Abstract
Stochastic volatility models decompose the time series of financial returns into the product of a volatility factor and an iid noise factor. Assuming a slow dynamic for the volatility factor, we show via nonparametric tests that both the index as well as its individual stocks share a common volatility factor. While the noise component is Gaussian for the index, individual stock returns turn out to require a leptokurtic noise. Thus we propose a two-component model for stocks, given by the sum of Gaussian noise, which reflects market-wide fluctuations, and Laplacian noise, which incorporates firm-specific factors such as firm profitability or growth performance, both of which are known to be Laplacian distributed. In the case of purely Gaussian noise, the chi-squared probability for the density of individual stock returns is typically on the order of 10-20, while it increases to values of O(1) by adding the Laplace component.
Similar content being viewed by others
References
R. Cont, Quant. Financ. 1, 223 (2001)
N. Shephard, Stochastic Volatility Models: Selected Readings (Oxford University Press, Oxford, 2005)
D.H. Ahn, B. Gao, Rev. Financ. Stud. 12, 721 (1999)
T. Bollerslev, Rev. Econ. Stat. 69, 542 (1987)
J.C. Cox, J.E. Ingersoll, S.A. Ross, Econometrica 53, 385 (1985)
S.L. Heston, Rev. Financ. Stud. 6, 327 (1993)
J. Hull, A. White, Rev. Financ. Stud. 3, 573 (1990)
A.A. Dragulescu, V.M. Yakovenko, Quant. Financ. 2, 443 (2002)
S. Alfarano, T. Lux, F. Wagner, Comput. Econ. 26, 19 (2005)
S. Alfarano, T. Lux, F. Wagner, J. Econ. Dyn. Control 32, 101 (2008)
S. Alfarano, F. Wagner, M. Milaković, Appl. Financial Econ. Lett. 4, 311 (2008)
M.H. Stanley, L.A. Amaral, S.V. Buldyrev, H. Leschhorn, P. Maass, M.A. Salinger, H.E. Stanley, Nature 379, 804 (1996)
G. Bottazzi, A. Secchi, RAND J. Econ. 37, 235 (2006)
S. Alfarano, M. Milaković, A. Irle, J. Kauschke, A statistical equilibrium model of competitive firms, Economics Working Paper 2008-10, University of Kiel, 2008
F. Wagner, Physica A 364, 369 (2006)
T. Lux, M. Ausloos, in Theories of Disaster — Scaling Laws Governing Weather, Body, and Stock Market Dynamics, edited by A. Bunde, J. Kropp, H.J. Schellnhuber (Springer, Berlin Heidelberg, 2002), pp. 373–409
J.P. Bouchaud, A. Matacz, M. Potters, Phys. Rev. Lett. 87, 228701(4) (2001)
D. Nelson, J. Econom. 45, 7 (1990)
T. Lux, Appl. Fin. Econ. 11, 299 (2001)
C. Anteneodo, R. Riera, Phys. Rev. E 72, 26106 (2005)
A. Kirman, Quart. J. Econ. 108, 137 (1993)
A. Kirman, G. Teyssière, Stud. Nonlinear Dyn. Econom. 5, 281 (2002)
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wagner, F., Milaković, M. & Alfarano, S. What distinguishes individual stocks from the index?. Eur. Phys. J. B 73, 23–28 (2010). https://doi.org/10.1140/epjb/e2009-00358-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2009-00358-1