arXiv subjects

Rosario N. Mantegna

Publications and source records attributed to Rosario N. Mantegna.

At least 55 records · Page 3Linked to original sources

arXiv2007

Scaling laws of strategic behaviour and size heterogeneity in agent dynamics

The dynamics of many socioeconomic systems is determined by the decision making process of agents. The decision process depends on agent's characteristics, such as preferences, risk aversion, behavioral biases, etc.. In addition, in some systems the size of agents can be highly heterogeneous leading to very different impacts of agents on the system dynamics. The large size of some agents poses challenging problems to agents who want to control their impact, either by forcing the system in a given direction or by hiding their intentionality. Here we consider the financial market as a model system, and we study empirically how agents strategically adjust the properties of large orders in order to meet their preference and minimize their impact. We quantify this strategic behavior by detecting scaling relations of allometric nature between the variables characterizing the trading activity of different institutions. We observe power law distributions in the investment time horizon, in the number of transactions needed to execute a large order and in the traded value exchanged by large institutions and we show that heterogeneity of agents is a key ingredient for the emergence of some aggregate properties characterizing this complex system.

q-fin.ST↗

arXiv2006

Market reaction to temporary liquidity crises and the permanent market impact

We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden, large variation of the spread, corresponding to a temporary crisis of liquidity in a double auction financial market. We find that the spread decays very slowly to its normal value as a consequence of the strategic limit order placement of liquidity providers. We consider several quantities, such as order placement rates and distribution, that affect the decay of the spread. We measure the permanent impact both of a generic event altering the spread and of a single transaction and we find an approximately linear relation between immediate and permanent impact in both cases.

physics.soc-ph↗

arXiv2005

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

physics.soc-ph↗

arXiv2005

Cluster analysis for portfolio optimization

We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters N (number of assets) and T (investment horizon). The predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method.

physics.soc-ph↗

arXiv2004

Value-at-Risk and Tsallis statistics: risk analysis of the aerospace sector

In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is well described by Tsallis distribution. We explore this result and modify the standard Value-at-Risk (VaR), financial risk assessment methodology in order to reflect an asset which obeys Tsallis non-extensive statistics.

cond-mat.stat-mech↗

arXiv2003

Power law relaxation in a complex system: Omori law after a financial market crash

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power law relaxation decay of its typical scale. Our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models.

cond-mat.stat-mech↗

arXiv2003

Noise dressing of the correlation matrix of factor models

We study the spectral density of factor models of multivariate time series. By making use of the Random Matrix Theory we analytically quantify the effect of noise dressing on the spectral density due to the finiteness of the sample. We consider a broad range of models ranging from one factor models in time and frequency domain to hierarchical multifactor models.

cond-mat.stat-mech↗

arXiv2002

Degree stability of a minimum spanning tree of price return and volatility

We investigate the time series of the degree of minimum spanning trees obtained by using a correlation based clustering procedure which is starting from (i) asset return and (ii) volatility time series. The minimum spanning tree is obtained at different times by computing correlation among time series over a time window of fixed length $T$. We find that the minimum spanning tree of asset return is characterized by stock degree values, which are more stable in time than the ones obtained by analyzing a minimum spanning tree computed starting from volatility time series. Our analysis also shows that the degree of stocks has a very slow dynamics with a time-scale of several years in both cases.

cond-mat.stat-mech↗

arXiv2002

Dynamics of a financial market index after a crash

We discuss the statistical properties of index returns in a financial market just after a major market crash. The observed non-stationary behavior of index returns is characterized in terms of the exceedances over a given threshold. This characterization is analogous to the Omori law originally observed in geophysics. By performing numerical simulations and theoretical modelling, we show that the nonlinear behavior observed in real market crashes cannot be described by a GARCH(1,1) model. We also show that the time evolution of the Value at Risk observed just after a major crash is described by a power-law function lacking a typical scale.

cond-mat.stat-mech↗

arXiv2002

Single Curve Collapse of the Price Impact Function for the New York Stock Exchange

We study the average price impact of a single trade executed in the NYSE. After appropriate averaging and rescaling, the data for the 1000 most highly capitalized stocks collapse onto a single function, giving average price shift as a function of trade size. This function increases as a power that is the order of 1/2 for small volumes, but then increases more slowly for large volumes. We obtain similar results in each year from the period 1995 - 1998. We also find that small volume liquidity scales as a power of the stock capitalization.

