Univariate and multivariate statistical aspects of equity volatility

  • Salvatore Miccichè
  • Fabrizio Lillo
  • Giovanni Bonanno
  • Rosario N. Mantegna
Conference paper


We discuss univariate and multivariate statistical properties of volatility time series of equities traded in a financial market. Specifically, (i) we introduce a two-region stochastic volatility model able to well describe the unconditional pdf of volatility in a wide range of values and (ii) we quantify the stability of the results of a correlation-based clustering procedure applied to synchronous time evolution of a set of volatility time series.


Autocorrelation Function Minimum Span Tree Stochastic Volatility Equity Market Survival Ratio 
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  1. 1.
    Hull, J.C, White, A. (1987) The pricing of options on assets with stochastic volatilities. Journal of Finance XLII 281–300.CrossRefGoogle Scholar
  2. 2.
    Miccichè, S., Bonanno, G., Lillo, F., Mantegna, R.N. (2002) Volatility in Financial Markets: Stochastic Models and Empirical Results. Physics A 314 756–761ADSMATHCrossRefGoogle Scholar
  3. 3.
    Markowitz, H. (1959) Portfolio Selection: Efficient Diversification of Investment, Wiley, NYGoogle Scholar
  4. 4.
    Elton, E.J., Gruber, M.J. (1995) Modern Portfolio Theory and Investment Analysis. Wiley, NYGoogle Scholar
  5. 5.
    Campbell, J.W., Lo, A.W., MacKinlay, A.C. (1997) The Econometrics of Financial Markets. Princeton Univ. Press, PrincetonMATHGoogle Scholar
  6. 6.
    Elton, E.J., Gruber, M.J. (1971) Improved forecasting through the design of homogeneous groups. J. Business 44 432–450CrossRefGoogle Scholar
  7. 7.
    Panton, D.B., Parker Lessig, V., Joy, Q.M. (1976) Comovement of international equity markets: A taxonomic approach. J. Financial Quant. Anal. 11 415–432CrossRefGoogle Scholar
  8. 8.
    Mantegna, R.N. (1999) Hierarchical Structure in Financial Markets. Eur. Phys. J. B 11 193–197ADSCrossRefGoogle Scholar
  9. 9.
    Kullmann, L., Kertesz, J., Mantegna, R.N. (2000) Identification of clusters of companies in. stock indices via Potts super-paramagnetic transitions. Physica A 287 412–419ADSCrossRefGoogle Scholar
  10. 10.
    Bonanno, G., Vandewalle, N., Mantegna, R.N. (2000) Taxonomy of Stock Market Indices. Physical Review E62 R7615–R7618ADSGoogle Scholar
  11. 11.
    Bonanno, G., Lillo, F., Mantegna, R.N. (2001) High-frequency Cross-correlation in a Set of Stocks. Quantitative Finance 1 96–104CrossRefGoogle Scholar
  12. 12.
    Bonanno, G., Caldarelli, G., Lillo, F., Mantegna, R.N. (2003) Topology of correlation based minimal spanning trees in real and model markets. Scholar
  13. 13.
    Micciché;, S., Bonanno, G., Lillo, F., Mantegna, R.N. (2003) Degree stability of a minimum spanning tree of price return and volatility, Physica A (in press)Google Scholar
  14. 14.
    Onnela, J-P., Chakraborti, A., Koski, K., KerteszJ.(2002) Dynamic asset trees and portfolio analysis. (2002).Google Scholar
  15. 15.
    Hull, J.C. (1997) Options, Futures and Other Derivatives. Prentice Hall, Inc.Google Scholar
  16. 16.
    Black, F., Schales, M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81 637–654CrossRefGoogle Scholar
  17. 17.
    Dacorogna, M.M., Gencay, R., Müller, U.A., Olsen, R.B., Pictet, O.V. (2001) An Introduction to High-Frequency Finance. Academic PressGoogle Scholar
  18. 18.
    Liu, Y., Gopikrishnan, P., Cizeau, P., Meyer, M., Peng, C.-K., Stanley, H.E., (1999) Statistical properties of the volatility of price fluctuations. Phys. Rev. E 60 1390–14011Google Scholar
  19. 19.
    Cizeau, P., Liu, Y., Meyer, M., Peng, C.-K., Stanley, H.E. (1997) Volatility distribution in the SP500 stock index. Physica A 245 441–445MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Pasquini, M., Serva, M. (1999) Multiscaling and clustering of volatility. Physica A 269 140–147ADSCrossRefGoogle Scholar
  21. 21.
    Lillo, F., Micciché;, S., Mantegna, R.N. (2003) Long-range correlated stationary Markovian processes. Scholar
  22. 22.
    Rammal, R., Toulouse, G., Virasoro, M.A. (1986) Ultrametricity for physicists. Rev. Mod. Phys. 58 765–788MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Mardia, K.V., Kent, J.T., Bibby, J.M. (1979) Multivariate Analysis. Academic Press, San Diego CAMATHGoogle Scholar
  24. 24.
    Mantegna, R.N., Stanley, H.E. (2000) An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge Univ. Press, Cambridge, UKGoogle Scholar
  25. 25.
    Embrechts, P., McNeil, A., Straumann, D (2002) in Risk Management: Value at Risk and Beyond, ed. M.A.H. Dempster, Cambridge University Press, Cambridge, pp 176–223CrossRefGoogle Scholar
  26. 26.
    Press, W.H., Teukolsky, S.A., Veterling, W.T., Flannery, S.P. (1992) Numerical Recipes in Fortran: the art of scientific computing. Cambridge Univ. Press, Cambridge, UK, 2nd Ed.Google Scholar
  27. 27.
    Onnela, J.-P., Chakraborti, A., Koski, K., Kertesz, J. (2002) Dynamic asset trees and Black Monday. Scholar

Copyright information

© Springer Japan 2004

Authors and Affiliations

  • Salvatore Miccichè
    • 1
    • 2
  • Fabrizio Lillo
    • 1
    • 2
  • Giovanni Bonanno
    • 1
    • 2
  • Rosario N. Mantegna
    • 1
    • 2
  1. 1.Istituto Nazionale per la Fisica della MateriaUnità di Palermo, Viale delle ScienzePalermoItalia
  2. 2.Dipartimento di Fisica e Tecnologie RelativeUniversità di Palermo, Viale delle ScienzePalermoItalia

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