articles by Shanshan Wang
Previous studies of the stock price response to trades focused on the dynamics of single stocks, ... more Previous studies of the stock price response to trades focused on the dynamics of single stocks, i.e. they addressed the self-response. We empirically investigate the price response of one stock to the trades of other stocks in a correlated market, i.e. the cross-responses. How large is the impact of one stock on others and vice versa? -- This impact of trades on the price change across stocks appears to be transient instead of permanent as we discuss from the viewpoint of market efficiency. Furthermore, we compare the self-responses on different scales and the self- and cross-responses on the same scale. We also find that the cross-correlation of the trade signs turns out to be a short-memory process.
Previous studies of the stock price response to individual trades focused on single stocks. We em... more Previous studies of the stock price response to individual trades focused on single stocks. We empirically investigate the price response of one stock to the trades of other stocks. How large is the impact of one stock on others and vice versa? -- This impact of trades on the price change across stocks appears to be transient instead of permanent. Performing different averages, we distinguish active and passive responses. The two average responses show different characteristic dependences on the time lag. The passive response exhibits a shorter response period with sizeable volatilities, and the active response a longer period. We also study the response for a given stock with respect to different sectors and to the whole market. Furthermore, we compare the self-response with the various cross-responses. The correlation of the trade signs is a short-memory process for a pair of stocks, but it turns into a long-memory process when averaged over different pairs of stocks.
Traffic systems are complex systems that exhibit non-stationary characteristics. Therefore, the i... more Traffic systems are complex systems that exhibit non-stationary characteristics. Therefore, the identification of temporary traffic states is significant. In contrast to the usual correlations of time series, here we study those of position series, revealing structures in time, i.e. the rich non-Markovian features of traffic. Considering the traffic system of the Cologne orbital motorway as a whole, we identify five quasi-stationary states by clustering reduced rank correlation matrices of flows using the k-means method. The five quasi-stationary states with nontrivial features include one holiday state, three workday states and one mixed state of holidays and workdays. In particular, the workday states and the mixed state exhibit strongly correlated time groups shown as diagonal blocks in the correlation matrices. We map the five states onto reduced-rank correlation matrices of velocities and onto traffic states where free or congested states are revealed in both space and time. Our study opens a new perspective for studying traffic systems. This contribution is meant to provide a proof of concept and a basis for further study.
There are non-vanishing price responses across different stocks in correlated financial markets. ... more There are non-vanishing price responses across different stocks in correlated financial markets. 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, the short memory of trade sign cross-correlation for stock pairs, the sign cross-correlation has long memory when averaged over different pairs of stocks.
We construct a price impact model between stocks in a correlated market. For the price change of ... more We construct a price impact model between stocks in a correlated market. For the price change of a given stock induced by the short-term liquidity of this stock itself and of the information about other stocks, we introduce a self- and a cross-impact function of the time lag. We model the average cross-response functions for individual stocks employing the impact functions of the time lag, the impact functions of traded volumes and the trade-sign correlators. We further quantify and interpret the price impacts of time lag in terms of temporary and permanent components. To support our model, we also analyze empirical data, in particular the memory properties of the sign self- and average cross-correlators. The relation between the average cross-responses and the traded volumes which are smaller than their average is of power-law form.
To understand the dynamics on complex networks, measurement of correlations is indispensable. In ... more To understand the dynamics on complex networks, measurement of correlations is indispensable. In a motorway network, it is not sufficient to collect information on fluxes and velocities on all individual links, i.e. parts of the freeways between ramps and highway crosses. The interdependencies and mutual connections are also of considerable interest. We analyze correlations in the complete motorway network in North Rhine-Westphalia, the most populous state in Germany. We view the motorway network as a complex system consisting of road sections which interact via the motion of vehicles, implying structures in the corresponding correlation matrices. In particular, we focus on collective behavior, i.e. coherent motion in the whole network or in large parts of it. To this end, we study the eigenvalue and eigenvector statistics and identify significant sections in the motorway network. We find collective behavior in these significant sections and further explore its causes. We show that collectivity throughout the network cannot directly be related to the traffic states (free, synchronous and congested) in Kerner's three-phase theory. Hence, the degree of collectivity provides a new, complementary observable to characterize the motorway network.
We extend the framework of trading strategies of Gatheral [2010] from single stocks to a pair of ... more We extend the framework of trading strategies of Gatheral [2010] from single stocks to a pair of stocks. Our trading strategy with the executions of two round-trip trades can be described by the trading rates of the paired stocks and the ratio of their trading periods. By minimizing the potential cost arising from cross-impacts, i.e., the price change of one stock due to the trades of another stock, we can find out an optimal strategy for executing a sequence of trades from different stocks. We further apply the model of the strategy to a specific case, where we quantify the cross-impacts of traded volumes and of time lag with empirical data for the computation of costs. We thus picture the influence of cross-impacts on the trading strategy.
