It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the market impact of hidden orders (orders that reflect the true intention of buying and selling) that matches the empirically measured result and that reproduces some of the non-trivial and universal properties of stock returns (returns are percent changes in stock price). The theory is based on a simple premise, that the stock market can be modeled in a mechanical way - as a device that translates order flow into an uncorrelated price stream. Given that order flow is highly autocorrelated, this premise requires that market impact (1) depends on past order flow and (2) is asymmetric for buying and selling. I derive the specific form for the dependence in (1) by assuming that current liquidity responds to information about all currently active hidden orders (liquidity is a measure of the price response to a transaction of a given size). This produces an equation that suggests market impact should scale logarithmically with total order size. Using data from the London Stock Exchange I empirically measure market impact and show that the result matches the theory. Also using empirical data, I qualitatively specify the asymmetry of (2). Putting all results together, I form a model for market impact that reproduces three universal properties of stock returns - that returns are uncorrelated, that returns are distributed with a power law tail, and that the magnitude of returns is highly autocorrelated (also known as clustered volatility).
This paper analyzes the quantitative relations between stock prices and quantities of tradable stock shares in Chinese stock markets at six time points by means of Exploratory Data Analysis (EDA) method. It is found the resulting formulae have the same structure but different parameters. This paper also uses these relationships in order to analyse the feasibility of policies for Chinese Government to sell the state-owned shares in Chinese stock markets.
We study the temporal evolution of the market efficiency in the stock markets using the complexity, entropy density, standard deviation, autocorrelation function, and probability distribution of the log return for Standard and Poor's 500 (S&P 500), Nikkei stock average index, and Korean composition stock price index (KOSPI). Based on the microscopic spin model, we also find that these statistical quantities in stock markets depend on the market efficiency.
Geography effect is investigated for the Chinese stock market including the Shanghai and Shenzhen stock markets, based on the daily data of individual stocks. The Shanghai city and the Guangdong province can be identified in the stock geographical sector. By investigating a geographical correlation on a geographical parameter, the stock location is found to have an impact on the financial dynamics, except for the financial crisis time of the Shenzhen market. Stock distance effect is further studied, with a crossover behavior observed for the stock distance distribution. The probability of the …
Volatility dynamics of wavelet - filtered stock price time series is studied. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative characteristics of volatility dynamics of denoised series are noticeably different from those of the raw data and the noise.
The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this, we introduce a market model consisting of randomly fluctuating stocks that occasionally synchronize their short term draw-downs. These synchronous events are parameterized by a ``fear factor'', that reflects the occurrence of dramatic external events which affect the financial market.
We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an uncorrelated stochastic process. We proposed a simple model with a memory that gives a qualitative agreement with real data.
Summarized by the efficient market hypothesis, the idea that stock prices fully reflect all available information is always confronted with the behavior of real-world markets. While there is plenty of evidence indicating and quantifying the efficiency of stock markets, most studies assume this efficiency to be constant over time so that its dynamical and collective aspects remain poorly understood. Here we define the time-varying efficiency of stock markets by calculating the permutation entropy within sliding time-windows of log-returns of stock market indices. We show that major world stock …
The NYSE and NASDAQ stock markets have very different structures and there is continuing controversy over whether differences in stock price behaviour are due to market structure or company characteristics. As the influence of market structure on stock prices may be obscured by exogenous factors such as demand and supply, we hypothesize that modulation of the flow of transactions due to market operations may carry a stronger imprint of the internal market mechanism. We analyse times between consecutive transactions (ITT) for NYSE and NASDAQ stocks, and we relate the dynamical properties of the…
We investigate the strength and the direction of information transfer in the U.S. stock market between the composite stock price index of stock market and prices of individual stocks using the transfer entropy. Through the directionality of the information transfer, we find that individual stocks are influenced by the index of the market.
In the age of globalization, it is natural that the stock market of each country is not independent form the other markets. In this case, collective behavior could be emerged form their dependency together. This article studies the collective behavior of a set of forty influential markets in the world economy with the aim of exploring a global financial structure that could be called world-stock-market network. Towards this end, we analyze the cross-correlation matrix of the indices of these forty markets using Random Matrix Theory (RMT). We find the degree of collective behavior among the mar…
In this paper we quantitatively investigate the statistical properties of an ensemble of {\it stock prices}. We selected 1200 stocks traded in the Tokyo Stock Exchange and formed a statistical ensemble of daily stock prices for each trading day in the 5 year period from January 4, 1988 to December 30, 1992. We found that the tail of the complementary cumulative distribution function of the ensembles is accurately described by a power-law distribution with an exponent that moves in the range of $ 1.7 < α< 2.2 $.
