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It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…
We conclude from an analysis of high resolution NYSE data that the distribution of the traded value $f_i$ (or volume) has a finite variance $\sigma_i$ for the very large majority of stocks $i$, and the distribution itself is non-universal…
We examine volatility of an Indian stock market in terms of aspects like participation, synchronization of stocks and quantification of volatility using the random matrix approach. Volatility pattern of the market is found using the BSE…
Financial volatility obeys two fascinating empirical regularities that apply to various assets, on various markets, and on various time scales: it is fat-tailed (more precisely power-law distributed) and it tends to be clustered in time.…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this…
We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S\&P 500 index prices and its modeling based on the L\'evy flights in two dimensions (2D). The efficacy of our proposed model is…
The distribution of returns in financial time series exhibits heavy tails. In empirical studies, it has been found that gaps between the orders in the order book lead to large price shifts and thereby to these heavy tails. We set up an…
Observations indicate that the distributions of stock returns in financial markets usually do not conform to normal distributions, but rather exhibit characteristics of high peaks, fat tails and biases. In this work, we assume that the…
We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow…
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…
The expOU stochastic volatility model is capable of reproducing fairly well most important statistical properties of financial markets daily data. Among them, the presence of multiple time scales in the volatility autocorrelation is perhaps…
We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $\sigma(t)$ which is directly observable from data. This quantity is usually…
The study of long-horizon returns has received a great deal of attention in recent years (see, for example, Boudoukh, Richardson, and Whitelaw (2008), Neuberger (2012) and Lee (2013), Fama and French (2018)). While most of the discussions…
It is commonly believed that the correlations between stock returns increase in high volatility periods. We investigate how much of these correlations can be explained within a simple non-Gaussian one-factor description with time…
We investigate the temporal correlations and multifractal nature of trading volume of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the trading volume exhibit size-dependent non-universal long memory and…
We establish the one-to one bilateral interrelations between an asymptotic behavior for the tail of distributions for random variables and its great moments evaluation. Our results generalize the famous Richter's ones.
In this paper we examine the relation between market returns and volatility measures through machine learning methods in a high-frequency environment. We implement a minute-by-minute rolling window intraday estimation method using two…
We select the $n$ stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the $k$ trading days of our database from the stock price time series. We study the ensemble return…
In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the…