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Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using…
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…
This paper contributes a new machine learning solution for stock movement prediction, which aims to predict whether the price of a stock will be up or down in the near future. The key novelty is that we propose to employ adversarial…
We empirically analyze the most volatile component of the electricity price time series from two North-American wholesale electricity markets. We show that these time series exhibit fluctuations which are not described by a Brownian Motion,…
Previous studies of the stock price response to individual trades focused on single stocks. We empirically investigate the price response of one stock to the trades of other stocks. How large is the impact of one stock on others and vice…
The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday return data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time…
We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of…
We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets: (a) the New York Stock Exchange, (b) the…
This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modelled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of…
In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…
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…
Firms having similar business activities are correlated. We analyze two different cross-correlation matrices C constructed from (i) 30-min price fluctuations of 1000 US stocks for the 2-year period 1994-95 and (ii) 1-day price fluctuations…
This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The…
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given…
We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is…
In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…
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…
How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different timescales. Here we reveal that price…
Stock prices are influenced over time by underlying macroeconomic factors. Jumping out of the box of conventional assumptions about the unpredictability of the market noise, we modeled the changes of stock prices over time through the…
The methodology presented provides a quantitative way to characterize investor behavior and price dynamics within a particular asset class and time period. The methodology is applied to a data set consisting of over 250,000 data points of…