Cryptocurrency Market Consolidation in 2020–2021

Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis of the minimal spanning trees calculated based on this matrix are applied for different positions of a moving window. The cryptocurrencies become more strongly cross-correlated among themselves than they used to be before. The average cross-correlations increase with time on a specific time scale in a way that resembles the Epps effect amplification when going from past to present. The minimal spanning trees also change their topology and, for the short time scales, they become more centralized with increasing maximum node degrees, while for the long time scales they become more distributed, but also more correlated at the same time. Apart from the inter-market dependencies, the detrended cross-correlations between the cryptocurrency market and some traditional markets, like the stock markets, commodity markets, and Forex, are also analyzed. The cryptocurrency market shows higher levels of cross-correlations with the other markets during the same turbulent periods, in which it is strongly cross-correlated itself.     

Empirical shape function of limit-order books in the Chinese stock market

We have analyzed the statistical probabilities of limit-order book (LOB) shape through building the book using the ultra-high-frequency data from 23 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the averaged LOB shape has a maximum away from the same best price for both buy and sell sides of the LOB. The LOB shape function has nice exponential form in the right tail. The buy side of the LOB is found to be abnormally thicker for the price levels close to the same best although there are much more sell orders on the book. We also find that the LOB shape functions for both buy and sell sides have periodic peaks with a period of five. The 1-min averaged volumes at fixed tick level follow log-normal distributions except for the left tails which display power-law behaviors, exhibit abnormal intraday patterns with increasing trend, and possess long memory that cannot be explained by the intraday patterns. Academic implications of our empirical results are also briefly discussed.     

Mutual Information between Order Book Layers

The order book is a list of all current buy or sell orders for a given financial security. The rise of electronic stock exchanges introduced a debate about the relevance of the information it encapsulates of the activity of traders. Here, we approach this topic from a theoretical perspective, estimating the amount of mutual information between order book layers, i.e., different buy/sell layers, which are aggregated by buy/sell orders. We show that (i) layers are not independent (in the sense that the mutual information is statistically larger than zero), (ii) the mutual information between layers is small (compared to the joint entropy), and (iii) the mutual information between layers increases when comparing the uppermost layers to the deepest layers analyzed (i.e., further away from the market price). Our findings, and our method for estimating mutual information, are relevant to developing trading strategies that attempt to utilize the information content of the limit order book.     

Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets

In this paper, we investigate the cross-correlations between the stock market in China and markets in Japan, South Korea and Hong Kong. We use not only the qualitative analysis of the cross-correlation test, but also the quantitative analysis of the MF-X-DFA. Our findings confirm the existence of cross-correlations between the stock market in China and markets in Japan, South Korea and Hong Kong, which have strongly multifractal features. We find that the cross-correlations display the characteristic of multifractality in the short term. Moreover, the cross-correlations of small fluctuations are persistent and those of large fluctuations are anti-persistent in the short term, while the cross-correlations of all kinds of fluctuations are persistent in the long term. Furthermore, based on the multifractal spectrum, we also find that the multifractality of cross-correlation between stock markets in China and Japan are stronger than those between China and South Korea, as well as between China and Hong Kong.     

Price–volume cross-correlation analysis of CSI300 index futures

We investigate the cross-correlation between price returns and trading volumes for the China Securities Index 300 (CSI300) index futures, which are the only stock index futures traded on the China Financial Futures Exchange (CFFEX). The basic statistics suggest that distributions of these two time series are not normal but exhibit fat tails. Based on the detrended cross-correlation analysis (DCCA), we obtain that returns and trading volumes are long-range cross-correlated. The existence of multifractality in the cross-correlation between returns and trading volumes has been proven with the multifractal detrended cross-correlation analysis (MFDCCA) algorithm. The multifractal analysis also confirms that returns and trading volumes have different degrees of multifractality. We further perform a cross-correlation statistic to verify whether the cross-correlation significantly exists between returns and trading volumes for CSI300 index futures. In addition, results of the test for lead-lag effect demonstrate that contemporaneous cross-correlation of return and trading volume series is stronger than cross-correlations of leaded or lagged series.     

Topological properties of stock networks based on minimal spanning tree and random matrix theory in financial time series

We investigated the topological properties of stock networks constructed by a minimal spanning tree. We compared the original stock network with the estimated network; the original network is obtained by the actual stock returns, while the estimated network is the correlation matrix created by random matrix theory. We found that the consistency between the two networks increases as more eigenvalues are considered. In addition, we suggested that the largest eigenvalue has a significant influence on the formation of stock networks.     

The oscillation of stock price by majority orienting traders with investment position

We consider an interacting particle system for the stock price fluctuation. The change of the stock price with a feedback by the price considering the herding behavior (majority orienting behavior) of traders, gives the van der Pol equation as a deterministic approximation. Considering the investment position of each trader, we introduce the delayed van der Pol equation. The history of investment positions, for example sell or buy, of each trader for a stock makes a memory effect, which is modeled by using the time retardation. The delayed van der Pol equation model seems to be natural and explains typical phenomena, for example triangle pattern, volatility jumps, price jumps and price trends, known for the time series of a stock price.     

