Related papers: Multifractal fluctuations in finance
This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when returns are…
Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both…
In statistical mechanics, evaluating finite-size macroscopic fluctuations typically relies on Edgeworth expansions. However, these perturbative methods append additive polynomial corrections that inevitably break down in the large deviation…
We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a…
We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail…
An interpretation of scale-invariant multiplicity fluctuations inside hadronic jets is presented. It is based on the branching mechanism with the angular ordering of soft partons in sequential branchings. A relationship with fractal…
In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale $q-$derivative in the non-extensive statistical mechanics and the axiomatic metric…
Let $\xi$ denote space-time white noise, and consider the following stochastic partial differential equations: (i) $\dot{u}=\frac{1}{2} u" + u\xi$, started identically at one; and (ii) $\dot{Z}=\frac12 Z" + \xi$, started identically at…
We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval $[0,T]$ in the limit $T \rightarrow \infty$. We further exhibit the asymptotic behaviour of the…
Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction…
We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space;…
We investigate the presence of residual multifractal background for monofractal signals which appears due to the finite length of the signals and (or) due to the long memory the signals reveal. This phenomenon is investigated numerically…
This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
The sub-fractional Brownian motion (sfBm) is a stochastic process, characterized by non-stationarity in their increments and long-range dependency, considered as an intermediate step between the standard Brownian motion (Bm) and the…
This paper develops a dynamic monetary model to study the (in)stability of the fractional reserve banking system. The model shows that the fractional reserve banking system can endanger stability in that equilibrium is more prone to exhibit…
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time…
We study the average shape of a fluctuation of a time series x(t), that is the average value <x(t)-x(0)>_T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law…
Recent technological development has enabled researchers to study social phenomena scientifically in detail and financial markets has particularly attracted physicists since the Brownian motion has played the key role as in physics. In our…
We describe the topology of superlevel sets of ($\alpha$-stable) L\'evy processes X by introducing so-called stochastic $\zeta$-functions, which are defined in terms of the widely used $\text{Pers}_p$-functional in the theory of persistence…