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 using daily close prices.
A Nested Factor Model for Equity Markets: Reconciling Multifractal Stock Returns and Rough Index Volatilities
Ceremade, CNRS-UMR 7534, Université Paris-Dauphine PSL（巴黎第九大学）；Chair of Econophysics and Complex Systems, École polytechnique（巴黎综合理工学院）；LadHyX UMR CNRS 7646, École polytechnique（巴黎综合理工学院）；Capital Fund Management（资本基金管理公司）；Académie des Sciences（法兰西科学院）；SPE CNRS-UMR 6134, Université de Corse（科西嘉大学）
We analyze realized volatilities constructed using high-frequency stock data on the Tokyo Stock Exchange. In order to avoid non-trading hours issue in volatility calculations we define two realized volatilities calculated separately in the two trading sessions of the Tokyo Stock Exchange, i.e. morning and afternoon sessions. After calculating the realized volatilities at various sampling frequencies we evaluate the bias from the microstructure noise as a function of sampling frequency. Taking into account of the bias to realized volatility we examine returns standardized by realized volatiliti…
We have performed detailed multifractal analysis on the minutely volatility of two indexes and 1139 stocks in the Chinese stock markets based on the partition function approach. The partition function $χ_q(s)$ scales as a power law with respect to box size $s$. The scaling exponents $τ(q)$ form a nonlinear function of $q$. Statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1% significance level. The individual securities can be well modeled by the $p$-model in turbulence with $p = 0.40 \pm 0.02$. Based on the idea of ensemble averaging (i…
This study was conducted to find an appropriate statistical model to forecast the volatilities of PSEi using the model Generalized Autoregressive Conditional Heteroskedasticity (GARCH). Using the R software, the log returns of PSEi is modeled using various ARIMA models and with the presence of heteroskedasticity, the log returns was modeled using GARCH. Based on the analysis, GARCH models are the most appropriate to use for the log returns of PSEi. Among the selected GARCH models, GARCH (1,2) has the lowest AIC value and also has the highest LL value implying that GARCH (1,2) is the best model…
Being able to forcast extreme volatility is a central issue in financial risk management. We present a large volatility predicting method based on the distribution of recurrence intervals between volatilities exceeding a certain threshold $Q$ for a fixed expected recurrence time $τ_Q$. We find that the recurrence intervals are well approximated by the $q$-exponential distribution for all stocks and all $τ_Q$ values. Thus a analytical formula for determining the hazard probability $W(Δt |t)$ that a volatility above $Q$ will occur within a short interval $Δt$ if the last volatility exceeding $Q$…
We point out a stunning time asymmetry in the short time cross correlations between intra-day and overnight volatilities (absolute values of log-returns of stock prices). While overnight volatility is significantly (and positively) correlated with the intra-day volatility during the \textit{following} day (allowing thus non-trivial predictions), it is much less correlated with the intra-day volatility during the \textit{preceding} day. While the effect is not unexpected in view of previous observations, its robustness and extreme simplicity are remarkable.
What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made, it remains challenging. Physicists usually apply the concepts and methods in statistical physics, such as temporal correlation functions, to study financial dynamics. However, the usual volatility-return correlation function, which is local in time, typically fluctuates around zero. Here we construct dynamic observables nonlocal in time to explore the volatil…
This study conducts a comprehensive analysis of time series segmentation on the Japanese stock prices listed on the first section of the Tokyo Stock Exchange during the period from 4 January 2000 to 30 January 2012. A recursive segmentation procedure is used under the assumption of a Gaussian mixture. The daily number of each quintile of volatilities for all the segments is investigated empirically. It is found that from June 2004 to June 2007, a large majority of stocks are stable and that from 2008 several stocks showed instability. On March 2011, the daily number of instable securities stee…
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…
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…
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.
In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces the interaction which couples to spins of other systems. Simulations from our model show that time series exhibit the volatility clustering that is often observed in the real financial markets. Furthermore we also find non-zero cross correlations between the volatilities from our model. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated.
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…
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…
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…
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.
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 …
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…
The financial market and turbulence have been broadly compared on account of the same quantitative methods and several common stylized facts they shared. In this paper, the She-Leveque (SL) hierarchy, proposed to explain the anomalous scaling exponents deviated from Kolmogorov monofractal scaling of the velocity fluctuation in fluid turbulence, is applied to study and quantify the hierarchical structure of stock price fluctuations in financial markets. We therefore observed certain interesting results: (i) The hierarchical structure related to multifractal scaling generally presents in all the…
We study the continuous time random walk theory from financial tick data of the yen-dollar exchange rate transacted at the Japanese financial market. The dynamical behavior of returns and volatilities in this case is particularly treated at the long-time limit. We find that the volatility for prices shows a power-law with anomalous scaling exponent k = 0.96 (one minute) and 0.86 (ten minutes), and that our behavior occurs in the subdiffusive process. Our result presented will be compared with that of recent numerical calculations.
