  We examine volatility of an Indian stock market in terms of aspects like
participation, synchronization of stocks and quantification of volatility using
the random matrix approach. Volatility pattern of the market is found using the
BSE index for the three-year period 2000-2002. Random matrix analysis is
carried out using daily returns of 70 stocks for several time windows of 85
days in 2001 to (i) do a brief comparative analysis with statistics of
eigenvalues and eigenvectors of the matrix C of correlations between price
fluctuations, in time regimes of different volatilities. While a bulk of
eigenvalues falls within RMT bounds in all the time periods, we see that the
largest (deviating) eigenvalue correlates well with the volatility of the
index, the corresponding eigenvector clearly shows a shift in the distribution
of its components from volatile to less volatile periods and verifies the
qualitative association between participation and volatility (ii) observe that
the Inverse participation ratio for the 'last' eigenvector is sensitive to
market fluctuations (the two quantities are observed to anti correlate
significantly) (iii) set up a variability index, V whose temporal evolution is
found to be significantly correlated with the volatility of the overall market
index.
