1. An Investigation of Market Dynamics and Wealth Distributions
Bounded Heterogonous Rational Agents in Artificial Stock Markets:
An Investigation of Market Dynamics and Wealth Distributions
Talal Alsulaiman
Stevens Institute of Technology
book. We use the price adjustment method as a function of bids and offers to discover the market price.
𝑝 (𝑡+1) = 𝑝 𝑡 1+𝛼 𝐷 𝑡 − 𝑆 𝑡
Where 𝑝 (𝑡+1) is the stock price at time t, 𝐷 𝑡 is the total bids at time 𝑡 , 𝑆 𝑡 is the total offers at time 𝑡 and 𝛼 is the sensitivity parameter.
Networks: network is one of the essential principles that characterize the complex systems. The dynamics of the networks are affected by the population and the structure of the network. These effects may be reflected in aggregate level
Learning: the development of learning in ASM varies from using zero intelligence agents to applying advanced artificial intelligence and machine learning techniques . The learning techniques in literature involves Bayesian learning, least square learning, genetic algorithm , genetic programming and artificial neural network.
The price is a function of dividend and risk free rate
𝑝 𝑡 = 𝑑 𝑡 𝑟
The fundamental investors know the process of the dividend but, yet they do not know the true value of the dividend at time 𝑡:
𝐸 𝑖 ln 𝑑 𝑡 =𝜇+ ln 𝑑 𝑡−1 + 𝜀 𝑖
𝐸 𝑖 𝑝 𝑡 = 𝐸 𝑖 ln 𝑑 𝑡 𝑟
Agent 𝑖 may share his expected price with the agents that have direct relationship with him as given:
𝐸 ∗ 𝑝 𝑡+1 =𝛼 𝑘 𝐸 𝑖 𝑝 𝑡+1 + 𝑑 𝑡+1 + (1+ 𝛼 𝑘 ) 𝑗+1,𝑗≠𝑖 𝑁 𝐼 𝑗 𝑗++1,𝑗≠𝑖 𝑁 𝐼 𝑗 𝐸 𝑗 𝑝 𝑡+1 + 𝑑 𝑡+1 𝑗++1,𝑗≠𝑖 𝑁 𝐼 𝑗 𝐸 𝑗 𝑝 𝑡+1 + 𝑑 𝑡+1
Where 𝛼 𝑘 is the weight given for agent’s expected price and expected dividend for the agent of type 𝑘.(𝑘=1 fundamental traders 𝑘=2 zero-intelligence traders)
𝐼 𝑗 = 1 𝑖𝑓 𝑎𝑔𝑒𝑛𝑡 𝑗 𝑖𝑠 𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑒𝑑 𝑡𝑜 𝑎𝑔𝑒𝑛𝑡 𝑖 0 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Returns
Background
Artificial stock markets (ASMs) aim to investigate the link between individual behaviors (micro level) and financial market dynamics (macro level). The variety of patterns at the macro level is a function of the ASM complexity. The financial market system is a complex system wherein the relation between the micro and macro level cannot be captured analytically. Computational approaches, such as simulation, are needed to understand this relation. Agent based simulation is commonly used to build ASMs. The basic components of the ASM are agents (investors), assets and assets prices.
Wealth
Objectives
The primary objective of this research will be achieved by answering the following questions:
1- What are the model’s most important parameters that reproduce patterns that observed in the real market and what are the optimal values of theses parameters?
2- What is the effect of population size of a certain type of agent?
3- Is there a significant effect of wealth amount at the beginning of investment period on wealth amount at the end of investment period?
4- What is the effect of communications and interactions between the agents on the statistical properties of the asset and the wealth of agents?
5- Are stylized facts fixed among the experiments?
Second Experiment Results
Flow of the Research
Movements of Stock Prices
Research Flow Chart
Parameter
Value
Network Type
Random
Connection 20
Fundamental Traders 10
Zero-intelligence
𝑑 𝑡
7.2 𝜇
0.01
𝜎 𝜀
𝛼 1 1
𝛼 2
0.25 𝑟
0.02
Define and formulate the components of the stock market
Developed the an agent based model the simulate the stock market
Verify the model
Is the model verified? No
Perform sensitivity analysis to find the important parameters
Calibrate the parameters
Is it a valid model?
Yes
Design the experiments
Test the hypotheses to measure the significant between the experiments by using Analysis of Variance
Returns
Network
Components of ASM
Wealth
Agents: the agents in our model are the investors. The investors in the real life have distinctive attributes. They have different preferences, investment and forecasting strategies , level of intelligence and ability to learn and their way of interacting. Similar to the real life , our model holds heterogeneous agents. The different actions of the investors would structure the market stock prices.
Assets: There are two different assets in our market that are risk free asset that  yields a constant risk free rate 𝑟 and risky stock that pays stochastic dividends 𝑑 𝑡 .
Price: in the literature, three pricing methods are widely used. The methods are price adjustment method, temporary equilibrium price and simulation of order
Experiments
The market consists of 20 agents by which 10 are zero-intelligence investors and 10 are investor who trades fundamentally. The stock is paying a stochastic dividend that follows random walks with drift:
ln 𝑑 𝑡 =𝜇+ ln 𝑑 𝑡−1 +𝜀
Where 𝜇 is the dividend growth rate and 𝜀~𝑁(0, 𝜎 𝜀 ).
First Experiment Results
There is no interaction in the first experiment
Movements of Stock Prices
This research was supported by Stevens Institute of Technology