We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two decades in the mean and volatility dynamics, including the underlying volatility persistence and volatility spillovers structure. Using daily data from several key stock market indices we find that stock market returns exhibit time varying persistence in their corresponding conditional variances. Furthermore, the results of our bivariate GARCH models show the e…
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.
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 distribution of returns with the exponent outside the Levy stable region, the short memory of returns and the long memory of volatilities. The Hurst exponent of our model is asymptotically 1/2. An explanation is also given for the profile of the autocorrelation function, which is responsible for the value of the Hurst exponent.
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.
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 …
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.
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.
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…
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
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.
We decompose, within an ARCH framework, the daily volatility of stocks into overnight and intra-day contributions. We find, as perhaps expected, that the overnight and intra-day returns behave completely differently. For example, while past intra-day returns affect equally the future intra-day and overnight volatilities, past overnight returns have a weak effect on future intra-day volatilities (except for the very next one) but impact substantially future overnight volatilities. The exogenous component of overnight volatilities is found to be close to zero, which means that the lion's share o…
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…
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 $Ψ_t$ …
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas for the implied volatility in the Stein-Stein and the Heston model are obtained.
Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into $k$ classes using the $k$-shell decomposition method. We investigate the influences of trading behaviors on the price impact by comparing a closed national market (A-shares) with an international market (B-shares), individuals and institutions, partially filled and filled trades, buyer-initiated and seller-initiated trades, a…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Department of Electrical & Computer Engineering（电气与计算机工程系）
In this work, we apply machine learning techniques to historical stock prices to forecast future prices. To achieve this, we use recursive approaches that are appropriate for handling time series data. In particular, we apply a linear Kalman filter and different varieties of long short-term memory (LSTM) architectures to historical stock prices over a 10-year range (1/1/2011 - 1/1/2021). We quantify the results of these models by computing the error of the predicted values versus the historical values of each stock. We find that of the algorithms we investigated, a simple linear Kalman filter …
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.
Praxis Business School（实践商学院）；NSHM Knowledge Campus（NSHM知识园区）
Building predictive models for robust and accurate prediction of stock prices and stock price movement is a challenging research problem to solve. The well-known efficient market hypothesis believes in the impossibility of accurate prediction of future stock prices in an efficient stock market as the stock prices are assumed to be purely stochastic. However, numerous works proposed by researchers have demonstrated that it is possible to predict future stock prices with a high level of precision using sophisticated algorithms, model architectures, and the selection of appropriate variables in t…
With the heightened volatility in stock prices during the Covid-19 pandemic, the need for price forecasting has become more critical. We investigated the forecast performance of four models including Long-Short Term Memory, XGBoost, Autoregression, and Last Value on stock prices of Facebook, Amazon, Tesla, Google, and Apple in COVID-19 pandemic time to understand the accuracy and predictability of the models in this highly volatile time region. To train the models, the data of all stocks are split into train and test datasets. The test dataset starts from January 2020 to April 2021 which cover…
We investigate the spatial and temporal structures of four financial markets in Greater China. In particular, we uncover different characteristics of the four markets by analyzing the sector and subsector structures which are detected through the random matrix theory. Meanwhile, we observe that the Taiwan and Hongkong stock markets show a negative return-volatility correlation, i.e., the so-called leverage effect. The Shanghai and Shenzhen stock markets are more complicated. Before the year 2000, the two markets exhibit a strong positive return-volatility correlation, which is called the anti-…
The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period Jan 1994 -- Dec 1995. A sample of 40 million data points is extracted, which is substantially larger than studied hitherto. We find an asymptotic power-law behavior for the cumulative distribution with an exponent alpha approximately 3, well outside the Levy regime 0< alpha <2.
News-Driven Stock Price Forecasting in Indian Markets: A Comparative Study of Advanced Deep Learning Models
Pegasystems India Worldwide Pvt Ltd（佩加系统印度私人有限公司）；Vardhaman College of Engineering（瓦尔达曼工程学院）；Vasavi College of Engineering（瓦萨维工程学院）；D. K. College（D.K.学院）
The Black-Scholes Option pricing model (BSOPM) has long been in use for valuation of equity options to find the prices of stocks. In this work, using BSOPM, we have come up with a comparative analytical approach and numerical technique to find the price of call option and put option and considered these two prices as buying price and selling price of stocks of frontier markets so that we can predict the stock price (close price). Changes have been made to the model to find the parameters strike price and the time of expiration for calculating stock price of frontier markets. To verify the resu…
The stock market is volatile and complicated, especially in 2020. Because of a series of global and regional "black swans," such as the COVID-19 pandemic, the U.S. stock market triggered the circuit breaker three times within one week of March 9 to 16, which is unprecedented throughout history. Affected by the whole circumstance, the stock prices of individual corporations also plummeted by rates that were never predicted by any pre-developed forecasting models. It reveals that there was a lack of satisfactory models that could predict the changes in stocks prices when catastrophic, highly unl…
