A Random Matrix Approach To Volatility In An Indian Financial Market

  • V. Kulkarni
  • N. Deo
Part of the New Economic Windows book series (NEW)


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.


Random Matrix Large Eigenvalue Daily Return Variability Index Cross Correlation Matrix 
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  1. 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. 2.
    Mantegna RN, Stanley HE (2000) An Introduction to Econophysics, Cambridge University PressGoogle Scholar
  3. 3.
    Mehta M (1991) Random Matrices, Academic PressGoogle Scholar
  4. 4.
    Laloux L, Cizeau P, Bouchaud J-P, Potters M (1999) Physical Review Letters 83:1467; (1999) Risk 12(3):69; Plerou V, Gopikrishnan P, Rosenow B, Amaral LAN, Stanley HE (1999) Phys. Rev. Lett. 83:1471; Potters M, Bouchaud J-P, Laloux L, arXiv:ppphysics/0507111.CrossRefADSGoogle Scholar
  5. 5.
    Liu Y, Gopikrishnan P, Cizeau P, Meyer M, Peng CK, Stanley HE (1999) Physical Review E 60(2)Google Scholar
  6. 6.
    Lillo F, Mantegna RN (2000) Physical Review E 62:6126–6134 Lillo F, Bonanno G, Mantegna RN (2002) Ed. by H. Takayasu, Springer-Verlag Tokyo; Micciche S, Bonanno G, Lillo F, Mantegna RN (2002) Physica A 314:756–761; Lillo F, Mantegna RN (2005) Physical Review E 72:016219CrossRefADSGoogle Scholar
  7. 7.
    Drozdz S, Grummer F, Gorski AZ, Ruf F, Speth J (2000) Physica A 287:440; Drozdz S, Grummer F, Ruf F, Speth J (2001) Physica A 294:226; Empirical Science of Financial Fluctuations, H. Takayasu (ed.), Springer-Verlag Tokio 2002, p.41.CrossRefADSGoogle Scholar
  8. 8.
    Gopikrishnan P, Rosenow B, Plerou V, Stanley HE (2001) Physical Review E 64:035106CrossRefADSGoogle Scholar
  9. 9.
    Plerou V, Gopikrishnan P, Rosenow B, Amaral LAN, Guhr T, Stanley HE (2002) Physical Review E 65:066126CrossRefADSGoogle Scholar
  10. 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. 11.
    Wilcox D, Gebbie T (2004) arXiv:cond-mat/0402389; arXiv:cond-mat/0404416Google Scholar
  12. 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. 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. 14.
    Mounfield C, Ormerod P (2001) Market Correlation and Market Volatility in US Blue Chip Stocks, Crowell Prize Submission, 2001Google Scholar
  15. 15.
    Kulkarni V, Deo N (2005) arXiv:Physics/0512169.Google Scholar

Copyright information

© Springer-Verlag Italia 2006

Authors and Affiliations

  • V. Kulkarni
    • 1
  • N. Deo
    • 1
  1. 1.Department of Physics and AstrophysicsUniversity of DelhiDelhiIndia

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