Stylized facts in internal rates of return on stock index and its derivative transactions

Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in normalized log returns, the probability distributions for such single asset encounters incorporate the time factor by means of the internal rate of return, defined as the continuous compound interest. Resulting stylized facts are shown in the probability distributions derived from the daily series of TOPIX, S & P 500 and FTSE 100 index close values. The application of the above analysis to minute-tick data of NIKKEI 225 and its futures market, respectively, reveals an interesting difference in the behavior of the two probability distributions, in case a threshold on the minimal duration of the long position is imposed. It is therefore suggested that the probability distributions of the internal rates of return could be used for causality mining between the underlying and derivative stock markets. The highly specific discrete spectrum, which results from noise trader strategies as opposed to the smooth distributions observed for fundamentalist strategies in single encounter transactions may be useful in deducing the type of investment strategy from trading revenues of small portfolio investors.     

Understanding agent-based models of financial markets: A bottom–up approach based on order parameters and phase diagrams

We describe a bottom–up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby N$N$ independent traders buy and sell M$M$ stocks through an order book that acts as a clearing house. The price of a stock increases whenever it is bought and decreases whenever it is sold. Price changes are updated by the order book before the next transaction takes place. In this deterministic model, all traders based their buy decisions on a call utility function, and all their sell decisions on a put utility function. We then make the agent-based model more realistic, by either having a fraction _fb$f_b$ of traders buy a random stock on offer, or a fraction _fs$f_s$ of traders sell a random stock in their portfolio. Based on our simulations, we find that it is possible to identify useful order parameters from the steady-state price distributions of all three models. Using these order parameters as a guide, we find three phases: (i) the dead market; (ii) the boom market; and (iii) the jammed market in the phase diagram of the deterministic model. Comparing the phase diagrams of the stochastic models against that of the deterministic model, we realize that the primary effect of stochasticity is to eliminate the dead market phase.     

Network structure of cross-correlations among the world market indices

We report the results of an investigation of the properties of the networks formed by the cross-correlations of the daily and weekly index changes of 143 stock market indices from 59 different countries. Analysis of the asset graphs, minimum spanning trees (MST) and planar maximally filtered graphs (PMFG) of the afermentioned networks confirms that globalization has been increasing in recent years. North American and European markets are observed to be much more strongly connected among themselves compared to the integration with the other geographical regions. Surprisingly, the integration of East Asian markets among themselves as well as to the Western markets is found to be rather weak. MST and PMFG of both daily and weekly return correlations indicates that the clustering of the indices is mostly geographical. The French fsbf250 index is found to be most important node of the MST and PMFG based on several graph centrality measures.     

Memory effect and multifractality of cross-correlations in financial markets

We introduce an instantaneous and an average instantaneous cross-correlation function to detect the temporal cross-correlations between individual stocks based on the daily data of the United States and the Chinese stock markets. The memory effect of the instantaneous cross-correlations is investigated by applying the detrended fluctuation analysis (DFA), where the DFA exponents can be partly explained by the correlation function from the common sense. Long-range memory is observed for the average instantaneous cross-correlations, and persists up to a month magnitude of timescale for the United States stock market and half a month magnitude of timescale for the Chinese stock market. In addition, multifractal nature is investigated by a multifractal detrended fluctuation analysis.     

Correlations and cross-correlations in the Brazilian agrarian commodities and stocks

We investigate the auto-correlations and cross-correlations of the volatility time series in the Brazilian stock and commodity market, using the recently introduced Detrended Cross-Correlation Analysis. We find that the auto-correlations in stock volatilities are weaker than the auto-correlations in the commodity volatility series, contrary to earlier findings for the USA market where commodity volatility exponents were found to be lower than for stocks. We also find that the cross-correlations in the Brazilian stock and commodity market are stronger than what would be expected from simple combinations of auto-correlations of individual series, implying that there may be hidden factors that govern the behavior of the observed volatility series. This enhanced cross-correlation behavior is found in a considerable fraction of Brazilian stocks and agricultural commodities considered in the present work, suggesting that further studies should be directed into investigating these super-cross-correlations, and pinpointing the exogenous variables responsible for such behavior.     

Multifractal detrended cross-correlations between the Chinese exchange market and stock market

Based on the daily price data of the Chinese Yuan (RMB)/US dollar exchange rate and the Shanghai Stock Composite Index, we conducted an empirical analysis of the cross-correlations between the Chinese exchange market and stock market using the multifractal cross-correlation analysis method. The results demonstrate the overall significance of the cross-correlation based on the analysis of a statistic. Multifractality exists in cross-correlations, and the cross-correlated behavior of small fluctuations is more persistent than that of large fluctuations. Moreover, using the rolling windows method, we find that the cross-correlations between the Chinese exchange market and stock market vary with time and are especially sensitive to the reform of the RMB exchange rate regime. The previous reduction in the flexibility of the RMB exchange rate in July 2008 strengthened the persistence of cross-correlations and decreased the degree of multifractality, whereas the enhancement of the flexibility of the RMB exchange rate in June 2010 weakened the persistence of cross-correlations and increased the multifractality. Finally, several relevant discussions are provided to verify the robustness of our empirical analysis.     

