Scaling and Memory in Stock Market and Currency Variations: Similarities to Earthquakes Shlomo Havlin Bar-Ilan, Israel in collaboration with Kazuko Yamasaki Tokyo, Japan Valerie Livina, Sergey Tuzov, Lev Muchnik Bar-Ilan, Israel Armin Bunde Giessen, Germany H. Eugene Stanley Boston, USA

Challenges: (a) Are there scaling laws in return intervals? (b) Is there memory in the records of return intervals? (c) Are there similarities between economy and earthquakes? (d) How can we improve forecast of extreme events? Return intervals Stock market dataCurrency series Earthquakes Normalized absolute return

Scaling in Zipf plots Stock market Currency Earthquakes Length return interval for a given threshold q Ranking in decreasing length Scaling function

Scaling in distributions probability distribution to have a return interval for a given q Stock market Currency Earthquakes Scaling function IBM Yen-Dollar Japan

Memory in the records Conditional probability for having a return interval after for

Memory in the distributions Stock market Currency Earthquakes Clustering of extreme events Scaling function

Memory in the averages Stock market Currency Earthquakes mean conditional return interval

Summary  Scaling of return intervals Well approximated by single scaled function.  Strong effect of memory  Origin: long-term correlations in the volatilities.  Strong similarity in both scaling (for different q) and memory to earthquakes.  Application: improving risk assessment.

V. Livina, S. Tuzov, S. Havlin, A.Bunde, Recurrence intervals between earthquakes strongly depend on history, preprint physics/ (Physica A, in press). A.Bunde, J. Eichner, J. Kantelhardt, S. Havlin, Long- term memory: natural mechanism for the clustering of extreme events and anomalous residual times in climate Records (PRL, to appear). K. Yamasaki, S. Havlin, A. Bunde, H. E. Stanley, Scaling and memory in volatility return intervals in stock markets (to appear) Bibliography