Scaling properties and universality of first-passage time probabilities in financial markets

TL;DR

This paper investigates the universal scaling and statistical properties of first-passage times in financial markets, revealing market-independent behaviors and potential applications in risk management and trading strategies.

Contribution

It demonstrates that first-passage time probabilities scale across different markets and time horizons, and proposes phenomenological models for their description.

Findings

Scaling of return with standard deviation collapses probabilities into single curves.

Survival probability exhibits a hyperbolic decay typical of Markovian processes.

Modified Weibull and Student distributions fit the data under certain regimes.

Abstract

Financial markets provide an ideal frame for the study of crossing or first-passage time events of non-Gaussian correlated dynamics mainly because large data sets are available. Tick-by-tick data of six futures markets are herein considered resulting in fat tailed first-passage time probabilities. The scaling of the return with the standard deviation collapses the probabilities of all markets examined, and also for different time horizons, into single curves, suggesting that first-passage statistics is market independent (at least for high-frequency data). On the other hand, a very closely related quantity, the survival probability, shows, away from the center and tails of the distribution, a hyperbolic $t^{-1/2}$ decay typical of a Markovian dynamics albeit the existence of memory in markets. Modifications of the Weibull and Student distributions are good candidates for the phenomenological description of first-passage time properties under certain regimes. The scaling strategies shown may be useful for risk control and algorithmic trading.