This paper tends to define the quantitative relationship between the stock price and time as a time function. Based on the empirical evidence that the log-return of a stock is the series of white noise, a mathematical model of the integral white noise is established to describe the phenomenon of stock price movement. A deductive approach is used to derive the auto-correlation function, displacement formula and power spectral density of the stock price movement, which reveals not only the characteristics and rules of the movement but also the predictability of the stock price. The deductive fun…
This paper examines the short-run relationships between oil prices and GCC stock markets. Since GCC countries are major world energy market players, their stock markets may be susceptible to oil price shocks. To account for the fact that stock markets may respond nonlinearly to oil price shocks, we have examined both linear and nonlinear relationships. Our findings show that there are significant links between the two variables in Qatar, Oman, and UAE. Thus, stock markets in these countries react positively to oil price increases. For Bahrain, Kuwait, and Saudi Arabia we found that oil price c…
We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov type strategies we find that martingale null hypotheses are rejected for many stock price processes.
While the use of volatilities is pervasive throughout finance, our ability to determine the instantaneous volatility of stocks is nascent. Here, we present a method for measuring the temporal behavior of stocks, and show that stock prices for 24 DJIA stocks follow a stochastic process that describes an efficiently priced stock while using a volatility that changes deterministically with time. We find that the often observed, abnormally large kurtoses are due to temporal variations in the volatility. Our method can resolve changes in volatility and drift of the stocks as fast as a single day us…
It seems to be very unlikely that all relevant information in the stock market could be fully encoded in a geometrical shape. Still,the present paper will reveal the geometry behind the stock market transactions. The prices of market index (DJIA) stock components are arranged in ascending order from the smallest one in the left to the highest in the right. In such arrangement, as stock prices changes due to daily market quotations, it could be noticed that the price of a certain stock get over /under the price of a neighbor stock. These stocks are crossing. Arranged this way, the diagram of su…
We use insight from a model of earth tectonic plate movement to obtain a new understanding of the build up and release of stress in the price dynamics of the worlds stock exchanges. Nonlinearity enters the model due to a behavioral attribute of humans reacting disproportionately to big changes. This nonlinear response allows us to classify price movements of a given stock index as either being generated due to specific economic news for the country in question, or by the ensemble of the worlds stock exchanges reacting together like a complex system. Similar in structure to the Capital Asset Pr…
In order to understand the origin of stock price jumps, we cross-correlate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and around news are quite different: jumps are followed by increased volatility, whereas news tend on average to be followed by lower volatility levels. The shape of the volatility relaxation is also markedly different in the two cases. Finally, we provide direct evidence that large tra…
A simple and elegant arrangement of stock components of a portfolio (market index-DJIA) in a recent paper [1], has led to the construction of crossing of stocks diagram. The crossing stocks method revealed hidden remarkable algebraic and geometrical aspects of stock market. The present paper continues to uncover new mathematical structures residing from crossings of stocks diagram by introducing topological properties stock market is endowed with. The crossings of stocks are categorized as overcrossings and undercrossings and interpreted as generators of braid that stocks form in the process o…
Stock market indices are one of the most investigated complex systems in econophysics. Here we extend the existing literature on stock markets in connection with nonextensive statistical mechanics. We explore the nonextensivity of price volatilities for 34 major stock market indices between 2010 and 2019. We discover that stock markets follow nonextensive statistics regarding equilibrium, relaxation and sensitivity. We find nonextensive behavior in stock markets for developed countries, but not for developing countries. Distances between nonextensive triplets suggest that some stock markets mi…
In this study, we establish a network structure of the Korean stock market, one of the emerging markets, with its minimum spanning tree through the correlation matrix. Base on this analysis, it is found that the Korean stock market doesn't form the clusters of the business sectors or of the industry categories. When the MSCI (Morgan Stanley Capital International Inc.) index is exploited, we found that the clusters of the Korean stock market is formed. This finding implicates that the Korean market, in this context, is characteristically different form the mature markets.
