Universal behaviour of interoccurrence times between losses in financial markets: An analytical description

We consider 16 representative financial records (stocks, indices, commodities, and exchange rates) and study the distribution P-Q(r) of the interoccurrence times r between daily losses below negative thresholds -Q, for fixed mean interoccurrence time R-Q. We find that in all cases, P-Q(r) follows the form P-Q(r) proportional to 1/[(1+(q - 1)beta r](1/(q-1)), where beta and q are universal constants that depend only on R-Q, but not on a specific asset. While beta depends only slightly on R-Q, the q-value increases logarithmically with R-Q, q = 1+ q(0) ln(R-Q/2), such that for R-Q -> 2, P-Q(r) approaches a simple exponential, P-Q(r) congruent to 2(-r). The fact that P-Q does not scale with R-Q is due to the multifractality of the financial markets. The analytic form of P-Q allows also to estimate both the risk function and the Value-at-Risk, and thus to improve the estimation of the financial risk. Copyright (C) EPLA, 2011