Date Published: February 28, 2017
Publisher: Public Library of Science
Author(s): Roberto Mota Navarro, Hernán Larralde, Wei-Xing Zhou.
We present an agent based model of a single asset financial market that is capable of replicating most of the non-trivial statistical properties observed in real financial markets, generically referred to as stylized facts. In our model agents employ strategies inspired on those used in real markets, and a realistic trade mechanism based on a double auction order book. We study the role of the distinct types of trader on the return statistics: specifically, correlation properties (or lack thereof), volatility clustering, heavy tails, and the degree to which the distribution can be described by a log-normal. Further, by introducing the practice of “profit taking”, our model is also capable of replicating the stylized fact related to an asymmetry in the distribution of losses and gains.
In the past five decades a great number of time series of prices of various financial markets have become available and have been subjected to analysis to characterize their statistical properties [1–5]. From the study of these time series, a set of statistical properties common to many different markets, time periods and instruments, have been identified. The universality of these properties is of interest because the size, the participants and the events that affect the changes of price (returns) in a certain market may differ enormously from those that affect another. Yet, these investigations show that the variations in prices indeed share non trivial statistical properties, generically called stylized facts. In this work we present and study a model of a financial market and its participants which reproduces these stylized facts.
In this section we present the results obtained in various simulations. Although these results correspond to a particular set of values for the parameters, reasonable changes in the values of these parameters generate the same qualitative properties in the statistics of the model. It is of critical importance for the stability of the system to have a flow of limit orders (liquidity) capable of filling the gaps that are created when market orders enter the order book. To achieve this, the parameters that govern the flow of limit and market orders emitted by the agents must not give rise to bursts of market orders with a volume so large that one side of the order book is emptied. It is in this sense that we speak above of reasonable changes in the values of the parameters. Thus, for example, if we were to allow greater volumes of market orders to be placed within shorter time windows, say, by including a larger number of technical agents in a simulation, then, the parameters that affect the input of limit orders must be chosen accordingly, in such a way that the fundamental agents have enough time to restore the liquidity consumed by the increased number of market orders. Thus, we calibrated the model to achieve stability in the simulations and to reproduce the statistical properties of the returns observed in real life and did not consider calibrating the model to reproduce the order book stylized facts  Chiarella C, Iori G and Perelló J did in their work .
In this work we studied an agent based model of a single asset financial market with agents employing simple heuristic rules, which is capable of replicating the stylized facts reported in the literature. As in the LM model , we divided the population of agents into two groups according to the type of trading strategy they use: fundamental agents and technical agents. Further, we added heterogeneity within each group by varying the values of the parameters that control each agent’s behavior. Our aim was to create a model whose agents behaved realistically, as in the LM model, but with equally realistic market structures, namely, trading via a limit order book. We find, in accordance with previous models, that when the population of agents include technical agents, the returns present volatility clustering and a heavy tailed distribution. Further, we found that essentially no autocorrelation of the returns was present for any configuration of the populations. In addition to these main stylized facts, we find that when we allow the population of technical agents to engage in profit taking, the distribution of returns displays negative skewness and an asymmetry between losses and gains appears. By varying the frequency with which technical agents engage in profit taking, we can generate return distributions with varying degrees of separation in the tails. This dependence of the skewness over the frequency of profit taking suggests that this practice may be one of the causes of the appearance of the asymmetry in real financial markets.