Lower bound of market index scaling

Abstract

Past studies of market index scaling have taken for granted that the lower bound of price sampling is determined by the maximum time in between trades. To date, scaling had only been studied for sampling intervals above one minute. We seek to go beyond this and explore scaling at sampling intervals lower than a minute up until the true lower bound determined by the data resolution found in an order book. We have found that while the scaling behavior of the standard deviation of a market index is approximated well by that of a random walk, the scaling behavior of its maxima is not. The effect of oversampling at the lower bound may not be as drastic as we would expect. This leads us to believe that the dynamics at sub threshold intervals may not be as trivial as we may think.