1. 1 Dynamical Models for Herd Behavior in Financial Markets I. Introduction II. Model - Markets - Agents - Links III. Numerical results IV. Conclusions Sungmin Lee, Yup Kim Kyung Hee University, Seoul, Korea

2. 2 I. Introduction S&P 500 high frequency data of price return ) ( 10 R P Log Price return :

3. 3 Financial crashes Financial market agent link Information cluster : Trade & isolated V. Eguiluz, M. Zimmermann PRL v85,5659 (2000) : link

4. 4 II. Model ○ Markets - Static : number of agents is fixed. (Canonical Ensemble) - Dynamic : number of agents is not fixed. (Grand Canonical Ensemble) Static market Dynamic market Join Trade & leave M. Zimmermann

5. 5 ○ Sort of Agents 2. Smart agent 1. Normal agent M. Zimmermann

6. 6 ○ Links - Random attachment (Random Graph) - Preferential attachment (Scale Free network) Random graph 1 1 1 6 1 6 Scale free 2 18 36 2 2 M. Zimmermann 1 2 1 18

7. 7 ○ State of agent - inactive state [waiting ] - two active states [buying or selling ] ○ Measurement - Aggregate state of the system : - Price index : - Price return : ○ model rule - with probability, one agent participates in the market - with, the network of links evolves dynamically in the following way (1) an agent is selected at random (2) with probability, the state of remains inactive and,instead, a new link between agent and other agent (normal / smart agent, random graph / scale free link) (3) with, the state of becomes active by randomly choosing the state 1 or -1, and instantly all agents belonging to the same cluster follow this same action by imitation. is measured. And all agents in the active cluster leave the market.

8. 8 III. Numerical results ○ Static market - Phase diagram ** Zimmermann : (Static market / Normal agent / Random graph)

9. 9 - The distribution of return R Normal agent crash(manipulation) Financial crash ○ Dynamic market C.E G.C.E

10. 10 Smart agent No crash Financial crash

11. 11 - The distribution of the normalized return Normal agent

12. 12 Smart agent

13. 13 - Phase diagram a q 0.30.10.010.0050.001 0.0005 0.1 xx △△⊙⊙ 0.3 x △⊙⊙⊙⊙ 0.5 x △○ a q 0.30.10.010.0050.001 0.0005 0.1 xxxX △△ 0.3 xx △△△ X 0.5 x △○ Exponential decay Power law decay Exponential decay Power law decay ⊙ : crash(manipulation) X : no crash △ : subtle ○ : financial crash

14. 14 IV. Conclusions ◆ In static market, a herd behavior is enhanced by smart agents and scale free type links. ◆ We suggest a model for a dynamic herd behavior in financial market. ◆ In dynamic market, smart agents didn’t show financial crash at. ◆ The distribution of return shows exponential decay at. ◆ The distribution of return shows power law decay at.