Modeling interactions of trading volumes in financial dynamics

A dynamic herding model with interactions of trading volumes is introduced. At time t, an agent trades with a probability, which depends on the ratio of the total trading volume at time t−1 to its own trading volume at its last trade. The price return is determined by the volume imbalance and number of trades. The model can reproduce the power-law distributions of the trading volume, number of trades and price return, and the probable relation between them. The exponents are tunable by adjusting the values of the parameters, but show slight deviation from those revealed in empirical studies. Moreover, the time series generated are long-range correlated. We demonstrate that the results are rather robust, and do not depend on the particular form of the trading probability.     

Crowded Trades,Market Clustering,and Price Instability

Crowded trades by similarly trading peers influence the dynamics of asset prices, possibly creating systemic risk. We propose a market clustering measure using granular trading data. For each stock, the clustering measure captures the degree of trading overlap among any two investors in that stock, based on a comparison with the expected crowding in a null model where trades are maximally random while still respecting the empirical heterogeneity of both stocks and investors. We investigate the effect of crowded trades on stock price stability and present evidence that market clustering has a causal effect on the properties of the tails of the stock return distribution, particularly the positive tail, even after controlling for commonly considered risk drivers. Reduced investor pool diversity could thus negatively affect stock price stability.     

Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis

Analyzing the Shanghai stock price index daily returns using MF-DFA method, it is found that there are two different types of sources for multifractality in time series, namely, fat-tailed probability distributions and non-linear temporal correlations. Based on that, a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation. It is found that when the stock price index fluctuates sharply, a strong variability is clearly characterized by the generalized Hurst exponents h(q). Therefore, two measures, and σ, based on generalized Hurst exponents were proposed to compare financial risks before and after Price Limits and Reform of Non-tradable Shares. The empirical results verify the validity of the measures, and this has led to a better understanding of complex stock markets.     

Preferred numbers and the distributions of trade sizes and trading volumes in the Chinese stock market

The distributions of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individualstocks exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the “q-Gamma” function for fitting the distribution by the Cramér-von Mises criterion. The empirical PDFs of tradingvolumes at different timescales Δt ranging from 1 min to 240 min can be well modeled. The applicability of the q-Gamma functions for multiple trades is restricted to the transaction numbers Δn≤ 8. We find that all the PDFs have power-law tails for large volumes. Using careful estimation of the average tail exponents α of the distributions of trade sizes and trading volumes, we get α> 2, well outside the Lévy regime.     

Pyramid scheme in stock market:A kind of financial market simulation

Artificial stock market simulation based on agent is an important means to study financial market. Based on the assumption that the investors are composed of a main fund, small trend and contrarian investors characterized by four parameters, we simulate and research a kind of financial phenomenon with the characteristics of pyramid schemes. Our simulation results and theoretical analysis reveal the relationships between the rate of return of the main fund and the proportion of the trend investors in all small investors, the small investors' parameters of taking profit and stopping loss,the order size of the main fund and the strategies adopted by the main fund. Our work is helpful to explain the financial phenomenon with the characteristics of pyramid schemes in financial markets, design trading rules for regulators and develop trading strategies for investors.     

Stochastic volatility of financial markets as the fluctuating rate of trading: An empirical study

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval Δt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a non-trivial distribution of log-returns for a given time interval Δt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.     

Grafting of higher-order correlations of real financial markets into herding models

In this work, we graft the volatility clustering observed in empirical financial time series into the Equiluz and Zimmermann (EZ) model, which was introduced to reproduce the herding behaviors of a financial time series. The original EZ model failed to reproduce the empirically observed power-law exponents of real financial data. The EZ model ordinarily produces a more fat-tailed distribution compared to real data, and a long-range correlation of absolute returns that underlie the volatility clustering. As it is not appropriate to capture the empirically observed correlations in a modified EZ model, we apply a sorting method to incorporate the nonlinear correlation structure of a real financial time series into the generated returns. By doing so, we observe that the slow convergence of distribution of returns is well established for returns generated from the EZ model and its modified version. It is also found that the modified EZ model leads to a less fat-tailed distribution.     

