Characterization of large price variations in financial markets

TL;DR

This paper analyzes large price drops in financial markets, revealing that most follow a stretched exponential distribution, while extreme drops are outliers linked to prior bubble formations, enhancing risk assessment models.

Contribution

It generalizes drawdown definitions to epsilon-drawdowns and establishes a connection between outliers and preceding log-periodic bubbles.

Findings

Most drawdowns follow a stretched exponential distribution.

Largest drawdowns are outliers with higher occurrence rates.

Epsilon-drawdowns are linked to prior bubble formations.

Abstract

Statistics of drawdowns (loss from the last local maximum to the next local minimum) plays an important role in risk assessment of investment strategies. As they incorporate higher ($>$ two) order correlations, they offer a better measure of real market risks than the variance or other cumulants of daily (or some other fixed time scale) of returns. Previous results have shown that the vast majority of drawdowns occurring on the major financial markets have a distribution which is well-represented by a stretched exponential, while the largest drawdowns are occurring with a significantly larger rate than predicted by the bulk of the distribution and should thus be characterized as outliers. In the present analysis, the definition of drawdowns is generalised to coarse-grained drawdowns or so-called epsilon-drawdowns and a link between such epsilon-outliers and preceding log-periodic power law bubbles previously identified is established.