Intermittency in Quantitative Finance

Abstract

Factorial moments are convenient tools in nuclear physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. For uncorrelated particle production within $\Delta$, Gaussian statistics holds and factorial moments $F_q$ are equal to unity for all orders $q$. Correlations between particles lead to a broadening of the multiplicity distribution and to dynamical fluctuations. In this case, the factorial moments increase above 1 with decreasing $\Delta$. This corresponds to what can be called intermittency. In this letter, we show that a similar analysis can be developed on financial price series, with an adequate definition of factorial moments. An intermittent behavior can be extracted using moments of order 2 ($F_2$), illustrating a sensitivity to non-Gaussian fluctuations within time resolution below 4 hours. This confirms that correlations between price returns start to play a role when the time resolution is below this threshold.