An agent-based approach to financial stylized facts

An important challenge of the financial theory in recent years is to construct more sophisticated models which have consistencies with as many financial stylized facts that cannot be explained by traditional models. Recently, psychological studies on decision making under uncertainty which originate in Kahneman and Tversky's research attract a lot of interest as key factors which figure out the financial stylized facts. These psychological results have been applied to the theory of investor's decision making and financial equilibrium modeling. This paper, following these behavioral financial studies, would like to propose an agent-based equilibrium model with prospect theoretical features of investors. Our goal is to point out a possibility that loss-averse feature of investors explains vast number of financial stylized facts and plays a crucial role in price formations of financial markets. Price process which is endogenously generated through our model has consistencies with, not only the equity premium puzzle and the volatility puzzle, but great kurtosis, asymmetry of return distribution, auto-correlation of return volatility, cross-correlation between return volatility and trading volume. Moreover, by using agent-based simulations, the paper also provides a rigorous explanation from the viewpoint of a lack of market liquidity to the size effect, which means that small-sized stocks enjoy excess returns compared to large-sized stocks.     

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.     

Does the market maker stabilize the market?

The market maker plays an important role in price formation, but his/her behavior and stabilizing impact on the market are relatively unclear, in particular in speculative markets. This paper develops a financial market model that examines the impact on market stability of the market maker, who acts as both a liquidity provider and an active investor in a market consisting of two types of boundedly rational speculative investors—the fundamentalists and trend followers. We show that the market maker does not necessarily stabilize the market when he/she actively manages the inventory to maximize profits, and that rather the market maker’s impact depends on the behavior of the speculators. Numerical simulations show that the model is able to generate outcomes for asset returns and market inventories that are consistent with empirical findings.     

Tick size and stock returns

Tick size is an important aspect of the micro-structural level organization of financial markets. It is the smallest institutionally allowed price increment, has a direct bearing on the bid-ask spread, influences the strategy of trading order placement in electronic markets, affects the price formation mechanism, and appears to be related to the long-term memory of volatility clustering. In this paper we investigate the impact of tick size on stock returns. We start with a simple simulation to demonstrate how continuous returns become distorted after confining the price to a discrete grid governed by the tick size. We then move on to a novel experimental set-up that combines decimalization pilot programs and cross-listed stocks in New York and Toronto. This allows us to observe a set of stocks traded simultaneously under two different ticks while holding all security-specific characteristics fixed. We then study the normality of the return distributions and carry out fits to the chosen distribution models. Our empirical findings are somewhat mixed and in some cases appear to challenge the simulation results.     

The endogenous dynamics of financial markets: Interaction and information dissemination

We investigate the process that different interactions between investors will prompt information to propagate along a differentiated path and construct a financial market model. As information spreads, increasingly investors are attracted to participate in trading, then the “herding effect” is magnified gradually, which will induce the topology of market network to change and the price to fluctuate. Especially, under different initial conditions or parameters, the peak and fat-tail property is produced and the obtained statistic values coincide with empirical results: the power-law exponents between the peak value of return probability distribution and the time scales range from 0.579 to 0.747, and the exponents between the accumulation distribution and the return on the tail are close to 3. Besides, the extent of volatility clustering in our produced price series is close to that of S&P 500 and locates between NASDAQ and HSI. All the results obtained here indicate that the continuous variation of the “herding effect” resulting from information propagation among interacting investors may be the origin of stylized facts of price fluctuations.     

Trading leads to scale-free self-organization

Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free behavior of the distribution of returns of different financial assets have been confirmed in a series of works. The existence of a Pareto-like distribution of the wealth of market participants has been connected with the scale-free distribution of trading volumes and price-returns. The origin of the Pareto-like wealth distribution, however, remained obscure. Here we show that in a market where the imbalance of supply and demand determines the direction of prize changes, it is the process of trading itself that spontaneously leads to a self-organization of the market with a Pareto-like wealth distribution for the market participants and at the same time to a scale-free behavior of return fluctuations and trading volume distributions.     

