An Behavioral Model of Various Stock Market Dynamic Regimes

1. An Behavioral Model of Various Stock Market Dynamic Regimes Yu Tongkui（于同奎） Department of Systems Science, School of Management, BNU 博士年会（数量经济学） Shanghai, China

4. An Behavioral Model of Various Stock Market Dynamic Regimes Yu Tongkui（于同奎） Department of Systems Science, School of Management, BNU 博士年会（数量经济学） Shanghai, China

5. Dynamic Regimes Source: www.sohu.com

6. Dynamic Regimes Source: www.sohu.com

7. Motivation • Aim: (1)to find an underlying mechanism producing various dynamic regimes; (2) to investigate the factors (traders’ behavioral propensities) determining the market in which regime. Similar trading rules Similar traders Various regimes

8. Related works • Many models have been built to replicate different dynamic regimes: • Chiarella, C. (1992,2001,2004) • Lux, T. (1995,1998,1999) • Brock, W. A., Hommes, C. H. (1997, 2001) • ……

9. Bottom-up modeling • Consider the behavioral pattern of traders (agents) and model it as the switch probability among different groups • Derive a dynamical system to approximate the market evolution • So, the dynamical system has parameters for traders’ propensities

10. Our work • Follows Lux’s bottom up approach. • Builds a multi-agent model with four kinds of dynamic regimes (fundamental equilibrium, non-fundamental equilibrium, periodicity and chaos). • Concentrates on analyzing the effect of traders’ propensities (mimetic propensity, price-chasing propensity and strategy-switching propensity) on market dynamic regimes • by both analytical and multi-agent simulation approach.

11. 3 Outline: 2 1

12. Multi-agent Stock Market Model • Market components (chartists) (optimistic chartists) (pessimistic chartists) (fundamentalists)

13. Multi-agent Stock Market Model • Traders behavior • Modeled as the switch probability among different groups

14. Model • Switch probability between optimistic and pessimistic chartists • : market sentiment index • : mimetic propensity • : price-chasing propensity

15. Model • Switch probability between fundamentalists and chartists • : strategy-switching propensity

16. Model • Price formation ED: Excess demand

17. Procedure: Multi-agent Stock Market Model

18. Outline: 2

19. Stock Market Dynamical System Where: market sentiment index market rationality index p : market price

20. 3 Outline:

21. Fundamental equilibrium Dynamic regime (I)

22. Multi-agent Simulation System

23. Typical Simulation results with Fundamental equilibrium parameters

24. Dynamic regime (II) • Symmetric non-fundamental equilibrium

25. Typical Simulation results with Non-fundamental equilibrium parameters

26. Dynamic regime (III) - Periodicity

27. Dynamic regime (IV) - Chaos

28. Typical Multi-agent Simulations with analytical results

29. Traders’ propensities to dynamic regimes – Bifurcation diagram

30. Traders’ propensities to dynamic regimes – phase diagram

31. (Strategy-switching propensity)

32. Conclusion • Present an underlying mechanism that gives reasonable explanations to four kinds of market regimes. • Traders' behavioral propensities play an important role in determining market dynamic regimes.

33. Further research • A model with endogenous agent number N (Different degrees of attraction of additional traders may play an important role in real market). • Fast parameters (price) and slow parameters (traders’ propensities).

34. Prediction: if >4000 then >5000

35. Thanks for patience！Suggestions welcome!