Scaling theory of temporal correlations and size-dependent fluctuations in the traded value of stocks

Abstract

Records of the traded value of fi stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average <fi>: sigma(i) is proportional to <fi> alpha, with a strong time scale dependence alpha(Delta(t)). The nontrivial (i.e., neither 0.5 nor 1) value of alpha may have different origins and provides information about the microscopic dynamics. We present a set of stylized facts and then show their connection to such behavior. The functional form alpha(Delta(t)) originates from two aspects of the dynamics: Stocks of larger companies both tend to be traded in larger packages and also display stronger correlations of traded value. The results are integrated into a general framework that can be applied to a wide range of complex systems.

Multifactor analysis of multiscaling in volatility return intervals

“…We also test the relation between γ and share volume, and find no clear dependence, similar to that for number of trades. Although there is a certain relation between those measures, for instance, the number of trades depends on the capitalization [29], it does not guarantee that γ depend on the number of trades. For a company of a given number of trades, its capitalization has a range of values, and for a company of a given capitalization, its γ also distributes in a certain interval.…”

“…Market activity such as the intertrade time shows multiscaling in its distribution [28,29]. Recently we suggested that the return intervals distribution has multiscaling characteristics based on cumulative distributions and moments of scaled intervals for 500 constituents of the Standard & Poor's 500 index [24].…”

Why do Hurst Exponents of Traded Value Increase as the Logarithm of Company Size?

“…The trading of different stocks, on different markets and for various time periods is assumed to follow the same laws, and this is -at least qualitatively -indeed found in the case of many stylized facts [4,5]. However, recent studies [7,10] have pointed out, that this is not completely general. In this section, we present two properties of trading, that appear robust between markets and time periods, and which are related to a distinct company size dependence.…”

“…[7,10]), and smaller than β ≈ 1 for London's FTSE-100 [11]. In some sense trades appear to "stick together": Once a stock is traded more and more intensively, traders seem to prefer to increase their size as the frequency cannot be increased beyond limits.…”

“…In this paper we revisit a previously introduced framework for financial fluctuations [7], that can be used to explicitly show the absence of universal behavior in trading activity. The paper is organized as follows.…”