On the interplay between multiscaling and stock dependence

Abstract

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this result conditional on the stocks' capitalization and on the kurtosis of stocks' log-returns in order to search for possible confounding effects. We show that a linear dependence with the logarithm of the capitalization and the logarithm of kurtosis does not explain the observed stylized fact, which we interpret as being originated from a deeper relationship.

On the statistics of scaling exponents and the multiscaling value at risk

“…where τ is defined in the range τ = [τ min , τ max ] and q = [q min , q max ] (Di Matteo 2007). A multiscaling proxy can be obtained by fitting the measured scaling exponent with a second degree polynomial (Buonocore, Aste, and Matteo 2016;Buonocore et al 2019) of the form 2…”

“…The measured B, B, represents the curvature of qH q . If B = 0, the process is uniscaling, while if B = 0, the process is multiscaling (Buonocore, Aste, and Matteo 2016;Buonocore et al 2019). In order to widely apply the multiscaling formalism in Finance, it is of vital importance the ability to correctly estimate the value of qH q and consequently, of A and B.…”

“…econophysics and mathematical Finance. The former devoted most of the attention to price and returns series in order to understand the source of multifractality from an empirical and theoretical point of view (Mandelbrot 1963(Mandelbrot , 1967Mantegna and Stanley 1995;Lux and Marchesi 1999;Mantegna and Stanley 1999;Gençay et al 2001;Calvet and Fisher 2002;Lux 2004;Di Matteo, Aste, and Dacorogna 2005;Di Matteo 2007;Buonocore et al 2019) and has recently identified a new stylized fact which relates (non-linearly) the strength of multiscaling and the dependence between stocks (Buonocore et al 2019). The latter instead, builds on the work of (Gatheral, Jaisson, and Rosenbaum 2018) on rough volatility and has been used to construct stochastic models with anti-persistent volatility dynamics (Gatheral, Jaisson, and Rosenbaum 2018;Livieri et al 2018;Fukasawa, Takabatake, and Westphal 2019;Takaishi 2020).…”

Econophysics and sociophysics: Their milestones & challenges

“…Network filtering procedures are also allowing to construct probabilistic sparse modeling for financial systems that can be used for forecasting, stress testing and risk allocation [113,114,115]. The problem of studying the economic growth patterns across countries is actually a subject of great attention to economists and econophysicists [116,117].…”

Coupled Criticality Analysis of Inflation and Unemployment

“…Scaling analysis has proven successful to address a wide range of phenomena in nature; see for example [ 53 , 54 , 55 , 56 , 57 , 58 ]. Economic indices are not an exception [ 49 , 50 , 59 , 60 , 61 , 62 ]. Moreover, these multiscaling features can be also described through an entropy function and free energy as introduced for multifractals [ 63 , 64 , 65 ].…”