Order-splitting and long-memory in an order-driven market

Recent empirical research has documented long-memories of trading volume, volatility, and order-signs in stock markets. We conjecture that traders’ order-splitting is related to these empirical features. This study conducts simulations on an order-driven economy where agents split their orders into small pieces and execute piece by piece to reduce price impact. We demonstrate that we can replicate the long-memories in our order-splitting economy and conclude that order-splitting can be a possible cause for these empirical properties.     

Understanding agent-based models of financial markets: A bottom–up approach based on order parameters and phase diagrams

We describe a bottom–up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby N$N$ independent traders buy and sell M$M$ stocks through an order book that acts as a clearing house. The price of a stock increases whenever it is bought and decreases whenever it is sold. Price changes are updated by the order book before the next transaction takes place. In this deterministic model, all traders based their buy decisions on a call utility function, and all their sell decisions on a put utility function. We then make the agent-based model more realistic, by either having a fraction _fb$f_b$ of traders buy a random stock on offer, or a fraction _fs$f_s$ of traders sell a random stock in their portfolio. Based on our simulations, we find that it is possible to identify useful order parameters from the steady-state price distributions of all three models. Using these order parameters as a guide, we find three phases: (i) the dead market; (ii) the boom market; and (iii) the jammed market in the phase diagram of the deterministic model. Comparing the phase diagrams of the stochastic models against that of the deterministic model, we realize that the primary effect of stochasticity is to eliminate the dead market phase.     

Analysis of a Japan government intervention on the domestic agriculture market

We investigate an economic system in which one large agent—the Japan government changes the environment of numerous smaller agents—the Japan agriculture producers by indirect regulation of prices of agriculture goods. The reason for this intervention was that before the oil crisis in 1974 Japan agriculture production prices exhibited irregular and large amplitude changes. By means of analysis of correlations and a combination of singular spectrum analysis (SSA), principal component analysis (PCA), and time delay phase space construction (TDPSC) we study the influence of the government measures on the domestic piglet prices and production in Japan. We show that the government regulation politics was successful and lead: (i) to a decrease of the nonstationarities and to increase of predictability of the piglet price; (ii) to a coupling of the price and production cycles; and (iii) to increase of determinism of the dynamics of the fluctuations of piglet price around the year average price. The investigated case is an example confirming the thesis that a large agent can change in a significant way the environment of the small agents in complex (economic or financial) systems which can be crucial for their survival or extinction.     

Frequency analysis of tick quotes on the foreign exchange market and agent-based modeling: A spectral distance approach

High-frequency financial data of the foreign exchange market (EUR/CHF, EUR/GBP, EUR/JPY, EUR/NOK, EUR/SEK, EUR/USD, NZD/USD, USD/CAD, USD/CHF, USD/JPY, USD/NOK, and USD/SEK) are analyzed by utilizing the Kullback-Leibler divergence between two normalized spectrograms of the tick frequency and the generalized Jensen-Shannon divergence among them. The temporal structure variations of the similarity between currency pairs is detected and characterized. A simple agent-based model in which N market participants exchange M currency pairs is proposed. The equation for the tick frequency is approximately derived theoretically. Based on the analysis of this model, the spectral distance of the tick frequency is associated with the similarity of the behavior (perception and decision) of the market participants in exchanging these currency pairs.     

Self-organized patterns and traffic flow in Colonies of organisms: from bacteria and social insects to vertebrates

Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebras and giraffes, the patterns of our interest are transient although different patterns change over different timescales. The aesthetic beauty of these patterns has attracted the attention of poets and philosophers for centuries. Scientists from various disciplines, however, are in search of common underlying principles that give rise to the transient patterns in colonies of organisms. Such patterns are observed not only in colonies of organisms as simple as single-cell bacteria, but also in social insects like ants and termites. They are also observed in colonies of vertebrates as complex as birds and fish, and in human societies. In recent years, physicists have utilized the framework of statistical physics to understand these patterns. In this article, we present an overview emphasizing the common trends that rely on theoretical modeling of these systems using the so-called agent-based Lagrangian approach.     

