19 October 2015All rights reserved, Edward Tsang & Serafin Martinez jaramillo CHASM Co-evolutionary...

20 April 2023 All rights reserved, Edward Tsang & Serafin Martinez jaramillo

CHASMCo-evolutionary Heterogeneous

Artificial Stock Markets

Serafín Martínez Jaramillo

Edward Tsang

CCFEA, Essex


CHASM Research Summary

Ref: AI-ECON, Giardina et al 2003, other markets

Questions: How does the

price change?What is the

effect of learning by traders?

Artificial Marketendogenous

EDDIEEDDIEEDDIE

EDDIEEDDIEFundamental

EDDIEEDDIENoise

Poly

mor

phic

CHASM Platform

0

1000

2000

3000

4000

5000

6000

7000

8000


CHASM Overview

EDDIE AgentsAgents evolveHeterogeneous beliefsExample agent

Agents: technical, fundamental, noise or hybrid (mode switching)Experimenter controls the number of agents in each group


Experimenter’s controls

Users have control over:• Market Mechanisms• Number of traders• Etc.


Heterogeneity

LIMIT ORDERS

FUNDAMENTALIST

% TO TRADE

INDICATORS

COMPUTING POWER TIME & RETURN

LEARNING

No

Agents learn:Periodic ¦ Red Queen

Homogeneity

HeterogeneityHomogeneity

Heterogeneity

Homogeneity

50%

100%

Partial ¦ CompleteNo

Buy ¦ Sell

No

Base Case for Stylized Facts

Seven dimensions explored


Summary of Base Case

• Agents must be competent and use balanced training data (realistic expectation)

• Presence of fundamental traders needed

• Limit orders (trading strategies) essential

• % traded and time & return matter

• Heterogeneous computing power and beliefs not essential


A condition for stylized facts

Limit Order Yes No

Fundamental Traders

Partial / Complete

No

Computing Power

Homogeneous Heterogeneous

% to Trade 50% 100%

Indicators Heterogeneous Homogeneous

Time & Return Homogeneous Heterogeneous

Evolving agents No Yes


Learning Improves Performance


Learning under Red Queen


Prices and ReturnsStock price under Red Queen constraint

245

250

255

260

265

270

275

1 78 155 232 309 386 463 540 617 694 771 848 925

Period

Pri

ce

Return under the Red Queen constraint

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

Period

Ret

urn

Stock price under Ad Hoc retraining

252254256258260262264266268270272274

1 77 153 229 305 381 457 533 609 685 761 837 913 989

Period

Pri

ce

Return under Ad Hoc retraining

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

Period

Ret

urn


Artificial Finance Market Conclusions

• Platform developed– It supports a wide range of experiments

• Conditions for stylized facts identified in endogenous, realistic market

• Agents must be competent and realistic– Some must observe fundamental values

• Learning agents (EDDIE-based):– Statistical properties of returns and wealth distribution

changed– No need for fundamental trader!


CHASMCo-evolutionary Heterogeneous

Artificial Stock Market

Details and Explanations


CHASM Market Details

Assets

Market Mechanism

Excess Demand

Rationing

Wealth Dynamics

GIARDINA, I.A. and J.P.A. BOUCHAUD, 2003. Bubbles, crashes and intermittency in agent based market models. The European Physical Journal B-Condensed Matter , Vol.31, 421-437


Assets

The market participant i will be able to hold at time t, two different types of assets:

– a risky asset, denoted by hi(t) or

– cash, denoted by ci(t)

The stock price at time t will be denoted by P(t)

)(thi


Market Mechanism

• Agent i will take decision di(t) at time t: di(t) = 1 to buy

di(t) = –1 to sell

di(t) = 0 to do nothing

• Agent i makes a bid or offer of a fraction qi(t) of its current holding:

0)(0

1)()(

1)()(

)(

)(

tdif

tdiftgh

tdiftp

tcg

tq

i

ii

ii

i

g is a parameterci is cashhi is stock holdingp is price of stock


Excess Demand• The aggregated volume of bids: B(t)

• The aggregated volume of offers: O(t)

• Excess demand: D(t)

)(tB

)()()( tOtBtD

• Price is calculated in the following way:(λ is a parameter):

/)()1()( tDtPtP


Rationing

The amount of shares that the agent i will actually buy or sell is:

1)()(

1)()(

)()(

tdifthg

tdiftP

tCg

t

ii

ii

i


Wealth dynamics

Finally we can update the traders’ holdings of cash and the risky asset:

)()1()( tthth iii

)()()1()( tPttctc iii


CHASM Traders

Details and Explanations


Evolving Agents

• Evolution:– The wealth of an investor is the main factor to

search an improvement on his prediction rules (Red Queen dynamics)

• Benchmark and calibration:– Stylised facts

• Time:– Discrete time jumps


Example Agent

ITE

Buy ITEAnd

= Sell Hold= Not

<MV_12 233

TRB_5 27.3

VOL_12 -16.5


Traders Heterogeneity

• Noise traders– Homogeneous

• Fundamentalists– Departure from the fundamentals T– Threshold value

• Technical traders– Computational Capabilities– Indicators set– Rate of return and time horizon– Fundamental behavior– Limit orders


Traders

The market is composed by technical, fundamental and noise traders. We define NT as the number of technical traders, NF as the number of fundamental traders, NN as the number of noise traders and N as the total number of traders in the market.


Noise traders

The noise traders will take a decision to buy, sell or do nothing with different probabilities, pb, ps and pn respectively. Such probabilities are defined before the simulation and remain with the same value during the simulation.


Fundamentalists

• They will change their position on the risky asset if the price departs from a value that they perceive as the fundamental one. These traders will continue to adjust their positions until such difference T, is lower than a certain threshold value Farmer 1998.

• The above mentioned values will be generated for each individual trader by drawing random numbers from uniform intervals [Tmin, Tmax] for T and [min max] for . – These limits of such intervals are user specified.


Technical traders

Technical analysis is a key feature of the behavior of these agents. Technical analysis is an important tool for decision making in investment. Besides, there is strong evidence that technical analysis is being used extensively in financial markets.

We are not restricted to use just technical indicators. We use some momentum indicators as well.

EDDIE is the basic framework to the design of the investment strategy of our agents


Technical traders

The technical traders forecast if the price is going to rise by a certain r% within a certain number of days n.

They will be equipped with up to eight different technical and momentum indicators.

Under certain circumstances they will be able to behave like fundamentalists.


Limit orders

• A realistic investment strategy was necessary to complete the design of the agents.

• For that reason, limit orders were created as part of their exit strategy. – Orders to buy or sell at certain prices

• The technical traders can generate two types of limit orders:– Profit taking– Stop loss


CHASM Results


Artificial Financial Markets

• Santa Fe Artificial Stock Market• Zero Intelligence Agents• Minority Game• Microscopic simulation• Econo-physics• Genetic Programming• Neural Networks• Learning Classifier Systems


GP Markets comparison

• AI-ECON– Price based on excess

demand (Farmer’s work)

– Each tree is an agent– Business School:

Fixed retraining periodicity (exogenous)

– Notion of ranking

• CHASM – Price based on excess

demand– Each Trader has a

population of trees– Fixed periodicity and

“Red Queen” dynamics (endogenous)

– Relative Wealth drives the desire to improve

No Limit Order


No Fundamental Trader


Heterogeneous Computing Power


Trading 100% of capital


Homogeneous Indicators


Heterogeneous time and return


19 October 2015All rights reserved, Edward Tsang & Serafin Martinez jaramillo CHASM Co-evolutionary...

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