We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price according to a power-law, and it isn't randomly drawn from the distribution, but has a strong correlation with the size of cumulative unexecuted limit orders on the price. It was also found that the limit price, on the coarse-grained price scale, tends to gather around the price whi…
We propose improved methods to identify stock groups using the correlation matrix of stock price changes. By filtering out the marketwide effect and the random noise, we construct the correlation matrix of stock groups in which nontrivial high correlations between stocks are found. Using the filtered correlation matrix, we successfully identify the multiple stock groups without any extra knowledge of the stocks by the optimization of the matrix representation and the percolation approach to the correlation-based network of stocks. These methods drastically reduce the ambiguities while finding …
How an investor invests in the market is largely influenced by the market efficiency because if a market is efficient, it is extremely difficult to make excessive returns because in an efficient market there will be no undervalued securities i.e. securities whose value is less than its assumed intrinsic value, which offer returns that are higher than the deserved expected returns, given their risk. However, there is a possibility of making excessive returns if the market is not efficient. This article analyses the five popular stock indices of BSE. This would not only test the efficiency of th…
We analyze the interaction between stock prices of big companies in the USA and Germany using Granger Causality. We claim that the increase in pair-wise Granger causality interaction between prices in the times of crisis is the consequence of simultaneous response of the markets to the outside events or external stimulus that is considered as a common driver to all the stocks, not a result of real causal predictability between the prices themselves. An alternative approach through recurrence analysis in single stock price series supports this claim. The observed patterns in the price of stocks…
Recent academic work has developed a method to determine, in real time, if a given stock is exhibiting a price bubble. Currently there is speculation in the financial press concerning the existence of a price bubble in the aftermath of the recent IPO of LinkedIn. We analyze stock price tick data from the short lifetime of this stock through May 24, 2011, and we find that LinkedIn has a price bubble.
This paper investigates the effect of cross-shareholding on stock price synchronicity, as a measure of price informativeness, of the listed firms in the Chinese stock market. We gauge firms' levels of cross-shareholdings in terms of centrality in the cross-shareholding network. It is confirmed that it is through a noise-reducing process that cross-shareholding promotes price synchronicity and reduces price delay. More importantly, this effect on price informativeness is pronounced for large firms and in the periods of market downturns. Overall, our analyses provide insights into the relation b…
Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders' short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit their up-limits and down-limits from time to time. However, the behaviors of price limit hits are not well studied partially due to the fact that main stock markets such as the US markets and most European markets do not set price limits. Here, we perform detailed analyses of the high-frequency data of all A-share common stocks traded on the Shanghai Stock E…
The article presents calculations that prove practical importance of the earlier derived theoretical relationship between the interest rate on the interbank credit market, volume of investment and the quantity of securities tradable on the stock exchange.
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 a large collection of data from three different stock markets, we present evidence that a modification to the random model -- adding a slow, but significant, fluctuation to the standard deviation of the process -- accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we…
Stock prices are driven by various factors. In particular, many individual investors who have relatively little financial knowledge rely heavily on the information from news stories when making investment decisions in the stock market. However, these stories may not reflect future stock prices because of the subjectivity in the news; stock prices may instead affect the news contents. This study aims to discover whether it is news or stock prices that have a greater impact on the other. To achieve this, we analyze the relationship between news sentiment and stock prices based on time series ana…
Stock price prediction can be made more efficient by considering the price fluctuations and understanding the sentiments of people. A limited number of models understand financial jargon or have labelled datasets concerning stock price change. To overcome this challenge, we introduced FinALBERT, an ALBERT based model trained to handle financial domain text classification tasks by labelling Stocktwits text data based on stock price change. We collected Stocktwits data for over ten years for 25 different companies, including the major five FAANG (Facebook, Amazon, Apple, Netflix, Google). These …
Price fluctuations in financial markets can be characterized by Lévy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long term, they similarly indicated an unique value. On the other hand, when analyzed in short term, parameters and the stock prices fluctuated with correlation, which shows that the stock markets are instable.
To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack o…
We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal properties of both stocks and commodities can be attributed mainly to the broad probability distribution of price fluctuations and secondarily to their temporal organization. Furthermore, we propose that, for commodities, stronger higher order correlations in price fluctuations result in broader multifractal spectra.
