Correlations in financial time series: established versus emerging markets

Long-time correlations in both well-developed and emerging market indexes are studied. The Hurst exponent as well as detrended fluctuations analysis (DFA) are used as technical tools. Some features that seem to be specific for developing markets are discovered and briefly discussed. Received 17 October 2000     

Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks

In human societies the probability of strategy adoption from a given person may be affected by the personal features. Now we investigate how an artificially imposed restricted ability to reproduce, overruling ones fitness, affects an evolutionary process. For this purpose we employ the evolutionary prisoner's dilemma game on different complex graphs. Reproduction restrictions can have a facilitative effect on the evolution of cooperation that sets in irrespective of particularities of the interaction network. Indeed, an appropriate fraction of less fertile individuals may lead to full supremacy of cooperators where otherwise defection would be widespread. By studying cooperation levels within the group of individuals having full reproduction capabilities, we reveal that the recent mechanism for the promotion of cooperation is conceptually similar to the one reported previously for scale-free networks. Our results suggest that the diversity in the reproduction capability, related to inherently different attitudes of individuals, can enforce the emergence of cooperative behavior among selfish competitors.     

Statistical analysis of discrimination games

The hypothesis that meanings originate from discrimination tasks, in which an individual attempts to categorize N objects using a set of M sensory channels, is examined within a quantitative statistical perspective. Failure in discrimination triggers the refinement of a randomly-chosen sensory channel, starting thus an ongoing process, termed discrimination game, that ends only when all objects are differentiated. We show that the expected number of trials of a discrimination game diverges in the case of a single channel and scales with the power N^2/M for M ≥2.     

Increasing market efficiency in the stock markets

We study the temporal evolutions of three stock markets; Standard and Poor's 500 index, Nikkei 225 Stock Average, and the Korea Composite Stock Price Index. We observe that the probability density function of the log-return has a fat tail but the tail index has been increasing continuously in recent years. We have also found that the variance of the autocorrelation function, the scaling exponent of the standard deviation, and the statistical complexity decrease, but that the entropy density increases as time goes over time. We introduce a modified microscopic spin model and simulate the model to confirm such increasing and decreasing tendencies in statistical quantities. These findings indicate that these three stock markets are becoming more efficient. An erratum to this article is available at .     

World currency exchange rate cross-correlations

World currency network constitutes one of the most complex structures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes of the daily foreign exchange rates within the basket of 60 currencies in the period December 1998–May 2005. Such a dynamics turns out to predominantly involve one outstanding eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends however crucially on which currency is used as a base currency for the remaining ones. Most prominent it looks from the perspective of a peripheral currency. This largest eigenvalue is seen to systematically decrease and thus the structure of correlations becomes more heterogeneous, when more significant currencies are used as reference. An extreme case in this later respect is the USD in the period considered. Besides providing further insight into subtle nature of complexity, these observations point to a formal procedure that in general can be used for practical purposes of measuring the relative currencies significance on various time horizons.     

Cooperative dynamics of snowdrift game on spatial distance-dependent small-world networks

We investigate the evolution of cooperative behaviors of small-world networking agents in a snowdrift game mode, where two agents (nodes) are connected with probability depending on their spatial Euclidean lattice distance in the power-law form controlled by an exponent α. Extensive numerical simulations indicate that the game dynamics crucially depends on the spatial topological structure of underlying networks with different values of the exponent α. Especially, in the distance-independent case of α=0, the small-world connectivity pattern contributes to an enhancement of cooperation compared with that in regular lattices, even for the case of having a high cost-to-benefit ratio r. However, with the increment of α>0, when r≥0.4, the spatial distance-dependent small-world (SDSW) structure tends to inhibit the evolution of cooperation in the snowdrift game.     

The distribution and scaling of fluctuations for Hang Seng index in Hong Kong stock market

The statistical properties of the Hang Seng index in the Hong Kong stock market are analyzed. The data include minute by minute records of the Hang Seng index from January 3, 1994 to May 28, 1997. The probability distribution functions of index returns for the time scales from 1 minute to 128 minutes are given. The results show that the nature of the stochastic process underlying the time series of the returns of Hang Seng index cannot be described by the normal distribution. It is more reasonable to model it by a truncated Lévy distribution with an exponential fall-off in its tails. The scaling of the maximium value of the probability distribution is studied. Results show that the data are consistent with scaling of a Lévy distribution. It is observed that in the tail of the distribution, the fall-off deviates from that of a Lévy stable process and is approximately exponential, especially after removing daily trading pattern from the data. The daily pattern thus affects strongly the analysis of the asymptotic behavior and scaling of fluctuation distributions. Received 9 August 2000 and Received in final form 28 August 2000     

