Agentbased Financial Markets and Volatility Dynamics

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Agent-based Financial Markets and Volatility
Dynamics

• Blake LeBaron
• International Business School
• Brandeis University
• www.brandeis.edu/blebaron

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Fundamental Input
Market Output
Price Volatility Volume d/p ratios Liquidity
Geometric Random Walk
Agent-based Financial Market
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Overview

• Agent-based financial markets
• Example market
• Prices and volatility
• Future challenges

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Agent-based Financial Markets

• Many interacting strategies
• Emergent features
• Correlations and coordination
• Macro dynamics
• Bounded rationality

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Bounded Rationality andSimple Rules

• Why?
• Computational limitations
• Environmental complexity
• Behavioral arguments
• Psychological biases
• Simple, robust heuristics
• Computationally tractable strategies

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Agent-based Economic Models

• WebsiteLeigh Tesfatsion at Iowa
  St.http//www.econ.iastate.edu/tesfatsi/ace.htm
• Handbook of Computational Economics (vol 2),
  Tesfatsion and Judd, forthcoming 2006.

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Example Market

• Detailed description
• Calibrating an agent-based financial market

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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

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Agents

• 500 Agents
• Intertemporal CRRA(log) utility
• Consume constant fraction of wealth
• Myopic portfolio decisions

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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))

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Information Variables

• Past returns
• Trend indicators
• Dividend/price ratios

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Rules as Dynamic Strategies
Portfolio weight
1
f(info(t))
0
Time
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Portfolio Decision

• Maximize expected log portfolio returns
• Estimate over memory length histories
• Olsen et al.
• Levy, Levy, Solomon(1994,2000)
• Restrictions
• No borrowing
• No short sales

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Heterogeneous Memories(Long versus Short Memory)
Present
Return History
Future
Past
2 years
5 years
6 months
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Short Memory Psychology and Econometrics

• Gamblers fallacy/Law of small numbers
• Is this really irrational?
• Regime changes
• Parameter changes
• Model misspecification

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Agent Wealth Dynamics
Short
Long
Memory
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New Rules Genetic Algorithm

• Parent set rules in use
• Modify neural network weights
• Operators
• Mutation
• Crossover
• Initialize

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GA Replaces Unused Rules
In Use
Unused
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Trading

• Rules chosen
• Demand f(p)
• Numerically clear market
• Temporary equilibrium

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Homogeneous Equilibrium

• Agents hold 100 percent equity
• Price is proportional to dividend
• Price/dividend constant
• Useful benchmark

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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)

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Financial Data

• Weekly SP (Schwert and Datastream)
• Period 1947 - 2000 (Wednesday)
• Simple nominal returns (w/o dividends)
• Weekly IBM returns and volume (Datastream)
• Annual SP (Shiller)
• Real SP and dividends
• Short term interest

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Price ComparisonAll Memory
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Price ComparisonLong Memory
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Price ComparisonReal SP 500 (Shiller)
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Weekly Returns
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Weekly Return Histograms
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Quantile RangesQ(1-x)-Q(x) Divided by Normal
ranges
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Price/return Features

• Mean
• Variance
• Excess kurtosis (Fat tails)
• Predictability (little)
• Long horizons (1 year)
• Near Gaussian
• Slow convergence to fundamentals

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Volatility Features

• Persistence/long memory
• Volatility/volume
• Volatility asymmetry

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Absolute Return Autocorrelations
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Trading Volume Autocorrelations
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Volume/Volatility Correlation
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Returns /Absolute Returns
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Crashes and Volume

• Large price decreases and
• Trading volume
• Rule dispersion

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Price and Trading Volume
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Price and Rule Dispersion
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Summary

• Replicating many volatility features
• Persistence
• Volume connections
• Asymmetry
• Crashes, homogeneity, and liquidity (price
  impact)
• Simple behavioral foundations
• Not completely rational
• Well defined

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Future Challenges

• Model implementation
• Validation
• Applications

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Model Implementation

• Complicated
• Compute bound
• Nonlinear features
• Estimation
• Ergodicity

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Future Validation Tools

• Data inputs
• Price and dividend series training
• Wealth distributions
• Agent calibration
• Micro data
• Experimental data
• Live market information/interaction

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Applications

• Volatility/volume models
• Estimation and identification
• Risk prediction (crash probabilities)
• Market and trader design
• Policy
• Interventions
• Systemic risk
• Forecasting