This article studies the financial integration between the six main Latin American markets and the US market in a nonlinear framework. Using the threshold cointegration techniques of Hansen and Seo (2002), we show significant threshold stock market linkages between Mexico, Chile and the US. Thus, the dynamics of these markets depends simultaneously on local and global risk factors. More importantly, our results show an on-off threshold financial integration process that is activated only when the stock price adjustment exceeds some level.
Prediction of stock price and stock price movement patterns has always been a critical area of research. While the well-known efficient market hypothesis rules out any possibility of accurate prediction of stock prices, there are formal propositions in the literature demonstrating accurate modeling of the predictive systems that can enable us to predict stock prices with a very high level of accuracy. In this paper, we present a suite of deep learning-based regression models that yields a very high level of accuracy in stock price prediction. To build our predictive models, we use the historic…
We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock prices traded in are consistent approximately with the Zipf's law or a power law. It is also obtained that the probability density of normalized returns for listed stocks almost has the form of the exponential function. Our results are compared with those of other numerical calculations.
China's stock market is the largest emerging market all over the world. It is widely accepted that the Chinese stock market is far from efficiency and it possesses possible linear and nonlinear dependence. We study the predictability of returns in the Chinese stock market by employing the wild bootstrap automatic variance ratio test and the generalized spectral test. We find that the return predictability vary over time and significant return predictability is observed around market turmoils. Our findings are consistent with the Adaptive Markets Hypothesis and have practical implications for m…
The importance of considering the volumes to analyze stock prices movements can be considered as a well-accepted practice in the financial area. However, when we look at the scientific production in this field, we still cannot find a unified model that includes volume and price variations for stock assessment purposes. In this paper we present a computer model that could fulfill this gap, proposing a new index to evaluate stock prices based on their historical prices and volumes traded. Besides the model can be considered mathematically very simple, it was able to improve significantly the per…
This paper presents a novel approach to predicting stock prices using technical analysis. By utilizing Ito's lemma and Euler-Maruyama methods, the researchers develop Heston and Geometric Brownian Motion models that take into account volatility, interest rate, and historical stock prices to generate predictions. The results of the study demonstrate that these models are effective in accurately predicting stock prices and outperform commonly used statistical indicators. The authors conclude that this technical analysis-based method offers a promising solution for stock market prediction.
We empirically investigated the effects of market factors on the information flow created from N(N-1)/2 linkage relationships among stocks. We also examined the possibility of employing the minimal spanning tree (MST) method, which is capable of reducing the number of links to N-1. We determined that market factors carry important information value regarding information flow among stocks. Moreover, the information flow among stocks evidenced time-varying properties according to the changes in market status. In particular, we noted that the information flow increased dramatically during periods…
We study precursors to the global market crash that occurred on all main stock exchanges throughout the world in October 2008 about three weeks after the bankruptcy of Lehman Brothers Holdings Inc. on 15 September. We examine the collective behavior of stock returns and analyze the market mode, which is a market-wide collective mode, with constituent issues of the FTSE 100 index listed on the London Stock Exchange. Before the market crash, a sharp rise in a measure of the collective behavior was observed. It was shown to be associated with news including the words "financial crisis." They did …
We report statistical regularities of the opening and closing auctions of French equities, focusing on the diffusive properties of the indicative auction price. Two mechanisms are at play as the auction end time nears: the typical price change magnitude decreases, favoring underdiffusion, while the rate of these events increases, potentially leading to overdiffusion. A third mechanism, caused by the strategic behavior of traders, is needed to produce nearly diffusive prices: waiting to submit buy orders until sell orders have decreased the indicative price and vice-versa.
