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IntroductionLeBaron’s Model
Research Direction/Conclusion
Artificial Agent-Based Stock Markets
Sherif Ragab
Department of Computer ScienceThe American University in Cairo
October 21, 2008
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Outline
Introduction
LeBaron’s Model
Research Direction/Conclusion
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Outline
Introduction
LeBaron’s Model
Research Direction/Conclusion
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Outline
Introduction
LeBaron’s Model
Research Direction/Conclusion
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Objective & Motivation
I Objective: To successfully imitate real markets, in terms of1. Statistical Properties.2. Behavior.
I Motivation:1. Fundamental insight into how markets work.2. Prediction of behavior.3. Experimentation.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Objective & Motivation
I Objective: To successfully imitate real markets, in terms of1. Statistical Properties.2. Behavior.
I Motivation:1. Fundamental insight into how markets work.2. Prediction of behavior.3. Experimentation.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Real Markets
I Traders engage in buying and selling of a good or service.
I How are prices determined?1. Demand: How badly do people want it?2. Supply: How available is it?
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Real Markets
I Traders engage in buying and selling of a good or service.
I How are prices determined?1. Demand: How badly do people want it?2. Supply: How available is it?
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Real Markets
I Traders engage in buying and selling of a good or service.
I How are prices determined?1. Demand: How badly do people want it?2. Supply: How available is it?
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Supply & Demand
pe
qe
price
quantity
demand supply
pe = equilibrium priceqe = equilibrium quantity
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Supply & Demand
pe
qe
price
quantity
demand supply
pe = equilibrium priceqe = equilibrium quantity
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Supply & Demand
pe
qe
pe'
qe'
price
quantity
demand supply
pe = equilibrium priceqe = equilibrium quantity
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Constant Supply
pe
qe
price
quantity
demand
constantsupply
pe = equilibrium priceqe = equilibrium quantity
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Constant Supply
pe
qe
price
quantity
demand
constantsupply
pe'
pe = equilibrium priceqe = equilibrium quantity
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Market Structure
I Only one stock.
I n artificial agentssi −→ stock holdings of agent ici −→ cash of agent iwi −→ total wealth of agent ip −→ current price
wi = si · p + ci
Total number of stocks (∑
i∈A si ) is constant.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Market Structure
I Only one stock.
I n artificial agentssi −→ stock holdings of agent ici −→ cash of agent iwi −→ total wealth of agent ip −→ current price
wi = si · p + ci
Total number of stocks (∑
i∈A si ) is constant.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Artificial Trading Agents
I Represented by a demand function.
Di(p, ~z) =αi(p, ~z) · wi
p(1)
where: ~z = information vectorI Aggregate Demand:
N∑i=0
Di(p, ~z) = S (2)
where: N = number of agents, S = total supply of stocks
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Artificial Trading Agents
I Represented by a demand function.
