A Random Matrix Approach To Volatility In An Indian Financial Market
The volatility of an Indian stock market is examined 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 Bombay Stock 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 Random Matrix Theory bounds in all the time periods, we see that the largest (deviating) eigenvalue correlates well with the volatility of the index (ii) observe 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 (iii) set up a variability index, V whose temporal evolution is found to be significantly correlated with the volatility of the overall market index.
KeywordsRandom Matrix Large Eigenvalue Daily Return Variability Index Cross Correlation Matrix
Unable to display preview. Download preview PDF.
- 1.Bachelier L (1900) ‘Theorie de la speculation’ [Ph.D. thesis in mathematics], Annales Scientifiques de l’Ecole Normale Superieure III-17, pp.21–86; Kulkarni S (1978) Sankhya: The Indian Journal of Statistics V40 Series DGoogle Scholar
- 2.Mantegna RN, Stanley HE (2000) An Introduction to Econophysics, Cambridge University PressGoogle Scholar
- 3.Mehta M (1991) Random Matrices, Academic PressGoogle Scholar
- 5.Liu Y, Gopikrishnan P, Cizeau P, Meyer M, Peng CK, Stanley HE (1999) Physical Review E 60(2)Google Scholar
- 10.Burda Z, Jurkiewiez J, Nowak MA, Papp G, Zahed I (2001) cond-mat/0103108; Burda Z, Goerlich A, Jarosz A, Jurkiewicz J (2003) cond-mat/0305627Google Scholar
- 11.Wilcox D, Gebbie T (2004) arXiv:cond-mat/0402389; arXiv:cond-mat/0404416Google Scholar
- 12.Gençay R, Dacorogna M, Muller U, Pictet O, Olsen R (2001) An Introduction to High Frequency Finance, Academic Press Inc. (London)Google Scholar
- 13.Shalen C (1999) International Stock Index Spread Opportunities in Volatile Markets, The CBOT Dow Jones Industrial Average Futures and Future Options, 02613Google Scholar
- 14.Mounfield C, Ormerod P (2001) Market Correlation and Market Volatility in US Blue Chip Stocks, Crowell Prize Submission, 2001Google Scholar
- 15.Kulkarni V, Deo N (2005) arXiv:Physics/0512169.Google Scholar