1. Agent-based Financial Markets and Volatility Dynamics Blake LeBaron International Business School Brandeis University www.brandeis.edu/~blebaron

2. Geometric Random Walk Price Volatility Volume d/p ratios Liquidity Agent-based Financial Market Fundamental InputMarket Output

3. Overview Agent-based financial markets Example market Prices and volatility Future challenges

4. Agent-based Financial Markets Many interacting strategies Emergent features Correlations and coordination Macro dynamics Bounded rationality

5. Bounded Rationality and Simple Rules Why? Computational limitations Environmental complexity Behavioral arguments Psychological biases Simple, robust heuristics Computationally tractable strategies

6. Agent-based Economic Models Website: Leigh Tesfatsion at Iowa St. http://www.econ.iastate.edu/tesfatsi/ace.htm http://www.econ.iastate.edu/tesfatsi/ace.htm Handbook of Computational Economics (vol 2), Tesfatsion and Judd, forthcoming 2006.

7. Example Market Detailed description: Calibrating an agent-based financial market

8. 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

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

10. 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))

11. Information Variables Past returns Trend indicators Dividend/price ratios

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

13. 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

14. Heterogeneous Memories ( Long versus Short Memory) Return History 2 years 5 years 6 months Past Future Present

15. Short Memory: Psychology and Econometrics Gamblers fallacy/Law of small numbers Is this really irrational? Regime changes Parameter changes Model misspecification

16. Agent Wealth Dynamics Memory ShortLong

17. New Rules: Genetic Algorithm Parent set = rules in use Modify neural network weights Operators: Mutation Crossover Initialize

18. GA Replaces Unused Rules In Use Unused

19. Trading Rules chosen Demand = f(p) Numerically clear market Temporary equilibrium

20. Homogeneous Equilibrium Agents hold 100 percent equity Price is proportional to dividend Price/dividend constant Useful benchmark

21. 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)

22. 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

23. Price Comparison All Memory

24. Price Comparison Long Memory

25. Price Comparison Real S&P 500 (Shiller)

26. Weekly Returns

27. Weekly Return Histograms

28. Quantile Ranges Q(1-x)-Q(x): Divided by Normal ranges S&P weeklyAll memory Q(0.95)-Q(0.05)0.860.88 Q(0.99)-Q(0.01)1.171.19

29. Price/return Features Mean Variance Excess kurtosis (Fat tails) Predictability (little) Long horizons (1 year) Near Gaussian Slow convergence to fundamentals

30. Volatility Features Persistence/long memory Volatility/volume Volatility asymmetry

31. Absolute Return Autocorrelations

32. Trading Volume Autocorrelations

33. Volume/Volatility Correlation

34. Returns /Absolute Returns

35. Crashes and Volume Large price decreases and Trading volume Rule dispersion

36. Price and Trading Volume

37. Price and Rule Dispersion

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

39. Future Challenges Model implementation Validation Applications

40. Model Implementation Complicated Compute bound Nonlinear features Estimation Ergodicity

41. Future Validation Tools Data inputs Price and dividend series training Wealth distributions Agent calibration Micro data Experimental data Live market information/interaction

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