”Illusion of control” in Time-Horizon Minority and Parrondo Games

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive [J.D. Taylor, S.E. Brown, Psych. Bull. 103, 193 (1988); A. Bandura, Self-efficacy: the exercise of control (WH Freeman, New York, 1997)]. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate [E. Langer, J. Pers. Soc. Psych. 7, 185 (1975)] or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Time-Horizon Minority Game [M.L. Hart, P. Jefferies, N.F. Johnson, Phys. A 311, 275 (2002)] and the Parrondo Game [J.M.R. Parrondo, G.P. Harmer, D. Abbott, Phys. Rev. Lett. 85, 5226 (2000); J.M.R. Parrondo, How to cheat a bad mathematician (ISI, Italy, 1996)], that agents who optimize their strategy based on past information may actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the “illusion of control” in certain set-ups a priori defined to emphasize the importance of optimization. An erratum to this article is available at .     

Illusory versus genuine control in agent-based games

In the Minority, Majority and Dollar Games (MG, MAJG, $G) agents compete for rewards, acting in accord with the previously best-performing of their strategies. Different aspects/kinds of real-world markets are modelled by these games. In the MG, agents compete for scarce resources; in the MAJG agents imitate the group to exploit a trend; in the $G agents attempt to predict and benefit both from trends and changes in the direction of a market. It has been previously shown that in the MG for a reasonable number of preliminary time steps preceding equilibrium (Time Horizon MG, THMG), agents’ attempt to optimize their gains by active strategy selection is “illusory”: the hypothetical gains of their strategies is greater on average than agents’ actual average gains. Furthermore, if a small proportion of agents deliberately choose and act in accord with their seemingly worst performing strategy, these outperform all other agents on average, and even attain mean positive gain, otherwise rare for agents in the MG. This latter phenomenon raises the question as to how well the optimization procedure works in the THMAJG and TH$G. We demonstrate that the illusion of control is absent in THMAJG and TH$G. This provides further clarification of the kinds of situations subject to genuine control, and those not, in set-ups a priori defined to emphasize the importance of optimization.     

The prediction of periods of high volatility in exchange markets

A statistical connection is identified between the current spread in a market over a given time period and the drift of the market during previous time periods. It is shown that periods of high spread are likely to be preceded by periods with relatively large market drifts. Several markets, including the UK pound per US Dollar, US Dollar per Yen, UK pound per Euro, and the UK FT100 index have been analysed from 1991 to 2000 over variable periods of weeks, months and quarters. Within each period, i the natural logarithm of the daily end-of-trade market value has been least squares fitted to a linear regression line, and evaluations made of the regression line slope μ _i, the direct spread s_i with respect to the mean value, and the regression spread r_i of the deviations from the regression line. Significant correlations have been observed between the current monthly direct spread s_i for each period i and the absolute value of the drifts |μ _i-j| evaluated j periods earlier. This correlation coefficient is as high as 0.746 for a period of one quarter (j = 1) and appears to die away after around 9 months for quarterly averages, after around 4 months for monthly averages and after around 2 months for weekly averages. Received 11 October 2000     

Beyond Black-Scholes: semimartingales and Lévy processes for option pricing

We consider the problem of option pricing when the underlying asset follows a general semimartingale process. After reviewing the foundations of arbitrage pricing theory for semimartingales and the link with Lévy processes, we introduce a general method to price options in this framework based on Fourier and Wavelet analysis. Received 4 September 2000     

Bubbles,crashes and intermittency in agent based market models

We define and study a rather complex market model, inspired from the Santa Fe artificial market and the Minority Game. Agents have different strategies among which they can choose, according to their relative profitability, with the possibility of not participating to the market. The price is updated according to the excess demand, and the wealth of the agents is properly accounted for. Only two parameters play a significant role: one describes the impact of trading on the price, and the other describes the propensity of agents to be trend following or contrarian. We observe three different regimes, depending on the value of these two parameters: an oscillating phase with bubbles and crashes, an intermittent phase and a stable `rational' market phase. The statistics of price changes in the intermittent phase resembles that of real price changes, with small linear correlations, fat tails and long range volatility clustering. We discuss how the time dependence of these two parameters spontaneously drives the system in the intermittent region. We analyze quantitatively the temporal correlation of activity in the intermittent phase, and show that the `random time strategy shift' mechanism that we proposed earlier allows one to understand the observed long ranged correlations. Other mechanisms leading to long ranged correlations are also reviewed. We discuss several other issues, such as the formation of bubbles and crashes, the influence of transaction costs and the distribution of agents wealth. Received 5 July 2002 / Received in final form 9 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: irene.giardina@roma1.infn.it     

Stable power laws in variable economies; Lotka-Volterra implies Pareto-Zipf

In recent years we have found that logistic systems of the Generalized Lotka-Volterra type (GLV) describing statistical systems of auto-catalytic elements posses power law distributions of the Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in market returns. These power laws and their exponent α are invariant to arbitrary variations in the total wealth of the system and to other endogenously and exogenously induced variations. Received 31 December 2001     

