Exploring Financial Instability Through Agent-based Modeling … · 2019-12-14 · Useful ﬁnance...

Exploring Financial InstabilityThrough Agent-based ModelingPart 1: Background and Early

Models

Blake LeBaronInternational Business School

Brandeis Universitywww.brandeis.edu/∼blebaron

Mini courseCIGI-INET: False Dichotomies

Course Road Map

Course Road Map

What AreAgent-basedModels?

Agent-basedFinancial Markets

Features of FinancialTime Series

Design Questions

A RepresentativeSimple Model

LeBaron CIGI/INET November 2012 – 2 / 38

Main goals and philosophy


⊲ Basic modeling tools




⊲ Short guide to literature





⊲ Contributions to understanding financial marketdynamics





⊲ Contributions to understanding financial marketdynamics

⊲ Macro economic connections

Where are we going?


⊲ Part 1:

•What are agent-based models?

•Simple models from finance

Where are we going?


⊲ Part 1:



⊲ Part 2:

•Adaptation and time series

•Heterogeneous gain learning

Where are we going?


⊲ Part 1:



⊲ Part 2:

•Adaptation and time series

•Heterogeneous gain learning

⊲ Part 3:

•Current directions in agent design and applications

•Empirical validation

• Instability and macro connections

Overview: Part 1


Course Road Map

What Are Agent-based Models?

Agent-based Financial Markets

Features of Financial Time Series

Design Questions

A Representative Simple Model

What Are Agent-basedModels?

Course Road Map




Design Questions



What are agent-based models?


⊲ Individual, autonomous agents




⊲ Distributions matter





⊲ Endogenous heterogeneity






⊲ Computational?

Where are they used?


⊲ Economics

⊲ Finance

⊲ Marketing



⊲ Economics

⊲ Finance

⊲ Marketing

⊲ Sociology

⊲ Political Science

⊲ Biology



⊲ Economics

⊲ Finance

⊲ Marketing

⊲ Sociology

⊲ Political Science

⊲ Biology

⊲ Applications

•Public policy

•Business

•Military

Simple model philosophy


⊲ Axelrod (1984)

⊲ Epstein and Axtell (1997)

⊲ Miller and Page (2007)

⊲ Schelling (1978)

Major resources in economics


⊲ Handbook:Leigh Tesfatsion and Kenneth L. Judd, editors. Handbook ofComputational Economics: Agent-based computationaleconomics. North-Holland, Amsterdam, 2006

http://www.econ.iastate.edu/tesfatsi/ace.htm

Major resources in economics


⊲ Handbook:Leigh Tesfatsion and Kenneth L. Judd, editors. Handbook ofComputational Economics: Agent-based computationaleconomics. North-Holland, Amsterdam, 2006

⊲ ACE website:http://www.econ.iastate.edu/tesfatsi/ace.htm

http://www.econ.iastate.edu/tesfatsi/ace.htm

Useful features for economic models


⊲ Endogenous coordination

⊲ Small independent, individual shocks → large macroshocks

Why simple finance models?


⊲ Understand financial price dynamics

⊲ Simpler agent behavior

⊲ Connections to macro

Why simple finance models?


⊲ Understand financial price dynamics

⊲ Simpler agent behavior

⊲ Connections to macro

⊲ Modeling:Et(Pt+1) > Pt

Agent-based FinancialMarkets

Course Road Map




Design Questions



Agent-based financial market goals


1.Replicate interesting time series features




2.Understand adaptive behavior and market ecology




2.Understand adaptive behavior and market ecology

3.More realistic modeling platform

Useful finance surveys


⊲ Chiarella et al. (2009)Carl Chiarella, Roberto Dieci, and Xue-Zhong He. Heterogeneity, market mechanisms, and asset price dynamics. In T. Hens and

K. R. Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution, pages 277–344. Elsevier, USA, 2009

⊲ Hommes and Wagener (2009)Cars H. Hommes and Florian Wagener. Complex evolutionary systems in behavioral finance. In Thorsten Hens and Klaus Reiner

Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution, pages 217–276. North-Holland, 2009

⊲ LeBaron (2006)B. LeBaron. Agent-based computational finance. In Leigh Tesfatsion and Kenneth L. Judd, editors, Handbook of Computational

Economics, pages 1187–1233. Elsevier, 2006

⊲ Lux (2009)Thomas Lux. Stochastic behavioral asset pricing models and the stylized facts. In Thorsten Hens and Klaus Reiner

Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution, pages 161–215. North-Holland, 2009

Key features


⊲ Interacting agents and/or strategies

⊲ Endogenous price time series


⊲ Self-contained learning:Learning → prices → learning → . . .

Time series and populations


Time series features Strategy populations

Features of Financial TimeSeries

Course Road Map




Design Questions



Financial empirical summary


⊲ Short term

•Uncorrelated returns

•Volatility persistence

•Leptokurtic (fat tailed) return distributions

Financial empirical summary


⊲ Short term

•Uncorrelated returns


•Leptokurtic (fat tailed) return distributions

⊲ Long term


•Return predictability

⋄Fundamental mean reversion

⋄Momentum (return persistence)

•Risk and return relationships

•Consumption and returns

Design Questions

Course Road Map




Design Questions



Design questions


⊲ Price determination

⊲ Learning and adaptation

⊲ Past data/learning gain

⊲ Information representations

⊲ Preferences

Very short history of agent-based finance


⊲ Multi-agent (many/open)

•Computational learning algorithms

• Interesting and rich evolutionary dynamics

•Difficult to analyze







⊲ Simple (few agent models)

•Relatively easy to analyze

•Simpler dynamics







⊲ Simple (few agent models)

•Relatively easy to analyze

•Simpler dynamics

⊲ Hybrid models (in between)

Examples of many type


⊲ Arthur et al. (1997)

⊲ Chen and Yeh (2002)

⊲ Tay and Linn (2001)

⊲ LeBaron (2001)

Many (open) type philosophy


⊲ Idealized features

•New strategies/types/firms appear to take advantageof environment

•Realistic

⊲ Problems

•How well can you build open ended systems?