This study presents an agent-based computational cross-market model for Chinese equity market structure, which includes both stocks and CSI 300 index futures. In this model, we design several stocks and one index futures to simulate this structure. This model allows heterogeneous investors to make investment decisions with restrictions including wealth, market trading mechanism, and risk management. Investors' demands and order submissions are endogenously determined. Our model successfully reproduces several key features of the Chinese financial markets including spot-futures basis distributi…
Stock market forecasting is a classic problem that has been thoroughly investigated using machine learning and artificial neural network based tools and techniques. Interesting aspects of this problem include its time reliance as well as its volatility and other complex relationships. To combine them, hidden markov models (HMMs) have been utilized to anticipate the price of stocks. We demonstrated the Maximum A Posteriori (MAP) HMM method for predicting stock prices for the next day based on previous data. An HMM is trained by analyzing the fractional change in the stock price as well as the i…
We introduce a non linear pricing model of individual stock returns that defines a stickiness parameter of the returns. The pricing model resembles the capital asset pricing model used in finance but has a non linear component inspired from models of earth quake tectonic plate movements. The link to tectonic plate movements happens, since price movements of a given stock index is seen adding stress to its components of individual stock returns, in order to follow the index. How closely individual stocks follow the indexs price movements, can then be used to define their stickiness
This paper tries to address the problem of stock market prediction leveraging artificial intelligence (AI) strategies. The stock market prediction can be modeled based on two principal analyses called technical and fundamental. In the technical analysis approach, the regression machine learning (ML) algorithms are employed to predict the stock price trend at the end of a business day based on the historical price data. In contrast, in the fundamental analysis, the classification ML algorithms are applied to classify the public sentiment based on news and social media. In the technical analysis…
There is convincing evidence showing that the probability distributions of stock returns in mature markets exhibit power-law tails and both the positive and negative tails conform to the inverse cubic law. It supports the possibility that the tail exponents are universal at least for mature markets in the sense that they do not depend on stock market, industry sector, and market capitalization. We investigate the distributions of one-minute intraday returns of all the A-share stocks traded in the Chinese stock market, which is the largest emerging market in the world. We find that the returns …
Price gap, defined as the logarithmic price difference between the first two occupied price levels on the same side of a limit order book (LOB), is a key determinant of market depth, which is one of the dimensions of liquidity. However, the properties of price gaps have not been thoroughly studied due to the less availability of ultrahigh frequency data. In the paper, we rebuild the LOB dynamics based on the order flow data of 26 A-share stocks traded on the Shenzhen Stock Exchange in 2003. Three key empirical statistical properties of price gaps are investigated. We find that the distribution…
Prediction of future movement of stock prices has been a subject matter of many research work. There is a gamut of literature of technical analysis of stock prices where the objective is to identify patterns in stock price movements and derive profit from it. Improving the prediction accuracy remains the single most challenge in this area of research. We propose a hybrid approach for stock price movement prediction using machine learning, deep learning, and natural language processing. We select the NIFTY 50 index values of the National Stock Exchange of India, and collect its daily price move…
We study the statistics of record-breaking events in daily stock prices of 366 stocks from the Standard and Poors 500 stock index. Both the record events in the daily stock prices themselves and the records in the daily returns are discussed. In both cases we try to describe the record statistics of the stock data with simple theoretical models. The daily returns are compared to i.i.d. RV's and the stock prices are modeled using a biased random walk, for which the record statistics are known. These models agree partly with the behavior of the stock data, but we also identify several interestin…
We describe and document three mechanisms by which corporations can influence or even control stock prices. (i) Parent and holding companies wield control over other publicly traded companies. (ii) Through clever management of treasury stock based on buyback programs and stock issuance, stock price fluctuations can be amplified or curbed. (iii) Finally, history shows a close interdependance between the level of stock prices on the one hand and merger and acquisition activity on the other hand. This perspective in which Boards of Directors of major companies shepherd the market offers a natural…
In this study, we have investigated empirically the effects of market properties on the degree of diversification of investment weights among stocks in a portfolio. The weights of stocks within a portfolio were determined on the basis of Markowitz's portfolio theory. We identified that there was a negative relationship between the influence of market properties and the degree of diversification of the weights among stocks in a portfolio. Furthermore, we noted that the random matrix theory method could control the properties of correlation matrix between stocks; this may be useful in improving …
The emergence of the COVID-19 pandemic, a new and novel risk factor, leads to the stock price crash due to the investors' rapid and synchronous sell-off. However, within a short period, the quality sectors start recovering from the bottom. A stock price model has been developed during such crises based on the net-fund-flow ($Ψ_t$) due to institutional investors, and financial antifragility ($ϕ$) of a company. We assume that during the crash, the stock price fall is independent of the $ϕ$. We study the effects of shock lengths and $ϕ$ on the stock price during the crises period using the $Ψ_t$ …
