313 research outputs found
The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics
The nature of fluctuations in the Indian financial market is analyzed in this
paper. We have looked at the price returns of individual stocks, with
tick-by-tick data from the National Stock Exchange (NSE) and daily closing
price data from both NSE and the Bombay Stock Exchange (BSE), the two largest
exchanges in India. We find that the price returns in Indian markets follow a
fat-tailed cumulative distribution, consistent with a power law having exponent
, similar to that observed in developed markets. However, the
distributions of trading volume and the number of trades have a different
nature than that seen in the New York Stock Exchange (NYSE). Further, the price
movement of different stocks are highly correlated in Indian markets.Comment: 10 pages, 7 figures, to appear in Proceedings of International
Workshop on "Econophysics of Stock Markets and Minority Games"
(Econophys-Kolkata II), Feb 14-17, 200
A correlated stochastic volatility model measuring leverage and other stylized facts
We present a stochastic volatility market model where volatility is
correlated with return and is represented by an Ornstein-Uhlenbeck process.
With this model we exactly measure the leverage effect and other stylized
facts, such as mean reversion, leptokurtosis and negative skewness. We also
obtain a close analytical expression for the characteristic function and study
the heavy tails of the probability distribution.Comment: 22 pages, 2 figures and 2 table
Variety and Volatility in Financial Markets
We study the price dynamics of stocks traded in a financial market by
considering the statistical properties both of a single time series and of an
ensemble of stocks traded simultaneously. We use the stocks traded in the
New York Stock Exchange to form a statistical ensemble of daily stock returns.
For each trading day of our database, we study the ensemble return
distribution. We find that a typical ensemble return distribution exists in
most of the trading days with the exception of crash and rally days and of the
days subsequent to these extreme events. We analyze each ensemble return
distribution by extracting its first two central moments. We observe that these
moments are fluctuating in time and are stochastic processes themselves. We
characterize the statistical properties of ensemble return distribution central
moments by investigating their probability density functions and temporal
correlation properties. In general, time-averaged and portfolio-averaged price
returns have different statistical properties. We infer from these differences
information about the relative strength of correlation between stocks and
between different trading days. Lastly, we compare our empirical results with
those predicted by the single-index model and we conclude that this simple
model is unable to explain the statistical properties of the second moment of
the ensemble return distribution.Comment: 10 pages, 11 figure
Quantifying Stock Price Response to Demand Fluctuations
We address the question of how stock prices respond to changes in demand. We
quantify the relations between price change over a time interval
and two different measures of demand fluctuations: (a) , defined as the
difference between the number of buyer-initiated and seller-initiated trades,
and (b) , defined as the difference in number of shares traded in buyer
and seller initiated trades. We find that the conditional expectations and of price change for a given or
are both concave. We find that large price fluctuations occur when demand is
very small --- a fact which is reminiscent of large fluctuations that occur at
critical points in spin systems, where the divergent nature of the response
function leads to large fluctuations.Comment: 4 pages (multicol fomat, revtex
Accounting for risk of non linear portfolios: a novel Fourier approach
The presence of non linear instruments is responsible for the emergence of
non Gaussian features in the price changes distribution of realistic
portfolios, even for Normally distributed risk factors. This is especially true
for the benchmark Delta Gamma Normal model, which in general exhibits
exponentially damped power law tails. We show how the knowledge of the model
characteristic function leads to Fourier representations for two standard risk
measures, the Value at Risk and the Expected Shortfall, and for their
sensitivities with respect to the model parameters. We detail the numerical
implementation of our formulae and we emphasizes the reliability and efficiency
of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur.
Phys. J.
Uncovering the Internal Structure of the Indian Financial Market: Cross-correlation behavior in the NSE
The cross-correlations between price fluctuations of 201 frequently traded
stocks in the National Stock Exchange (NSE) of India are analyzed in this
paper. We use daily closing prices for the period 1996-2006, which coincides
with the period of rapid transformation of the market following liberalization.
