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In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian…
We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H < 1/2$. This regime recently attracted a lot of attention both from the statistical and…
We give a stochastic microscopic modelling of stock markets driven by continuous double auction. If we take into account the mimetic behavior of traders, when they place limit order, our virtual markets shows the power-law tail of the…
We study the information dynamics between the largest Bitcoin exchange markets during the bubble in 2017-2018. By analysing high-frequency market-microstructure observables with different information theoretic measures for dynamical…
We consider the simulation of sample paths of a fractional Brownian motion with small values of the Hurst index and estimate the behavior of the expected maximum. We prove that, for each fixed $N$, the error of approximation $\mathbf…
The Kullback-Leibler cluster entropy $\mathcal{D_{C}}[P \| Q] $ is evaluated for the empirical and model probability distributions $P$ and $Q$ of the clusters formed in the realized volatility time series of five assets (SP\&500, NASDAQ,…
Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant…
Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical technique used to evaluate the strength of long-range correlations in empirical time series in terms of the Hurst exponent, $H$. Specifically, DFA quantifies the…
We consider assets for which price $X_t$ and squared volatility $Y_t$ are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT}, Y_{nT})$,…
Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…
Bitcoin is currently subject to a significant pay-for-speed trade-off. This is caused by lengthy and highly variable transaction confirmation times, especially during times of congestion. Users can reduce their transaction confirmation…
In this study, we consider a four-regime bubble model under the assumption of time-varying volatility and propose the algorithm of estimating the break dates with volatility correction: First, we estimate the emerging date of the explosive…
A review of the approximations in any time-dependent density functional calculation of excitation energies is given. The single-pole approximation for the susceptibility is used to understand errors in popular approximations for the…
This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To…
We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric…
Digital currencies have become popular in the last decade due to their non-dependency and decentralized nature. The price of these currencies has seen a lot of fluctuations at times, which has increased the need for prediction. As their…
Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…
While scale invariance is commonly observed in each component of real world multivariate signals, it is also often the case that the inter-component correlation structure is not fractally connected, i.e., its scaling behavior is not…
The mining of bitcoin is modeled using system dynamics, showing that the past evolution of the network hash rate can be explained to a large extent by an efficient market hypothesis applied to the mining of blocks. The possibility of a…