Extracting deep information from limited observations on an evolved social network

We provide empirical evidence that in a social network which evolves over time, it is possible to extract deep information about the system from limited observations. In this paper, we consider a simple piece of readily available evidence on access to financial services by individuals in the UK. Detailed statistical analysis has shown that the decisions of agents on whether or not to have a basic financial account such as a bank account is heavily influenced by other individuals on their social network. We consider a small amount of straightforward and readily accessible information. We deduce from this, using an agent-based model, the type of social network across which information and influence on behaviour flows between agents in this context. Specifically, we show that information appears to flow across a small world network.     

Herd behaviour experimental testing in laboratory artificial stock market settings. Behavioural foundations of stylised facts of financial returns

Many scholars express concerns that herding behaviour causes excess volatility, destabilises financial markets, and increases the likelihood of systemic risk. We use a special form of the Strongly Typed Genetic Programming (STGP) technique to evolve a stock market divided into two groups—a small subset of artificial agents called ‘Best Agents’ and a main cohort of agents named ‘All Agents’. The ‘Best Agents’ perform best in term of the trailing return of a wealth moving average. We then investigate whether herding behaviour can arise when agents trade Dow Jones, General Electric, and IBM financial instruments in four different artificial stock markets. This paper uses real historical quotes of the three financial instruments to analyse the behavioural foundations of stylised facts such as leptokurtosis, non-IIDness, and volatility clustering. We found evidence of more herding in a group of stocks than in individual stocks, but the magnitude of herding does not contribute to the mispricing of assets in the long run. Our findings suggest that the price formation process caused by the collective behaviour of the entire market exhibit less herding and is more efficient than the segmented market populated by a small subset of agents. Hence, greater genetic diversity leads to greater consistency with fundamental values and market efficiency.     

An analysis of cross-correlations in an emerging market

We apply random matrix theory to compare correlation matrix estimators C$C$ obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg stock exchange (JSE) from January 1993 to December 2002. We test the spectral properties of C$C$ against random matrix predictions and find some agreement between the distributions of eigenvalues, nearest neighbour spacings, distributions of eigenvector components and the inverse participation ratios for eigenvectors. We show that interpolating both missing data and illiquid trading days with a zero-order hold increases agreement with RMT predictions. For the more realistic estimation of correlations in an emerging market, we suggest a pairwise measured-data correlation matrix. For the data set used, this approach suggests greater temporal stability for the leading eigenvectors. An interpretation of eigenvectors in terms of trading strategies is given, as opposed to classification by economic sectors.     

The co-evolution of cultures,social network communities,and agent locations in an extension of Axelrod’s model of cultural dissemination

We introduce a variant of the Axelrod model of cultural dissemination in which agents change their physical locations, social links, and cultures. Numerical simulations are used to investigate the evolution of social network communities and the cultural diversity within and between these communities. An analysis of the simulation results shows that an initial peak in the cultural diversity within network communities is evident before agents segregate into a final configuration of culturally homogeneous communities. Larger long-range interaction probabilities facilitate the initial emergence of culturally diverse network communities, which leads to a more pronounced initial peak in cultural diversity within communities. At equilibrium, the number of communities, and hence cultures, increases when the initial cultural diversity increases. However, the number of communities decreases when the lattice size or population density increases. A phase transition between two regimes of initial cultural diversity is evident. For initial diversities below a critical value, a single network community and culture emerges that dominates the population. For initial diversities above the critical value, multiple culturally homogeneous communities emerge. The critical value of initial diversity at which this transition occurs increases with increasing lattice size and population density and generally with increasing absolute population size. We conclude that larger initial diversities promote cultural heterogenization, while larger lattice sizes, population densities, and in fact absolute population sizes promote homogenization.     

Effects of dynamic response time in an evolving market

Considering the time scales of global information and personal reaction, we study the role of dynamic response time in the evolution of collective behavior in an evolving market. The insensitiveness to the market information makes the population cluster around a kind of extreme behavior, in which they always follow what happened last time, while a sensitive population tends to self-segregate into opposing groups. The average success rate R among all the agents is found to have a nonmonotonic dependence on the time scale parameter q. There exists a critical value below (above) which R decreases (increases) with the rise of q. Theoretical analyses demonstrate that the higher efficiency found in the market with an insensitive population is related to its predictability. In such a predictable market, the agents following current prediction have a higher winning probability than those rejecting it. Analytical calculations are in good agreement with numerical data.     

