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

TLDR

The study examines interoccurrence times between daily losses below a threshold across 16 financial assets to characterize their distribution. The interoccurrence time distribution follows a universal q‑exponential form whose parameters depend only on the mean interoccurrence time, enabling accurate risk and Value‑at‑Risk estimation and revealing that multifractality prevents scaling with RQ.

Abstract

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.