The eigenvalue distribution of the cross-correlation matrix, , of
NSE is found to be similar to that of developed markets, such as the New York
Stock Exchange (NYSE): the majority of eigenvalues fall within the bounds
expected for a random matrix constructed from mutually uncorrelated time
series. Of the few largest eigenvalues that deviate from the bulk, the largest
is identified with market-wide movements. The intermediate eigenvalues that
occur between the largest and the bulk have been associated in NYSE with
specific business sectors with strong intra-group interactions. However, in the
Indian market, these deviating eigenvalues are comparatively very few and lie
much closer to the bulk. We propose that this is because of the relative lack
of distinct sector identity in the market, with the movement of stocks
dominantly influenced by the overall market trend. This is shown by explicit
construction of the interaction network in the market, first by generating the
minimum spanning tree from the unfiltered correlation matrix, and later, using
an improved method of generating the graph after filtering out the market mode
and random effects from the data. Both methods show, compared to developed
markets, the relative absence of clusters of co-moving stocks that belong to
the same business sector. This is consistent with the general belief that
emerging markets tend to be more correlated than developed markets.Comment: 15 pages, 8 figures, to appear in Proceedings of International
Workshop on "Econophysics & Sociophysics of Markets & Networks"
(Econophys-Kolkata III), Mar 12-15, 200
Statistical Properties of Share Volume Traded in Financial Markets
We quantitatively investigate the ideas behind the often-expressed adage `it
takes volume to move stock prices', and study the statistical properties of the
number of shares traded for a given stock in a fixed time
interval . We analyze transaction data for the largest 1000 stocks
for the two-year period 1994-95, using a database that records every
transaction for all securities in three major US stock markets. We find that
the distribution displays a power-law decay, and that the
time correlations in display long-range persistence. Further, we
investigate the relation between and the number of transactions
in a time interval , and find that the long-range
correlations in are largely due to those of . Our
results are consistent with the interpretation that the large equal-time
correlation previously found between and the absolute value of
price change (related to volatility) are largely due to
.Comment: 4 pages, two-column format, four figure
Long-Time Fluctuations in a Dynamical Model of Stock Market Indices
Financial time series typically exhibit strong fluctuations that cannot be
described by a Gaussian distribution. In recent empirical studies of stock
market indices it was examined whether the distribution P(r) of returns r(tau)
after some time tau can be described by a (truncated) Levy-stable distribution
L_{alpha}(r) with some index 0 < alpha <= 2. While the Levy distribution cannot
be expressed in a closed form, one can identify its parameters by testing the
dependence of the central peak height on tau as well as the power-law decay of
the tails. In an earlier study [Mantegna and Stanley, Nature 376, 46 (1995)] it
was found that the behavior of the central peak of P(r) for the Standard & Poor
500 index is consistent with the Levy distribution with alpha=1.4. In a more
recent study [Gopikrishnan et al., Phys. Rev. E 60, 5305 (1999)] it was found
that the tails of P(r) exhibit a power-law decay with an exponent alpha ~= 3,
thus deviating from the Levy distribution. In this paper we study the
distribution of returns in a generic model that describes the dynamics of stock
market indices. For the distributions P(r) generated by this model, we observe
that the scaling of the central peak is consistent with a Levy distribution
while the tails exhibit a power-law distribution with an exponent alpha > 2,
namely beyond the range of Levy-stable distributions. Our results are in
agreement with both empirical studies and reconcile the apparent disagreement
between their results
Trading activity as driven Poisson process: comparison with empirical data
We propose the point process model as the Poissonian-like stochastic sequence
with slowly diffusing mean rate and adjust the parameters of the model to the
empirical data of trading activity for 26 stocks traded on NYSE. The proposed
scaled stochastic differential equation provides the universal description of
the trading activities with the same parameters applicable for all stocks.Comment: 9 pages, 5 figures, proceedings of APFA
Statistical Properties of Cross-Correlation in the Korean Stock Market
We investigate the statistical properties of the correlation matrix between
individual stocks traded in the Korean stock market using the random matrix
theory (RMT) and observe how these affect the portfolio weights in the
Markowitz portfolio theory. We find that the distribution of the correlation
matrix is positively skewed and changes over time. We find that the eigenvalue
distribution of original correlation matrix deviates from the eigenvalues
predicted by the RMT, and the largest eigenvalue is 52 times larger than the
maximum value among the eigenvalues predicted by the RMT. The
coefficient, which reflect the largest eigenvalue property, is 0.8, while one
of the eigenvalues in the RMT is approximately zero. Notably, we show that the
entropy function with the portfolio risk for the original
and filtered correlation matrices are consistent with a power-law function,
, with the exponent and
those for Asian currency crisis decreases significantly
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