It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of probability affects the stability of the prices of the Stocks. Finally, we find the conditions under which the probability might be conserved in the market, challenging in this way the non-Hermitian nature of the Black-Scholes Hamiltonian.
We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the index is a tradable security, we also assume that it is efficient, in the following sense: we do not expect a prespecified self-financing trading strategy whose wealth is almost surely nonnegative at all times to outperform the index greatly. We show that, for a long investment horizon, the appreciation rate of the stock has to be close to the interest rate (assumed constant) plus the covariance between the volatility ve…
A surprising image of the stock market arises if the price time series of all Dow Jones Industrial Average stock components are represented in one chart at once. The chart evolves into a braid representation of the stock market by taking into account only the crossing of stocks and fixing a convention defining overcrossings and undercrossings. The braid of stocks prices has a remarkable connection with the topological quantum computer. Using pairs of quasi-particles, called non-abelian anyons, having their trajectories braided in time, topological quantum computer can effectively simulate the …
Existing surveys on stock market prediction often focus on traditional machine learning methods instead of deep learning methods. This motivates us to provide a structured and comprehensive overview of the research on stock market prediction. We present four elaborated subtasks of stock market prediction and propose a novel taxonomy to summarize the state-of-the-art models based on deep neural networks. In addition, we also provide detailed statistics on the datasets and evaluation metrics commonly used in the stock market. Finally, we point out several future directions by sharing some new pe…
A new model for the stock market price analysis is proposed. It is suggested to look at price as an everywhere discontinuous function of time of bounded variation.
We revisit the dynamic relationship between domestic economic policy uncertainty and stock markets using the symmetric thermal optimal path (TOPS) method. We observe different interaction patterns in emerging and developed markets. Economic policy uncertainty drives the stock market in China, while stock markets play a leading role in the UK and the US. Meanwhile, the lead-lag relationship of the three countries reacts significantly to extreme events. Our findings have important implications for investors and policy makers.
A new model for the stock market price analysis is proposed. It is suggested to look at price as an everywhere discontinuous function of time of bounded variation.
This article investigates the evolution of the Mexican stock market integration into the world market. First, we estimate the time-varying Mexican degree of market integration using an international conditional version of the CAPM with segmentation effects. Second, we study the structural breaks in this series. Finally, we relate the obtained results to important facts and economic events
Suppose one buys two very similar stocks and is curious about how much, after some time T, one of them will contribute to the overall asset, expecting, of course, that it should be around 1/2 of the sum. Here we examine this question within the classical Black and Scholes (BS) model, focusing on the evolution of the probability density function P(w) of a random variable w = a_T^{(1)}/(a_T^{(1)} + a_T^{(2)}) where a_T^{(1)} and a_T^{(2)} are the values of two (either European- or the Asian-style) options produced by two absolutely identical BS stochastic equations. We show that within the realm…
From the stock markets of six countries with high GDP, we study the stock indices, S&P 500 (NYSE, USA), SSE Composite (SSE, China), Nikkei (TSE, Japan), DAX (FSE, Germany), FTSE 100 (LSE, Britain) and NIFTY (NSE, India). The daily mean growth of the stock values is exponential. The daily price fluctuations about the mean growth are Gaussian, but with a non-zero asymptotic convergence. The growth of the monthly average of stock values is statistically self-similar to their daily growth. The monthly fluctuations of the price follow a Wiener process, with a decline of the volatility. The mean gro…
The main objective of this study is to check short term stress of COVID-19 on the American, European, Asian, and Pacific stock market indices, furthermore, the correlation between all the stock markets during the pandemic. Secondary data of 41 stock exchange from 32 countries have been collected from investing.com website from 1st July 2019 to 14th May 2020 for the stock market and the COVID-19 data has been collected according to the first cases reported in the country, stocks market are classified either developed or emerging economy, further divided according to the subcontinent i.e. Americ…
This study empirically re-examines fat tails in stock return distributions by applying statistical methods to an extensive dataset taken from the Korean stock market. The tails of the return distributions are shown to be much fatter in recent periods than in past periods and much fatter for small-capitalization stocks than for large-capitalization stocks. After controlling for the 1997 Korean foreign currency crisis and using the GARCH filter models to control for volatility clustering in the returns, the fat tails in the distribution of residuals are found to persist. We show that market cras…
This paper contributes to the literature on international stock market comovements and contagion. The novelty of our approach lies in application of wavelet tools to high-frequency financial market data, which allows us to understand the relationship between stock markets in a time-frequency domain. While major part of economic time series analysis is done in time or frequency domain separately, wavelet analysis combines these two fundamental approaches. Wavelet techniques uncover interesting dynamics of correlations between the Central and Eastern European (CEE) stock markets and the German D…
We investigate the behavior of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is presumed to oscillate and damp in a quantum spatial-periodic harmonic oscillator potential well. Complicated non-linear relations including inter-band positive correlation and intra-band negative correlation between the volatility and the trading volume of stocks are derived by considering the energy band structure of the model. The validity of price limitation is then examined and abnormal phenomena of a price-limited stock market (Shanghai Stoc…
We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market dynamics which we study both empirically and theoretically. We demonstrate that this model replicates observed market behavior on all relevant timescales (from days to years) reasonably well. Using the model, we obtain and discuss a number of results that pose implications for current market theory and offer potential practical applications.
