Universal behaviour of interoccurrence times between losses in financial markets: An analytical description
Institut für Theoretische Physik, Justus-Liebig-Universität Giessen - 35392 Giessen, Germany
2 Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems 22290-180 Rio de Janeiro-RJ, Brazil
3 Santa Fe Institute - Santa Fe, NM 87501, USA
Accepted: 29 July 2011
We consider 16 representative financial records (stocks, indices, commodities, and exchange rates) and study the distribution PQ(r) of the interoccurrence times r between daily losses below negative thresholds −Q, for fixed mean interoccurrence time RQ. We find that in all cases, PQ(r) follows the form PQ(r)∝1/[(1+(q− 1)βr]1/(q−1), where β and q are universal constants that depend only on RQ, but not on a specific asset. While β depends only slightly on RQ, the q-value increases logarithmically with RQ, q=1+q0 ln(RQ/2), such that for RQ→2, PQ(r) approaches a simple exponential, PQ(r)≅2−r. The fact that PQ does not scale with RQ is due to the multifractality of the financial markets. The analytic form of PQ allows also to estimate both the risk function and the Value-at-Risk, and thus to improve the estimation of the financial risk.
PACS: 89.65.Gh – Economics; econophysics, financial markets, business and management / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.75.Da – Systems obeying scaling laws
© EPLA, 2011