcements. The evolution of SMQ magnitudes from 2003 to 2009 is analysed across major currency pairs.

q-fin.TR↗

arXiv2010

Econophysics: Empirical facts and agent-based models

This article aims at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words Economics and Physics, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modelling), econometrics of financial bubbles and crashes, etc. In the first part of the review, we discuss on the emergence of Econophysics. Then we present empirical studies revealing statistical properties of financial time series. We begin the presentation with the widely acknowledged stylized facts which describe the returns of financial assets- fat tails, volatility clustering, autocorrelation, etc.- and recall that some of these properties are directly linked to the way time is taken into account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrating this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Finally, contributions to the study of correlations of assets such as random matrix theory and graph theory are presented. In the second part of the review, we deal with models in Econophysics through the point of view of agent-based modelling. Amongst a large number of multi-agent-based models, we have identified three representative areas. First, using previous work originally presented in the fields of behavioural finance and market microstructure theory, econophysicists have developed agent-based models of order-driven markets that are extensively presented here. Second, kinetic theory models designed to explain some empirical facts on wealth distribution are reviewed. Third, we briefly summarize game theory models by reviewing the now classic minority game and related problems.

q-fin.GN↗