The Information Conveyed in a SPAC′s Offering

The popularity of SPACs (Special Purpose Acquisition Companies) has grown dramatically in recent years as a substitute for the traditional IPO (Initial Public Offer). We modeled the average annual return for SPAC investors and found that this financial tool produced an annual return of 17.3%. We then constructed an information model that examined a SPAC′s excess returns during the 60 days after a potential merger or acquisition had been announced. We found that the announcement had a major impact on the SPAC’s share price over the 60 days, delivering on average 0.69% daily excess returns over the IPO portfolio and 31.6% cumulative excess returns for the entire period. Relative to IPOs, the cumulative excess returns of SPACs rose dramatically in the next few days after the potential merger or acquisition announcement until the 26th day. They then declined but rose again until the 48th day after the announcement. Finally, the SPAC’s structure reduced the investors’ risk. Thus, if investors buy a SPAC stock immediately after a potential merger or acquisition has been announced and hold it for 48 days, they can reap substantial short-term returns.     

A multifractal detrended fluctuation analysis of trading behavior of individual and institutional traders in Tehran stock market

Employing the multifractal detrended fluctuation analysis (MF-DFA), the multifractal properties of trading behavior of individual and institutional traders in the Tehran Stock Exchange (TSE) are numerically investigated. Using daily trading volume time series of these two categories of traders, the scaling exponents, generalized Hurst exponents, generalized fractal dimensions and singularity spectrum are derived. Furthermore, two main sources of multifractality, i.e. temporal correlations and fat-tailed probability distributions are also examined. We also compare our results with data of S&P 500. Results of this paper suggest that for both classes of investors in TSE, multifractality is mainly due to long-range correlation while for S&P 500, the fat-tailed probability distribution is the main source of multifractality.     

Moving average rules as a source of market instability

Despite the pervasiveness of the efficient markets paradigm in the academic finance literature, the use of various moving average (MA) trading rules remains popular with financial market practitioners. This paper proposes a stochastic dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Our simulations show that the MA is a source of market instability, and the interaction of the MA and market noises can lead to the tendency for the market price to take long excursions away from the fundamental. The model reveals various market price phenomena, the coexistence of apparent market efficiency and a large chartist component, price resistance levels, long memory and skewness and kurtosis of returns.     

Complex stock trading network among investors

We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extract detailed information of each executed order for each trading day and demonstrate that the trade size distributions for different trading days exhibit power-law tails and that most of the estimated power-law exponents are well within the Lévy stable regime. Based on the records of order matching among investors, we can construct a stock trading network for each trading day, in which the investors are mapped into nodes and each transaction is translated as a direct edge from the seller to the buyer with the trade size as its weight. We find that all the trading networks comprise a giant component and have power-law degree distributions and disassortative architectures. In particular, the degrees are correlated with order sizes by a power-law function. By regarding the size of executed order as its fitness, the fitness model can reproduce the empirical power-law degree distribution.     

What types of investors generate the two-phase phenomenon?

We examine the two-phase phenomenon described by Plerou, Gopikrishnan, and Stanley (2003)  [1] in the KOSPI 200 options market, one of the most liquid options markets in the world. By analysing a unique intraday dataset that contains information about investor type for each trade and quote, we find that the two-phase phenomenon is generated primarily by domestic individual investors, who are generally considered to be uninformed and noisy traders. In contrast, our empirical results indicate that trades by foreign institutions, who are generally considered informed and sophisticated investors, do not exhibit two-phase behaviour.     

An agent-based model of stock markets incorporating momentum investors

It has been widely accepted that there exist investors who adopt momentum strategies in real stock markets. Understanding the momentum behavior is of both academic and practical importance. For this purpose, we propose and study a simple agent-based model of trading incorporating momentum investors and random investors. The random investors trade randomly all the time. The momentum investors could be idle, buying or selling, and they decide on their action by implementing an action threshold that assesses the most recent price movement. The model is able to reproduce some of the stylized facts observed in real markets, including the fat-tails in returns, weak long-term correlation and scaling behavior in the kurtosis of returns. An analytic treatment of the model relates the model parameters to several quantities that can be extracted from real data sets. To illustrate how the model can be applied, we show that real market data can be used to constrain the model parameters, which in turn provide information on the behavior of momentum investors in different markets.