Di(p, ~z) =αi(p, ~z) · wi
p(1)
where: ~z = information vectorI Aggregate Demand:
N∑i=0
Di(p, ~z) = S (2)
where: N = number of agents, S = total supply of stocks
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Information Set (~z) / and the NN (α)
I ~z is a the output of 6 functions:z0 = rt = ln(pnew−pold
pold) return
z1 = rt−1 return 1 time-step agoz2 = rt−2 return 2 time-steps agoz3 = ln(r · p/d) dividend-price ratioz4 = ln(p/m1) moving price-average 1z5 = ln(p/m2) moving price-average 2
I Features for the NN!I NN is described by a weight vector w
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Information Set (~z) / and the NN (α)
I ~z is a the output of 6 functions:z0 = rt = ln(pnew−pold
pold) return
z1 = rt−1 return 1 time-step agoz2 = rt−2 return 2 time-steps agoz3 = ln(r · p/d) dividend-price ratioz4 = ln(p/m1) moving price-average 1z5 = ln(p/m2) moving price-average 2
I Features for the NN!I NN is described by a weight vector w
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Information Set (~z) / and the NN (α)
I ~z is a the output of 6 functions:z0 = rt = ln(pnew−pold
pold) return
z1 = rt−1 return 1 time-step agoz2 = rt−2 return 2 time-steps agoz3 = ln(r · p/d) dividend-price ratioz4 = ln(p/m1) moving price-average 1z5 = ln(p/m2) moving price-average 2
I Features for the NN!I NN is described by a weight vector w
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Neural Network Structurez0
��
z1
��
z6
��+
w10
��
w00oo +
w11
��
w01oo . . . +
w16
��
w06oo
tanh
w20
))SSSSSSSSSSSSSSSSS tanh
w21
��
tanh
w26
ssggggggggggggggggggggggggg
w3 // P
��λx → ex
1+ex
��α
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Evolving the Agents
I Agents’ fitness determined through past performanceI Crossover: combine weights from agents to replace
another.I Mutation: randomly change weights with probability
determined by fitness
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Evolving the Agents
I Agents’ fitness determined through past performanceI Crossover: combine weights from agents to replace
another.I Mutation: randomly change weights with probability
determined by fitness
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Evolving the Agents
I Agents’ fitness determined through past performanceI Crossover: combine weights from agents to replace
another.I Mutation: randomly change weights with probability
determined by fitness
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Results
-
6price
time
-
6volume
time
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Interpreting price series
“Realism” of price-series is determined by applying statisticalmeasures to returns (price changes) and to volume.
I Mean.I Standard deviation.I Kurtosis.I Skewedness.I others.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Interpreting price series
“Realism” of price-series is determined by applying statisticalmeasures to returns (price changes) and to volume.
I Mean.I Standard deviation.I Kurtosis.I Skewedness.I others.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Interpreting price series
“Realism” of price-series is determined by applying statisticalmeasures to returns (price changes) and to volume.
I Mean.I Standard deviation.I Kurtosis.I Skewedness.I others.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Interpreting price series
“Realism” of price-series is determined by applying statisticalmeasures to returns (price changes) and to volume.
I Mean.I Standard deviation.I Kurtosis.I Skewedness.I others.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Modifying Current Models
Much space for improvement on AI side.Possible examples:
I Introduce imitation (replace GA with PSO).I Change market structure (e.g. more than one stock).
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Modifying Current Models
Much space for improvement on AI side.Possible examples:
I Introduce imitation (replace GA with PSO).I Change market structure (e.g. more than one stock).
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Modifying Current Models
Much space for improvement on AI side.Possible examples:
I Introduce imitation (replace GA with PSO).I Change market structure (e.g. more than one stock).
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Creating a New Model
I Modeling different types of markets.I Must be tractable.I Must be realistic.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Creating a New Model
I Modeling different types of markets.I Must be tractable.I Must be realistic.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
Creating a New Model
I Modeling different types of markets.I Must be tractable.I Must be realistic.
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
References
1. Blake LeBaron, “Empirical Regularities From Interacting Long- and Short-Memory Investors in anAgent-Based Stock Market.” IEEE Transactions on Evolutionary Computation, Vol. 5, No. 5, October 2001
2. N. F. Johnson, D. Lampert, P. Jeffries, M. L. Hart, and S. Howison, “Application of multi-agent games to theprediction of financial time-series.” Physica A, 299:222
3. Shu-Heng Chen and Chia-Hsuan Yeh, “Evolving traders and the business school with genetic programming:A new architecture of the agent-based artificial stock market.” Journal of Economic Dynamics and Control,Volume 25, Issues 3-4, March 2001, Pages 363-393
4. Blake LeBarona and Ryuichi Yamamoto, “Long-memory in an order-driven market .” Physica A: StatisticalMechanics and its Applications, Volume 383, Issue 1, 1 September 2007, Pages 85-89
Artificial Agent-Based Stock Markets
IntroductionLeBaron’s Model
Research Direction/Conclusion
The End
Questions?
Artificial Agent-Based Stock Markets