Agent-based Financial Markets and Volatility

Dynamics

Blake LeBaron

International Business School

Brandeis University

www.brandeis.edu/~blebaron

GeometricRandom Walk

PriceVolatilityVolumed/p ratiosLiquidity

Agent-basedFinancial Market

Fundamental Input Market Output

Overview

Agent-based financial marketsExample marketPrices and volatilityFuture challenges

Agent-based Financial Markets

Many interacting strategiesEmergent features

Correlations and coordination Macro dynamics

Bounded rationality

Bounded Rationality andSimple Rules

Why? Computational limitations Environmental complexity

Behavioral arguments Psychological biases Simple, robust heuristics

Computationally tractable strategies

Agent-based Economic Models

Website:Leigh Tesfatsion at Iowa St.http://www.econ.iastate.edu/tesfatsi/ace.htm

Handbook of Computational Economics (vol 2), Tesfatsion and Judd, forthcoming 2006.

Example Market

Detailed description: Calibrating an agent-based financial

market

Assets

Equity Risky dividend (Weekly)

Annual growth = 2%, std. = 6% Growth and variability in U.S. annual data Fixed supply (1 share)

Risk free Infinite supply Constant interest: 0% per year

Agents

500 Agents Intertemporal CRRA(log) utility

Consume constant fraction of wealth Myopic portfolio decisions

Trading Rules

250 rules (evolving) Information converted to portfolio

weights Fraction of wealth in risky asset [0,1]

Neural network structure Portfolio weight = f(info(t))

Information Variables

Past returnsTrend indicatorsDividend/price ratios

Rules as Dynamic Strategies

Time

0

1

Portfolio weight

f(info(t))

Portfolio Decision

Maximize expected log portfolio returnsEstimate over memory length histories

Olsen et al. Levy, Levy, Solomon(1994,2000)

Restrictions No borrowing No short sales

Heterogeneous Memories(Long versus Short Memory)

Return History

2 years

5 years

6 months

Past Future

Present

Short Memory: Psychology and Econometrics

Gambler’s fallacy/Law of small numbers Is this really irrational?

Regime changes Parameter changes Model misspecification

Agent Wealth Dynamics

MemoryShort Long

New Rules: Genetic Algorithm

Parent set = rules in useModify neural network weightsOperators:

Mutation Crossover Initialize

GA Replaces Unused Rules

In Use

Unused

Trading

Rules chosenDemand = f(p)Numerically clear marketTemporary equilibrium

Homogeneous Equilibrium

Agents hold 100 percent equityPrice is proportional to dividend

Price/dividend constantUseful benchmark

Two Experiments

All Memory Memory uniform 1/2-60 years

Long Memory Memory uniform 55-60 years

Time series sample Run for 50,000 weeks (~1000 years) Sample last 10,000 weeks (~200 years)

Financial Data

Weekly S&P (Schwert and Datastream) Period = 1947 - 2000 (Wednesday) Simple nominal returns (w/o dividends)

Weekly IBM returns and volume (Datastream)

Annual S&P (Shiller) Real S&P and dividends Short term interest

Price ComparisonAll Memory

Price ComparisonLong Memory

Price ComparisonReal S&P 500 (Shiller)

Weekly Returns

Weekly Return Histograms

Quantile RangesQ(1-x)-Q(x): Divided by Normal ranges

S&P weekly All memory

Q(0.95)-Q(0.05) 0.86 0.88

Q(0.99)-Q(0.01) 1.17 1.19

Price/return Features

MeanVarianceExcess kurtosis (Fat tails)Predictability (little)Long horizons (1 year)

Near Gaussian Slow convergence to fundamentals

Volatility Features

Persistence/long memoryVolatility/volumeVolatility asymmetry

Absolute Return Autocorrelations

Trading Volume Autocorrelations

Volume/Volatility Correlation

Returns /Absolute Returns

Crashes and Volume

Large price decreases and Trading volume Rule dispersion

Price and Trading Volume

Price and Rule Dispersion

Summary

Replicating many volatility features Persistence Volume connections Asymmetry

Crashes, homogeneity, and liquidity (price impact)

Simple behavioral foundations Not completely rational Well defined

Future Challenges

Model implementationValidationApplications

Model Implementation

ComplicatedCompute boundNonlinear features

Estimation Ergodicity

Future Validation Tools

Data inputs Price and dividend series training Wealth distributions

Agent calibration Micro data Experimental data

Live market information/interaction

Applications

Volatility/volume models Estimation and identification Risk prediction (crash probabilities)

Market and trader designPolicy

Interventions Systemic risk

Forecasting