agent-based financial markets and volatility dynamics blake lebaron international business school...
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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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GeometricRandom Walk
PriceVolatilityVolumed/p ratiosLiquidity
Agent-basedFinancial Market
Fundamental Input Market Output
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Overview
Agent-based financial marketsExample marketPrices and volatilityFuture challenges
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Agent-based Financial Markets
Many interacting strategiesEmergent 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
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.
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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 returnsTrend indicatorsDividend/price ratios
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Rules as Dynamic Strategies
Time
0
1
Portfolio weight
f(info(t))
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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
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Heterogeneous Memories(Long versus Short Memory)
Return History
2 years
5 years
6 months
Past Future
Present
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Short Memory: Psychology and Econometrics
Gambler’s fallacy/Law of small numbers Is this really irrational?
Regime changes Parameter changes Model misspecification
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Agent Wealth Dynamics
MemoryShort Long
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New Rules: Genetic Algorithm
Parent set = rules in useModify neural network weightsOperators:
Mutation Crossover Initialize
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GA Replaces Unused Rules
In Use
Unused
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Trading
Rules chosenDemand = f(p)Numerically clear marketTemporary equilibrium
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Homogeneous Equilibrium
Agents hold 100 percent equityPrice is proportional to dividend
Price/dividend constantUseful 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 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
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Price ComparisonAll Memory
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Price ComparisonLong Memory
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Price ComparisonReal S&P 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
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
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Price/return Features
MeanVarianceExcess kurtosis (Fat tails)Predictability (little)Long horizons (1 year)
Near Gaussian Slow convergence to fundamentals
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Volatility Features
Persistence/long memoryVolatility/volumeVolatility 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 implementationValidationApplications
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Model Implementation
ComplicatedCompute boundNonlinear 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 designPolicy
Interventions Systemic risk
Forecasting