•Need to put in some assumptions/structure

Few type philosophy


⊲ Small (sometimes 2) set of strategies

⊲ Often fixed parameters

⊲ Analytic results

⊲ Tractable dynamics

Two types


⊲ Trend following, adaptive expectations

Ei,t(Pt+1) = Pt + g(Pt − Pt−1) g > 0 (1)

Two types



Ei,t(Pt+1) = Pt + g(Pt − Pt−1) g > 0 (1)

⊲ Fundamental/mean reverting

Ei,t(Pt+1) = Pf,t + ν(Pt − Pf,t) 0 ≤ ν ≤ 1 (2)Pf,t = Fundamental value (3)

Two types



Ei,t(Pt+1) = Pt + g(Pt − Pt−1) g > 0 (1)

⊲ Fundamental/mean reverting

Ei,t(Pt+1) = Pf,t + ν(Pt − Pf,t) 0 ≤ ν ≤ 1 (2)Pf,t = Fundamental value (3)

⊲ Building block for interesting dynamics

Two type models: Ancient history


⊲ Zeeman (1974)Catastrophe theory

⊲ Frankel and Froot (1988)U.S. dollar behavior in the 80’s

⊲ Kirman (1991)Ants and contagion

Few type models: Core approaches


⊲ Brock and Hommes (1998)

⊲ Chiarella and He (2001)

⊲ Day and Huang (1990)

⊲ De Grauwe and Grimaldi (2006)

⊲ Farmer and Joshi (2002)

⊲ Levy et al. (1994)

⊲ Lux and Marchesi (1999)

⊲ Westerhoff and Reitz (2003)

A Representative SimpleModel

Course Road Map




Design Questions



Quick model structure


Gaunersdorfer and Hommes (2007)

⊲ Trend following traders

⊲ Fundamental traders

⊲ Market clearing

⊲ Adaptive populations

====Andrea Gaunersdorfer and Cars Hommes. A nonlinear structural model for

volatility clustering. In A. Kirman and G. Teyssiere, editors, Micro Economic

Models for Long Memory in Economics, pages 265–288. Springer-Verlag, 2007



EF (Pt+1) = P ∗ + ν(Pt − P ∗) 0 ≤ ν ≤ 1

ET (Pt+1) = Pt + g(Pt − Pt−1) g > 0

Pt+1 =1

1 + r((1− nt)E

F (Pt+1) + ntET (Pt+1)) + y



EF (Pt+1) = P ∗ + ν(Pt − P ∗) 0 ≤ ν ≤ 1

ET (Pt+1) = Pt + g(Pt − Pt−1) g > 0

Pt+1 =1

1 + r((1− nt)E

F (Pt+1) + ntET (Pt+1)) + y

zTt =ET (Pt+1) + y − (1 + r)Pt

γσ2

zFt =EF (Pt+1) + y − (1 + r)Pt

γσ2



Rt = Pt + yt − (1 + r)Pt−1 yt = y + δt

uTt = RtzRt−1 + ηuTt−1

uFt = RtzFt−1 + ηuFt−1



Rt = Pt + yt − (1 + r)Pt−1 yt = y + δt

uTt = RtzRt−1 + ηuTt−1

uFt = RtzFt−1 + ηuFt−1

nt =eβu

T

t

eβuTt + eβu

Ft

nt = nte−(Pt−P ∗)2/α

Prices and returns in GH (no noise)


0 200 400 600 800 1000 1200 1400 1600 1800 2000900

950

1000

1050

1100P

rice

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.2

0.4

0.6

0.8

1

Tre

nd fo

llow

ers(

frac

tion)

Adding noise to pricing


EF (Pt+1) = P ∗ + ν(Pt − P ∗) 0 ≤ ν ≤ 1

ET (Pt+1) = Pt + g(Pt − Pt−1) g > 0

Pt+1 =1

1 + r((1− nt)E

F (Pt+1) + ntET (Pt+1)) + y + ǫt+1

Prices and returns in GH (noise)


0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

500

1000

1500

2000P

rice

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000−0.1

−0.05

0

0.05

0.1

Ret

urn

Prices and trend fractions (nt) in GH (noise)


0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

500

1000

1500P

rice

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.2

0.4

0.6

0.8

1

Tre

nd fo

llow

ers(

frac

tion)

Few type summary


⊲ Can get basic price dynamics

⊲ Two strategies as core dynamic

⊲ Other models similar

⊲ Requires noise for realistic prices

⊲ Generates large, erratic swings in strategy fractions

Overview: Part 1


Course Road Map

What Are Agent-based Models?

Agent-based Financial Markets

Features of Financial Time Series

Design Questions

A Representative Simple Model

Date post:	29-Jun-2020
Category:	Documents
Upload:	others
View:	0 times
Download:	0 times

Exploring Financial Instability Through Agent-based Modeling … · 2019-12-14 · Useful ﬁnance...

Documents