Models of financial markets as aggregates of dynamic heterogeneous adaptive agents faithfully replicate a large range of important stylized facts, and also offer us new insights into the under-lying behavior behind asset price movements. This paper presents a new market model contin-uing in this tradition. It is designed with learning mechanisms that are simple enough for easier analysis and interpretation, yet rich enough to pursue many of the experiments in evolution and heterogeneity present in older, more complex setups. The goal of this balance in market design is to provide a new foundational structure for understanding financial market dynamics from this different perspective.
Heterogeneous agent-based models have been applied to financial markets for quite some time. Their common theme is to consider worlds in which agents are adaptively learning over time, while they perceive and contribute to time series dynamics unfolding into the future. Endogenous price changes then feed back into the dynamic learning mechanisms. Agents are modeled as being boundedly rational, and the potential behavioral space for these systems is large. However, some distinctions in modeling strategies have emerged. One extreme of agent-based financial markets is what is known as a “few type” model where the number of potential trading strategies is limited to a small, and tractable set.
Dynamics of these markets can be determined analytically, and occasionally through computer simulations. Their simple structure often yields very easy and intuitive results. At the other extreme are what are known as “many type” models. In these cases the strategy space is large. In many cases it is infinite as agents are working to develop new and novel strategies. Obviously, the complexity of these models requires computational methods for analysis. This in itself is not a problem, but the abilities of researchers to analyze their detailed workings has been limited. The model presented here will try to seek a middle ground between these. It tries to be rich enough to generate interesting financial price and volume dynamics, but simple enough for careful analysis.
Traditionally, agent-based markets have used all kinds of internal structures to represent stock return forecasts. In this model simple linear forecasts will be used for both expected returns and conditional variances. These expectations of risk and return are the crucial inputs into a simplified, and standard portfolio choice problem. Linear forecasts will be drawn from four different forecast families which are chosen to be good general representations of what traders are doing. These include adaptive, or momentum, strategies, a mean reverting fundamental strategy, a short range predictive liquidity strategy, and a buy and hold benchmark. These four families are designed to provide a stylized representation of actual trader behavior, but should not be interpreted as literal trading strategies in actual use.
Several agent-based financial markets have highlighted the possibility for heterogeneity in the processing of past information by learning agents. This market will use differences in how the past is evaluated by traders to generate heterogeneous future forecasts. There are many good reasons for doing this. The most important is that the model explores the evolutionary interactions between short and long memory traders, with an interest in whether any of these types dominate. A second reason, is that this parameter is part of almost all learning algorithms. In this paper, learning will be of the constant gain variety, where a fixed gain parameter determines agents’ perception of how to process past data. Setting this to a specific value, constant across all agents, would impose a very large dynamic assumption on the model.
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Heterogeneous Gain Learning and the Dynamics of Asset Prices
