Local Estimation of Stock Market Efficiency

A dynamical measure is designed to assess the time-changing degree of efficiency of stock markets, under the hypothesis that the price process can be modeled by the Multifractional Processes with Random Exponent (MPRE), a class of stochastic processes recently defined by Ayache and Taqqu (2005) to make the fractional Brownian motion more versatile in describing complex dynamics. The model succeeds in seizing most of the stylized facts well known in quantitative finance and lends itself to frame the questionable notion of (permanent) efficiency into a more realistic dynamical perspective. Our findings show that inefficiency has decidedly grown after the 2007-2009 financial crisis