Waiting Time Distribution of Korean Stock-market Index

1. Waiting Time Distribution of Korean Stock-market Index Jae Woo Lee, Kyoung Eun Lee Department of Physics, Inha University Per Arne Rikvold School of Computational Science Florida State University, Tallahassee, USA

2. Contents • Introduction • Price Index and Return • Probability Distribution of Absolute Return • Waiting Time Distribution • Summary

3. Complex Systems Physics: Critical Phenomena,SOC, Percolation,Network, etc Economics: Stocks,Bonds,etc Complex Systems Bio-Systems: Population, Food Webs,etc Geology, Metheology: Quake,Tsunami,etc

4. Stylized Facts in Stock-market • Fat tail • Volatility clustering • Short-range correlations of return • Long-range correlation of volatility • Multiscaling • Avalanche • Network Structure

5. Korea Composite Stock Price Index(KOSPI) 1997.11(IMF) 1992.3 1999.11

6. Normalized Return

7. Waiting Time (or First Return Time) Distribution of Absolute Return threshold

8. Applications of WTD • Earthquakes • SOC(BS model, BTW model, etc.) • Solar flares • Sand piles, rice piles • CTRW • Financial markets

13. Power-law of WTD

14. slope=-1.5 Exponential Bin Plot

18. Average waiting time

22. Critical exponents of WTD

23. Summary of WTD • Probability Density Function shows a power-law. • WTD of return follows a power-law. • There is a critical threshold of return. • Exponential bin plot gives better exponents. • WTD characterizes the avalanche of the stock index.

24. Scaling function