Multiscale derivation of an augmented Smoluchowski equation

Smoluchowski and Fokker-Planck equations for the stochastic dynamics of order parameters have been derived previously. The question of the validity of the truncated perturbation series and the initial data for which these equations exist remains unexplored. To address these questions, we take a simple example, a nanoparticle in a host medium. A perturbation parameter ε, the ratio of the mass of a typical atom to that of the nanoparticle, is introduced and the Liouville equation is solved to O(ε²). Via a general kinematic equation for the reduced probability W of the location of the center-of-mass of the nanoparticle, the O(ε²) solution of the Liouville equation yields an equation for W to O(ε³). An augmented Smoluchowski equation for W is obtained from the O(ε²) analysis of the Liouville equation for a particular class of initial data. However, for a less restricted assumption, analysis of the Liouville equation to higher order is required to obtain closure.     

Large Signal Analysis of FM-AM Conversion in Dispersive Optical Fibers for PCM Systems Including Second Order Dispersion

By using large signal analysis for dispersive optical fiber, the FM-AM conversion with respect to binary intensity modulated PCM systems including second order dispersion term is discussed. The modified expression for power penalty has been derived and its impact on laser linewidth and bit rate has been investigated. For power penalty less than 0.5 dB, the plots between bit rate and transmission distance are plotted. It is seen that the transmission distance increases with decrease in linewidth over significant bit rates. The transmission distance with first order dispersion term for 300 MHz linewidth is approximately 800km. With proper first order dispersion compensation, i.e., with second order dispersion only, the transmission distance can be enhanced to 10 8 km for this linewidth. The linewidth requirements for systems with different bit rates and transmission distances are also calculated and discussed. Further, it is seen that by including the second-order dispersion term, the bit rate and transmission distance decreases. For higher linewidths, this decrease in bit rate and transmission distance is very less and vice versa. For 300 MHz linewidth, the decrease in transmission distance is just 30 km, and for 30 MHz linewidth, the decrease is approximately 600 km over significant bit rates.     

Buying on margin,selling short in an agent-based market model

Credit trading, or leverage trading, which includes buying on margin and selling short, plays an important role in financial markets, where agents tend to increase their leverages for increased profits. This paper presents an agent-based asset market model to study the effect of the permissive leverage level on traders’ wealth and overall market indicators. In this model, heterogeneous agents can assume fundamental value-converging expectations or trend-persistence expectations, and their effective demands of assets depend both on demand willingness and wealth constraints, where leverage can relieve the wealth constraints to some extent. The asset market price is determined by a market maker, who watches the market excess demand, and is influenced by noise factors. By simulations, we examine market results for different leverage ratios. At the individual level, we focus on how the leverage ratio influences agents’ wealth accumulation. At the market level, we focus on how the leverage ratio influences changes in the asset price, volatility, and trading volume. Qualitatively, our model provides some meaningful results supported by empirical facts. More importantly, we find a continuous phase transition as we increase the leverage threshold, which may provide a further prospective of credit trading.     

Microstructure of multilayer interface in an Al matrix composite reinforced by TiNi fiber

A multilayer interface was formed in the Al matrix composite which was reinforced by 30% volume fraction of TiNi fiber. The composite was fabricated by pressure infiltration process and the interface between the TiNi fiber and Al matrix was investigated by transmission electron microscopy (TEM) and energy dispersive spectroscopy (EDS). When the TiNi fiber was pre-oxidized in the air at 773 K for 1 h, three layers have been found and characterized in the interface: TiNi–B₂ layer near the TiNi fiber, Ti–Al compound layer with Ti and granular TiO₂ near the Al matrix, and Ti–Ni compound layer between TiNi–B₂ and Ti–Al compound layers. The effect of the multilayer interface on the mechanical properties of the composite was also discussed. The result showed that the uniaxial tensile strength of the composite at room temperature was 318 MPa, which was very close to the theoretical calculation value of 326 MPa. Moreover, the composite with good ductility exhibited a typical ductile-fracture pattern.     