Modeling and asset allocation for financial markets based on a discrete time microstructure model

On the basis of the market microstructure theory and the continuous time stochastic volatility-style microstructure model, a discrete time stochastic volatility microstructure model with state-observability is proposed for describing the dynamics of financial markets. From the discrete time microstructure model proposed, estimates of two immeasurable state variables representing the market excess demand and liquidity respectively may be obtained. A simple trading strategy for dynamic asset allocation, based on the indirectly obtained excess demand information instead of the prediction for price, is presented. An approach to the estimation of the discrete time microstructure model using the extended Kalman filter and the maximum likelihood method is also presented. Case studies on financial market modeling and the estimated model-based asset dynamic allocation control for the JPY/USD (Japanese Yen/US Dollar) exchange rate and Japan TOPIX (TOkyo stock Price IndeX) show satisfactory modeling precision and control performance. Received 11 March 2002 / Received in final form 4 November 2002 Published online 4 February 2003 RID="a" ID="a"Currently a visiting researcher at the Institute of Statistical Mathematics, 4-6-7 Minami Azabu, Minato-ku, Tokyo 106-8569, Japan e-mail: peng@ism.ac.jp     

Portfolio optimization with short-selling and spin-glass

In this paper, we solve a general problem of optimizing a portfolio in a futures markets framework, extending the previous work of Galluccio et al. [Physica A 259, 449 (1998)]. We allow for long buying/short selling of a relatively large number of assets, assuming a fixed level of margin requirement. Because of non-linearity in the constraint, we derive a multiple equilibrium solution, in a size exponential respect to the number of assets. That means that we can not obtain the unique efficiency frontier, but many of them and each one is related to different levels of risk. Such a problem is analogous to that of finding the ground state in long-ranged Ising spin glass with external field. In order to get the best portfolio (i.e. that is along the best efficiency frontier), we have to implement a two-step procedure, performing the exhaustive enumeration of all local minima. We develop a concrete application, where the different part of the proposed solution are computed. Received 31 December 2001     

Forecast in foreign exchange markets

We perform a statistical study of weak efficiency in Deutschemark/US dollar exchange rates using high frequency data. The presence of correlations in the returns sequence implies the possibility of a statistical forecast of market behavior. We show the existence of correlations and how information theory can be relevant in this context. Received 5 October 2000     

Statistical equilibrium in simple exchange games I

Simple stochastic exchange games are based on random allocation of finite resources. These games are Markov chains that can be studied either analytically or by Monte Carlo simulations. In particular, the equilibrium distribution can be derived either by direct diagonalization of the transition matrix, or using the detailed balance equation, or by Monte Carlo estimates. In this paper, these methods are introduced and applied to the Bennati-Dragulescu-Yakovenko (BDY) game. The exact analysis shows that the statistical-mechanical analogies used in the previous literature have to be revised. An erratum to this article is available at .     

The grounds for time dependent market potentials from dealers’ dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers’ feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market’s potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.     

Rules extraction in short memory time series using genetic algorithms

Data mining is performed using genetic algorithm on artificially generated time series data with short memory. The extraction of rules from a training set and the subsequent testing of these rules provide a basis for the predictions on the test set. The artificial time series are generated using the inverse whitening transformation, and the correlation function has an exponential form with given time constant indicative of short memory. A vector quantization technique is employed to classify the daily rate of return of this artificial time series into four categories. A simple genetic algorithm based on a fixed format of rules is introduced to do the forecasting. Comparing to the benchmark tests with random walk and random guess, genetic algorithms yield substantially better prediction rates, between 50% to 60%. This is an improvement compared with the 47% for random walk prediction and 25% for random guessing method. Received 29 August 2000     

The effects of behavioral and structural assumptions in artificial stock market

Recent literature has developed the conjecture that important statistical features of stock price series, such as the fat tails phenomenon, may depend mainly on the market microstructure. This conjecture motivated us to investigate the roles of both the market microstructure and agent behavior with respect to high-frequency returns and daily returns. We developed two simple models to investigate this issue. The first one is a stochastic model with a clearing house microstructure and a population of zero-intelligence agents. The second one has more behavioral assumptions based on Minority Game and also has a clearing house microstructure. With the first model we found that a characteristic of the clearing house microstructure, namely the clearing frequency, can explain fat tail, excess volatility and autocorrelation phenomena of high-frequency returns. However, this feature does not cause the same phenomena in daily returns. So the Stylized Facts of daily returns depend mainly on the agents’ behavior. With the second model we investigated the effects of behavioral assumptions on daily returns. Our study implicates that the aspects which are responsible for generating the stylized facts of high-frequency returns and daily returns are different.