We investigate how the local fluctuations of the signed traded volumes affect the dependence of d... more We investigate how the local fluctuations of the signed traded volumes affect the dependence of demands between stocks. We analyze the empirical dependence of demands using copulas and show that they are well described by a bivariate copula density function. We find that large local fluctuations strongly increase the positive dependence but lower slightly the negative one in the copula density. This interesting feature is due to cross-correlations of volume imbalances between stocks. Also, we explore the asymmetries of tail dependencies of the copula density, which are moderate for the negative dependencies but strong for the positive ones. For the latter, we reveal that large local fluctuations of the signed traded volumes trigger stronger dependencies of demands than of supplies, probably indicating a bull market with persistent raising of prices.
In a motorway network, correlations between parts or, more precisely, between the sections of (di... more In a motorway network, correlations between parts or, more precisely, between the sections of (different) motorways, are of considerable interest. Knowledge of flows and velocities on individual motorways is not sufficient, rather, their correlations determine or reflect, respectively, the functionality of and the dynamics on the network. These correlations are time-dependent as the dynamics on the network is highly non-stationary. Apart from the conceptual importance, correlations are also indispensable to detect risks of failure in a traffic network. Here, we proceed with revealing a certain hierarchy of correlations in traffic networks that is due to the presence and to the extent of collectivity. In a previous study, we focused on the collectivity motion present in the entire traffic network, i.e. the collectivity of the system as a whole. Here, we manage to subtract this dominant effect from the data and identify the subdominant collectivities which affect different, large parts of the traffic network. To this end, we employ a spectral analysis of the correlation matrix for the whole system. We thereby extract information from the virtual network induced by the correlations and map it on the true topology, i.e. on the real motorway network. The uncovered subdominant collectivities provide a new characterization of the traffic network. We carry out our study for the large motorway network of North Rhine-Westphalia (NRW), Germany.
We empirically analyze the price and liquidity responses to trade signs, traded volumes and signe... more We empirically analyze the price and liquidity responses to trade signs, traded volumes and signed traded volumes. Utilizing the singular value decomposition, we explore the interconnections of price responses and of liquidity responses across the whole market. The statistical characteristics of their singular vectors are well described by the t location-scale distribution. Furthermore, we discuss the relation between prices and liquidity with respect to their overlapping factors. The factors of price and liquidity changes are non-random when these factors are related to the traded volumes. This means that the traded volumes play a critical role in the price change induced by the liquidity change. In contrast, the two kinds of factors are weakly overlapping when they are related to the trade signs and signed traded volumes. Hence, an imbalance of liquidity is related to the price change.
The price impact for a single trade is estimated by the immediate response on an event time scale... more The price impact for a single trade is estimated by the immediate response on an event time scale, i.e., the immediate change of midpoint prices before and after a trade. We work out the price impacts across a correlated financial market. We quantify the asymmetries of the distributions and of the market structures of cross-impacts, and find that the impacts across the market are asymmetric and non-random. Using spectral statistics and Shannon entropy, we visualize the asymmetric information in price impacts. Also, we introduce an entropy of impacts to estimate the randomness between stocks. We show that the useful information is encoded in the impacts corresponding to small entropy. The stocks with large number of trades are more likely to impact others, while the less traded stocks have higher probability to be impacted by others.
The quantum phase transition in mesoscopic noncircular loops threaded by an Aharonov-Bohm flux is... more The quantum phase transition in mesoscopic noncircular loops threaded by an Aharonov-Bohm flux is systematically investigated by numerically solving the Bogoliubov-de Gennes equations self-consistently. We focus on the magnetic flux dependence of the 𝑠-wave superconducting order parameter and current in symmetric and asymmetric samples. The influence of surface indentation or bulge defects positioned at the inner or outer edge of the sample on the periodic oscillation is also discussed. We find various ℎ𝑐/𝑒-flux periodicity evolution patterns, and the periodic phase transitions between the superconducing state and the resistive/normal state are demonstrated besides the superconducing state transitions. Our investigation may shed new light on material engineering and provide important insights to designing superconducting quantum devices.
Based on the time-dependent Ginzburg–Landau equations, we study numerically the vortex configurat... more Based on the time-dependent Ginzburg–Landau equations, we study numerically the vortex configuration and motion in mesoscopic superconducting cylinders. We find that the effects of the geometric symmetry of the system and the noncircular multiply-connected boundaries can significantly influence the steady vortex states and the vortex matter moving. For the square cylindrical loops, the vortices can enter the superconducting region in multiples of 2 and the vortex configuration exhibits the axial symmetry along the square diagonal. Moreover, the vortex dynamics behavior exhibits more complications due to the existed centered hole, which can lead to the vortex entering from different edges and exiting into the hole at the phase transitions.
phdtheses by Shanshan Wang
Duisburg-Essen Publications online, 2017
In econophysics, physicists apply physical theories and methods to address economics problems. Du... more In econophysics, physicists apply physical theories and methods to address economics problems. Due to an enormous amount of available data, financial markets can be statistically analyzed by physicists. The applied methods find their applications also in the context of other complex systems. In particular, with the development of the high-frequency trading, the market microstructure has gained growing attention. In this thesis, we will focus on the microstructure of financial markets, particularly on the correlation of order flow, the price impact and the dependence of demands.