Multifractal detrended cross-correlation analysis in the MENA area

In this paper, we investigated multifractal cross-correlations qualitatively and quantitatively using a cross-correlation test and the Multifractal detrended cross-correlation analysis method (MF-DCCA) for markets in the MENA area. We used cross-correlation coefficients to measure the level of this correlation. The analysis concerns four stock market indices of Morocco, Tunisia, Egypt and Jordan. The countries chosen are signatory of the Agadir agreement concerning the establishment of a free trade area comprising Arab Mediterranean countries. We computed the bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively the cross-correlations. By analyzing the results, we found the existence of multifractal cross-correlations between all of these markets. We compared the spectrum width of these indices; we also found which pair of indices has a strong multifractal cross-correlation.     

Self-organizing Ising model of financial markets

We study a dynamical Ising-like model of agents' opinions (buy or sell) with learning, in which the coupling coefficients are re-assessed continuously in time according to how past external news (time-varying magnetic field) have explained realized market returns. By combining herding, the impact of external news and private information, we find that the stylized facts of financial markets are reproduced only when agents misattribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the Ising critical point.     

Average cross-responses in correlated financial markets

There are non-vanishing price responses across different stocks in correlated financial markets, reflecting non-Markovian features. We further study this issue by performing different averages, which identify active and passive cross-responses. The two average cross-responses show different characteristic dependences on the time lag. The passive cross-response exhibits a shorter response period with sizeable volatilities, while the corresponding period for the active cross-response is longer. The average cross-responses for a given stock are evaluated either with respect to the whole market or to different sectors. Using the response strength, the influences of individual stocks are identified and discussed. Moreover, the various cross-responses as well as the average cross-responses are compared with the self-responses. In contrast to the short-memory trade sign cross-correlations for each pair of stocks, the sign cross-correlations averaged over different pairs of stocks show long memory.     

Testing for relationships between Shanghai and Shenzhen stock markets: A threshold cointegration perspective

We investigate the relationships between Shanghai and Shenzhen stock market, and reveal the evidence of cross-correlations between the two stock markets. Our main findings show that Shanghai and Shenzhen stock market are cointegrated, and also present the evidence of strong error-correction effect in the short-rate equation, whereas the point estimate for the error-correction term is small and not statistical significance in the long-rate equation. Finally, Shanghai stock market ECT coefficient shows the evidence of long-term equilibrium in the first regime, while in the second regime the coefficient of correction term is larger than that of the first regime, indicating the rate convergence to long-term equilibrium is not uniform.     

A study of correlations between crude oil spot and futures markets: A rolling sample test

In this article, we investigate the asymmetries of exceedance correlations and cross-correlations between West Texas Intermediate (WTI) spot and futures markets. First, employing the test statistic proposed by Hong et al. [Asymmetries in stock returns: statistical tests and economic evaluation, Review of Financial Studies 20 (2007) 1547–1581], we find that the exceedance correlations were overall symmetric. However, the results from rolling windows show that some occasional events could induce the significant asymmetries of the exceedance correlations. Second, employing the test statistic proposed by Podobnik et al. [Quantifying cross-correlations using local and global detrending approaches, European Physics Journal B 71 (2009) 243–250], we find that the cross-correlations were significant even for large lagged orders. Using the detrended cross-correlation analysis proposed by Podobnik and Stanley [Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series, Physics Review Letters 100 (2008) 084102], we find that the cross-correlations were weakly persistent and were stronger between spot and futures contract with larger maturity. Our results from rolling sample test also show the apparent effects of the exogenous events. Additionally, we have some relevant discussions on the obtained evidence.     

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Mar?enko–Pastur distribution.     

Identifying the structure of group correlation in the Korean financial market

We investigate the structure of the cross-correlation in the Korean stock market. We analyze daily cross-correlations between price fluctuations of 586 different Korean stock entities for the 6-year time period from 2003 to 2008. The main purpose is to investigate the structure of group correlation and its stability by undressing the market-wide effect using the Markowitz multi-factor model and the network-based approach. We find the explicit list of significant firms in the few largest eigenvectors from the undressed correlation matrix. We also observe that each contributor is involved in the same business sectors. The structure of group correlation can not remain constant during each 1-year time period with different starting points, whereas only two largest eigenvectors are stable for 6 years 8-9 eigenvectors remain stable for half-year. The structure of group correlation in the Korean financial market is disturbed during a sufficiently short time period even though the group correlation exists as an ensemble for the 6-year time period in the evolution of the system. We verify the structure of group correlation by applying a network-based approach. In addition, we examine relations between market capitalization and businesses. The Korean stock market shows a different behavior compared to mature markets, implying that the KOSPI is a target for short-positioned investors.