The order with respect to oxygen and the activation energy for the burning of an anthracitic char in O2 in a fluidised bed, as measured using a rapid analyser for CO and CO2

Measurements of the oxidation of a coal char in a fluidised bed have the advantages that the rates of heat and mass transfer to and from a reacting particle are large and characterised well. However, problems have arisen from a combination of the slow, but typical, response–time (4 s) of the analysers for CO and CO₂ and the slow mixing of gases when filling a fairly large fluidised bed. The resulting time constant for the sampling system was 8 s and comparable to the time for combustion at 900 °C or above. The purpose of this work was to measure the kinetics of oxidation of a char in a smaller fluidised bed (with a shorter mixing time) using an analyser for CO and CO₂ with a response time as low as 0.1 s. The result is that the oxidation of an anthracitic char is now found to be first order in O₂ between 700 and 900 °C; at 900 °C the order previously measured was almost zero. The activation energy is now measured here to be 145 ± 25 kJ/mol, in agreement with some early work.     

Numerical simulations of the flow field ahead of an accelerating flame in an obstructed channel

The development of the unburned gas flow field ahead of a flame front in an obstructed channel was investigated using large eddy simulation (LES). The standard Smagorinsky–Lilly and dynamic Smagorinsky–Lilly subgrid models were used in these simulations. The geometry is essentially two-dimensional. The fence-type obstacles were placed on the top and bottom surfaces of a square cross-section channel, equally spaced along the channel length at the channel height. The laminar rollup of a vortex downstream of each obstacle, transition to turbulence, and growth of a recirculation zone between consecutive obstacles were observed in the simulations. By restricting the simulations to the early stages of the flame acceleration and by varying the domain width and domain length, the three-dimensionality of the vortex rollup process was investigated. It was found that initially the rollup process was two-dimensional and unaffected by the domain length and width. As the recirculation zone grew to fill the streamwise gap between obstacles, the length and width of the computational domain started to affect the simulation results. Three-dimensional flow structures formed within the shear layer, which was generated near the obstacle tips, and the core flow was affected by large-scale turbulence. The simulation predictions were compared to experimental schlieren images of the convection of helium tracer. The development of recirculation zones resulted in the formation of contraction and expansion regions near the obstacles, which significantly affected the centerline gas velocity. Oscillations in the centerline unburned gas velocity were found to be the dominate cause for the experimentally observed early flame-tip velocity oscillations. At later simulation times, regular oscillations in the unburned streamwise gas velocity were not observed, which is contrary to the experimental evidence. This suggests that fluctuations in the burning rate might be the source of the late flame-tip velocity oscillations. The effect of the obstacle blockage ratio (BR) on the development of the unburned gas flow field was also investigated by varying the obstacle height. Simulation predictions show favorable agreement with the experimental results and indicate that turbulence production increases with increasing obstacle BR.     

The effect of a market factor on information flow between stocks using the minimal spanning tree

We empirically investigated the effects of market factors on the information flow created from N(N−1)/2 linkage relationships among stocks. We also examined the possibility of employing the minimal spanning tree (MST) method, which is capable of reducing the number of links to N−1. We determined that market factors carry important information value regarding information flow among stocks. Moreover, the information flow among stocks showed time-varying properties according to the changes in market status. In particular, we noted that the information flow increased dramatically during periods of market crises. Finally, we confirmed, via the MST method, that the information flow among stocks could be assessed effectively with the reduced linkage relationships among all links among stocks from the perspective of the overall market.     

Self-organized criticality and stock market dynamics: an empirical study

The stock market is a complex self-interacting system, characterized by intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically the possibility that the market is in a self-organized critical state (SOC). A wavelet transform method is used in order to separate high activity periods, related to the avalanches found in sandpile models, from quiescent. A statistical analysis of the filtered data shows a power law behaviour in the avalanche size, duration and laminar times. The memory process, implied by the power law distribution of the laminar times, is not consistent with classical conservative models for self-organized criticality. We argue that a “near-SOC” state or a time dependence in the driver, which may be chaotic, can explain this behaviour.