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In this comment we discuss the problem of reconciling the linear efficiency of price returns with the long-memory of supply and demand. We present new evidence that shows that efficiency is maintained by a liquidity imbalance that co-moves…
We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily…
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic…
The performance of a number of different measures of nonlinearity in a time series is compared numerically. Their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by Monte Carlo simulation for a number…
Working on different aspects of algorithmic trading we empirically discovered a new market invariant. It links together the volatility of the instrument with its traded volume, the average spread and the volume in the order book. The…
The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change…
Long-ranged, or power-law, behavior of correlation functions in both space and time is discussed for classical systems and for quantum systems at finite temperature, and is compared with the corresponding behavior in quantum systems at zero…
The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over $2\%$, and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type…
We perform a scaling analysis on NYSE daily returns. We show that volatility correlations are power-laws on a time range from one day to one year and, more important, that they exhibit a multiscale behaviour.
We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the…
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying…
In an asset return series there is a conditional asymmetric dependence between current return and past volatility depending on the current return's sign. To take into account the conditional asymmetry, we introduce new models for asset…
We propose a new volatility model based on two stylized facts of the volatility in the stock market: clustering and leverage effect. We calibrate our model parameters, in the leading order, with 77 years Dow Jones Industrial Average data.…
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in…
We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite…
This study aims to compare multiple deep learning-based forecasters for the task of predicting volatility using multivariate data. The paper evaluates a range of models, starting from simpler and shallower ones and progressing to deeper and…
We study the time dependent cross correlations of stock returns, i.e. we measure the correlation as the function of the time shift between pairs of stock return time series using tick-by-tick data. We find a weak but significant effect…
Can uncertainty about credit availability trigger a slowdown in real activity? This question is answered by using a novel method to identify shocks to uncertainty in access to credit. Time-variation in uncertainty about credit availability…
HYGARCH process is the commonly used long memory process in modeling the long-rang dependence in volatility. Financial time series are characterized by transition between phases of different volatility levels. The smooth transition HYGARCH…
We study the long-term memory in diverse stock market indices and foreign exchange rates using the Detrended Fluctuation Analysis(DFA). For all daily and high-frequency market data studied, no significant long-term memory property is…