cond-mat.stat-mech↗

arXiv2002

Long-range correlated stationary Markovian processes

We introduce a new class of stochastic processes which are stationary, Markovian and characterized by an infinite range of time-scales. By transforming the Fokker-Planck equation of the process into a Schrodinger equation with an appropriate quantum potential we determine the asymptotic behavior of the autocorrelation function of the process in an analytical way. We find the conditions needed to observe a stationary long-range correlated Markovian process. In the presence of long-range correlation, for selected values of the control parameters, the process has a 1/f-like spectral density for low frequency values.

cond-mat.stat-mech↗

arXiv2002

Volatility in Financial Markets: Stochastic Models and Empirical Results

We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pdf in the region of low values of volatility whereas the Hull and White model better approximates the empirical pdf for large values of volatility. Both models fails in describing the empirical pdf over a moderately large volatility range.

cond-mat.stat-mech↗

arXiv2002

Comparative genomics study of inverted repeats in bacteria

We investigate the number of inverted repeats observed in 37 complete genomes of bacteria. The number of inverted repeats observed is much higher than expected using Markovian models of DNA sequences in most of the eubacteria. By using the information annotated in the genomes we discover that in most of the eubacteria the inverted repeats of stem length longer than 8 nucleotides preferentially locate near the 3' end of the nearest coding regions. We also show that IRs characterized by large values of the stem length locate preferentially in short non-coding regions bounded by two 3' ends of convergent genes. By using the program TransTerm recently introduced to predict transcription terminators in bacterial genomes, we conclude that only a part of the observed inverted repeats fullfills the model requirements characterizing rho-independent termination in several genomes.

cond-mat.stat-mech↗

arXiv2001

Ensemble properties of securities traded in the NASDAQ market

We study the price dynamics of stocks traded in the NASDAQ market by considering the statistical properties of an ensemble of stocks traded simultaneously. For each trading day of our database, we study the ensemble return distribution by extracting its first two central moments. According to previous results obtained for the NYSE market, we find that the second moment is a long-range correlated variable. We compare time-averaged and ensemble-averaged price returns and we show that the two averaging procedures lead to different statistical results.

cond-mat.stat-mech↗

arXiv2001

Introducing Variety in Risk Management

We review the recently introduced concept of variety of a financial portfolio and we sketch its importance for risk control purposes. The empirical behaviour of variety, correlation, exceedance correlation and asymmetry of the probability density function of daily returns is discussed. The results obtained are compared with the ones of a one-factor model showing strengths and limitations of this model.

cond-mat.stat-mech↗

arXiv2001

Variety of Stock Returns in Normal and Extreme Market Days: The August 1998 Crisis

We investigate the recently introduced variety of a set of stock returns traded in a financial market. This investigation is done by considering daily and intraday time horizons in a 15-day time period centered at the August 31st, 1998 crash of the S&P500 index. All the stocks traded at the NYSE during that period are considered in the present analysis. We show that the statistical properties of the variety observed in analyses of daily returns also hold for intraday returns. In particular the largest changes of the variety of the return distribution turns out to be most localized at the opening or (to a less degree) at the closing of the market.

cond-mat.stat-mech↗

arXiv2001

Levels of complexity in financial markets

We consider different levels of complexity which are observed in the empirical investigation of financial time series. We discuss recent empirical and theoretical work showing that statistical properties of financial time series are rather complex under several ways. Specifically, they are complex with respect to their (i) temporal and (ii) ensemble properties. Moreover, the ensemble return properties show a behavior which is specific to the nature of the trading day reflecting if it is a normal or an extreme trading day.

cond-mat.stat-mech↗

arXiv2000

High-frequency Cross-correlation in a Set of Stocks

The high-frequency cross-correlation existing between pairs of stocks traded in a financial market are investigated in a set of 100 stocks traded in US equity markets. A hierarchical organization of the investigated stocks is obtained by determining a metric distance between stocks and by investigating the properties of the subdominant ultrametric associated with it. A clear modification of the hierarchical organization of the set of stocks investigated is detected when the time horizon used to determine stock returns is changed. The hierarchical location of stocks of the energy sector is investigated as a function of the time horizon.

cond-mat.stat-mech↗