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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 11: Poster Session
SOE 11.12: Poster
Dienstag, 15. März 2011, 18:05–18:45, P2
Universal behavior in the dynamics of finanical markets — •Josef Ludescher1, Constantino Tsallis1,2, and Armin Bunde1 — 1Institut fur Theoretische Physik, Justus-Liebig-Universitat Giessen, 35392 Giessen, Germany — 2present address: Centro Brasileiro de Pesquisas Fisicas 22290-180 Rio de Janeiro-RJ, Brazil
In financial markets, the central quantity are the relative losses or gains of an asset in a certain fixed period of time. The time evolution of these returns can be characterized by the set of interoccurence times r between losses below a negative threshold Q, in particular by their mean interoccurence time RQ and their distribution function PQ(r). Here we consider daily losses in 16 representative financial records (stocks, indices, commodities and exchange rates). We find that in all cases PQ(r) follows the q-exponential form PQ(r)=1/(1+(q−1)βQ r)1/(q−1) , where β is a monotonously decreasing function for small RQ and becomes a constant for RQ>10. A is a normalization constant. The q-value appearing in the exponent of PQ decreases logarithmically with decreasing RQ, such that for RQ → 2, q tends to 1 and thus PQ(r) becomes a simple exponential. The fact that PQ does not scale with RQ is due to the multifractality of financial markets. The analytic form of the distribution allows also to estimate both the functional form of the risk function as well as the value-at-risk, and thus to improve estimation of the financial risk.