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system--a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenbe…
The structure of return spillovers is examined by constructing Granger causality networks using daily closing prices of 20 developed markets from 2nd January 2006 to 31st December 2013. The data is properly aligned to take into account non-synchronous trading effects. The study of the resulting networks of over 94 sub-samples revealed three significant findings. First, after the recent financial crisis the impact of the US stock market has declined. Second, spatial probit models confirmed the role of the temporal proximity between market closing times for return spillovers, i.e. the time dista…
We applied Deep Q-Network with a Convolutional Neural Network function approximator, which takes stock chart images as input, for making global stock market predictions. Our model not only yields profit in the stock market of the country where it was trained but generally yields profit in global stock markets. We trained our model only in the US market and tested it in 31 different countries over 12 years. The portfolios constructed based on our model's output generally yield about 0.1 to 1.0 percent return per transaction prior to transaction costs in 31 countries. The results show that there…
In this paper we provide compelling evidence of cyclical mean reversion and multiperiod stock return predictability over horizons of about 30 years with a half-life of about 15 years. This implies that the US stock market follows a long-term rhythm where a period of above average returns tends to be followed by a period of below average returns. We demonstrate that this long-term stock market rhythm moves in lockstep with corresponding long-term economic, social, and political rhythms in the US. Assuming that the past relationship between these rhythms will hold unaltered in the future, we pro…
We analyze how investor expectations about economic growth and stock returns changed during the February-March 2020 stock market crash induced by the COVID-19 pandemic, as well as during the subsequent partial stock market recovery. We surveyed retail investors who are clients of Vanguard at three points in time: (i) on February 11-12, around the all-time stock market high, (ii) on March 11-12, after the stock market had collapsed by over 20\%, and (iii) on April 16-17, after the market had rallied 25\% from its lowest point. Following the crash, the average investor turned more pessimistic ab…
This paper investigates the impact of economic policy uncertainty (EPU) on the crash risk of US stock market during the COVID-19 pandemic. To this end, we use the GARCH-S (GARCH with skewness) model to estimate daily skewness as a proxy for the stock market crash risk. The empirical results show the significantly negative correlation between EPU and stock market crash risk, indicating the aggravation of EPU increase the crash risk. Moreover, the negative correlation gets stronger after the global COVID-19 outbreak, which shows the crash risk of the US stock market will be more affected by EPU …
The p-adic theory of the stock market is presented. It is shown that the price dynamics is very naturally described by the adelic function. The procedure of derivation of the functional integral formulation of adelic type is derived from microscopic models using generalized supercoherent states.
The efficiency of the stock market has a significant impact on the potential return on investment. An efficient market eliminates the possibility of arbitrage and unexploited profit opportunities. This study analyzes the weak form efficiency of the Indian Stock market based on the two major Indian stock exchanges, viz., BSE and NSE. The daily closing values of Sensex and Nifty indices for the period from April 2010 to March 2019 are used to perform the Runs test, the Autocorrelation test, and the Autoregression test. The study confirms that the Indian Stock market is weak form inefficient and …
The crowd panic and its contagion play non-negligible roles at the time of the stock crash, especially for China where inexperienced investors dominate the market. However, existing models rarely consider investors in networking stocks and accordingly miss the exact knowledge of how panic contagion leads to abrupt crash. In this paper, by networking stocks of sharing common mutual funds, a new methodology of investigating the market crash is presented. It is surprisingly revealed that the herding, which origins in the mimic of seeking for high diversity across investment strategies to lower in…
Yuan Ze University（元智大学）；National Taiwan University of Science and Technology（台湾科技大学）；Omniscient Cloud Technology（全知云技术公司）
Stock market prediction is still a challenging problem because there are many factors effect to the stock market price such as company news and performance, industry performance, investor sentiment, social media sentiment and economic factors. This work explores the predictability in the stock market using Deep Convolutional Network and candlestick charts. The outcome is utilized to design a decision support framework that can be used by traders to provide suggested indications of future stock price direction. We perform this work using various types of neural networks like convolutional neura…
