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Register a new userMarket Ecology, Pareto Wealth Distribution and Leptokurtic Returns in Microscopic Simulation of the LLS Stock Market Model
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The LLS stock market model is a model of heterogeneous quasi-rational investors operating in a complex environment about which they have incomplete information. We review the main features of this model and several of its extensions. We study the effects of investor heterogeneity and show that predation, competition, or symbiosis may occur between different investor populations. The dynamics of the LLS model lead to the empirically observed Pareto wealth distribution. Many properties observed in actual markets appear as natural consequences of the LLS dynamics: truncated Levy distribution of short-term returns, excess volatility, a return autocorrelation U-shape pattern, and a positive correlation between volume and absolute returns.
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Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a fair market, the wealth distribution among individual investors fulfills a power law. We then argue that fair play for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent $alpha sim 3/2$. In particular we relate it to the average number of individuals L depending on the average wealth: $alpha sim L/(L-1)$. Then we connect it to certain power exponents characterising the stock markets. We obtain that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent $beta sim alpha sim 3/2$. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order $gamma sim 2 alpha sim 3$. These results are consistent with recent experimental measurements of these power law exponents ([Maslov 2001] for $beta$ and [Gopikrishnan et al. 1999] for $gamma$).
Standard approaches to the theory of financial markets are based on equilibrium and efficiency. Here we develop an alternative based on concepts and methods developed by biologists, in which the wealth invested in a financial strategy is like the abundance of a species. We study a toy model of a market consisting of value investors, trend followers and noise traders. We show that the average returns of strategies are strongly density dependent, i.e. they depend on the wealth invested in each strategy at any given time. In the absence of noise the market would slowly evolve toward an efficient equilibrium, but the statistical uncertainty in profitability (which is adjusted to match real markets) makes this noisy and uncertain. Even in the long term, the market spends extended periods of time away from perfect efficiency. We show how core concepts from ecology, such as the community matrix and food webs, give insight into market behavior. The wealth dynamics of the market ecology explain how market inefficiencies spontaneously occur and gives insight into the origins of excess price volatility and deviations of prices from fundamental values.
Based on the minute-by-minute data of the Hang Seng Index in Hong Kong and the analysis of probability distribution and autocorrelations, we find that the index fluctuations for the first few minutes of daily opening show behaviors very different from those of the other times. In particular, the properties of tail distribution, which will show the power law scaling with exponent about -4 or an exponential-type decay, the volatility, and its correlations depend on the opening effect of each trading day.
We discuss price variations distributions in foreign exchange markets, characterizing them both in calendar and business time frameworks. The price dynamics is found to be the result of two distinct processes, a multi-variance diffusion and an error process. The presence of the latter, which dominates at short time scales, leads to indeterminacy principle in finance. Furthermore, dynamics does not allow for a scheme based on independent probability distributions, since volatility exhibits a strong correlation even at the shortest time scales.
The agent-based Yard-Sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a parameter $lambda$. Our numerical results indicate that the model has a critical point at $lambda=1$ between a phase for $lambda < 1$ with economic mobility and exponentially growing wealth of all agents and a non-stationary phase for $lambda geq 1$ with wealth condensation and no mobility. We define the energy of the system and show that the system can be considered to be in thermodynamic equilibrium for $lambda < 1$. Our estimates of various critical exponents are consistent with a mean-field theory (see following paper). The exponents do not obey the usual scaling laws unless a combination of parameters that we refer to as the Ginzburg parameter is held fixed as the transition is approached. The model illustrates that both poorer and richer agents benefit from economic growth if its distribution does not favor the richer agents too strongly. This work and the accompanying theory paper contribute to understanding whether the methods of equilibrium statistical mechanics can be applied to economic systems.
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