We begin by developing a method to identify trade signs with a TAQ data set. With the identified trade signs, we carry out an analysis of empirical data for the price cross-response to trades and the cross-correlation of trade signs. To obtain a stable observation, we also average them. The average cross-correlation of trade signs turns out to be long memory. Meanwhile, the non-vanishing cross-response reflects non-Markovian features of prices. According to the average cross-responses, we identify the influencing and influenced stocks.
We then extend the price impact model of Bouchaud et al. (2004) to interpret our empirical results. The extended model contains the impacts of traded volumes, which are empirically revealed as power-law functions. The model also includes a self- and a cross-impact function of time lag. To quantify them, we propose a construction to fix the parameters and employ a diffusion function to corroborate the parameters. We thus quantify and interpret the price impacts in terms of the temporary and permanent components.
We further extend the framework of trading strategies of Gatheral (2010) from single stocks to the two-dimensional case. Thus, we can introduce the cross-impact to the strategy for executing two round-trip trades of two stocks. We apply the strategy to a specific case, in which we quantify the cross-impacts with empirical data and give a view of how the cross-impact affect the trading strategy.
We finally analyze the dependence of demands between stocks by a copula method. The empirical dependence of demands can be well described by a K copula density function. We also investigate how the large local fluctuations of the signed traded volumes affect the dependence of demands. Furthermore, we explore the asymmetries of tail dependencies of the copula density.
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articles by Shanshan Wang
phdtheses by Shanshan Wang
We begin by developing a method to identify trade signs with a TAQ data set. With the identified trade signs, we carry out an analysis of empirical data for the price cross-response to trades and the cross-correlation of trade signs. To obtain a stable observation, we also average them. The average cross-correlation of trade signs turns out to be long memory. Meanwhile, the non-vanishing cross-response reflects non-Markovian features of prices. According to the average cross-responses, we identify the influencing and influenced stocks.
We then extend the price impact model of Bouchaud et al. (2004) to interpret our empirical results. The extended model contains the impacts of traded volumes, which are empirically revealed as power-law functions. The model also includes a self- and a cross-impact function of time lag. To quantify them, we propose a construction to fix the parameters and employ a diffusion function to corroborate the parameters. We thus quantify and interpret the price impacts in terms of the temporary and permanent components.
We further extend the framework of trading strategies of Gatheral (2010) from single stocks to the two-dimensional case. Thus, we can introduce the cross-impact to the strategy for executing two round-trip trades of two stocks. We apply the strategy to a specific case, in which we quantify the cross-impacts with empirical data and give a view of how the cross-impact affect the trading strategy.
We finally analyze the dependence of demands between stocks by a copula method. The empirical dependence of demands can be well described by a K copula density function. We also investigate how the large local fluctuations of the signed traded volumes affect the dependence of demands. Furthermore, we explore the asymmetries of tail dependencies of the copula density.
We begin by developing a method to identify trade signs with a TAQ data set. With the identified trade signs, we carry out an analysis of empirical data for the price cross-response to trades and the cross-correlation of trade signs. To obtain a stable observation, we also average them. The average cross-correlation of trade signs turns out to be long memory. Meanwhile, the non-vanishing cross-response reflects non-Markovian features of prices. According to the average cross-responses, we identify the influencing and influenced stocks.
We then extend the price impact model of Bouchaud et al. (2004) to interpret our empirical results. The extended model contains the impacts of traded volumes, which are empirically revealed as power-law functions. The model also includes a self- and a cross-impact function of time lag. To quantify them, we propose a construction to fix the parameters and employ a diffusion function to corroborate the parameters. We thus quantify and interpret the price impacts in terms of the temporary and permanent components.
We further extend the framework of trading strategies of Gatheral (2010) from single stocks to the two-dimensional case. Thus, we can introduce the cross-impact to the strategy for executing two round-trip trades of two stocks. We apply the strategy to a specific case, in which we quantify the cross-impacts with empirical data and give a view of how the cross-impact affect the trading strategy.
We finally analyze the dependence of demands between stocks by a copula method. The empirical dependence of demands can be well described by a K copula density function. We also investigate how the large local fluctuations of the signed traded volumes affect the dependence of demands. Furthermore, we explore the asymmetries of tail dependencies of the copula density.