Characterization of large price variations in financial markets

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 [1, 2]. In the present analysis, the definition of drawdowns is generalised to coarse-grained drawdowns or so-called ǫ-drawdowns and a link between such ǫ-outliers and preceding log-periodic power law bubbles previously identified [3] is established.