Abstract

http://ssrn.com/abstract=301266
 
 

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Tail Dependence of Factor Models


Yannick Malevergne


University of Saint Etienne - Graduate School of Economics and Business Administration (ISEAG); EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control

Didier Sornette


Swiss Finance Institute; ETH Zurich

March 2002


Abstract:     
Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also undergone a large loss) as a function of the parameters of the underlying factor model and of the tail parameters of the distributions of the factor and of the idiosyncratic noise of each stock. Our formula holds for arbitrary marginal distributions and in addition does not require any parameterization of the multivariate distributions of the market and stocks. The determination of the extreme parameter, which is not accessible by a direct statistical inference, is made possible by the measurement of parameters whose estimation involves a significant part of the data with sufficient statistics. Our empirical tests find a good agreement between the calibration of the tail dependence coefficient and the realized large losses over the period from 1962 to 2000. Nevertheless, a bias is detected which suggests the presence of an outlier in the form of the crash of October 1987.

Number of Pages in PDF File: 29

Keywords: Factor model, Nonparametric estimation, Tail dependence

JEL Classification: C14, G10

working papers series


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Date posted: February 23, 2002  

Suggested Citation

Malevergne, Yannick and Sornette, Didier, Tail Dependence of Factor Models (March 2002). Available at SSRN: http://ssrn.com/abstract=301266 or http://dx.doi.org/10.2139/ssrn.301266

Contact Information

Yannick Malevergne
University of Saint Etienne - Graduate School of Economics and Business Administration (ISEAG) ( email )
2, Rue Tréfilerie
F-42023 St. Etienne Cedex 2
France
EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control ( email )
23 av. Guy de Collongue BP 174
69132 Ecully Cedex
France
HOME PAGE: http://www.em-lyon.com/english/faculty/professors/efc/malevergne/index.aspx
Didier Sornette (Contact Author)
Swiss Finance Institute ( email )
c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
Switzerland
ETH Zurich ( email )
Department of Management, Technology and Economics
Scheuchzerstrasse 7
8092 Zurich
Switzerland
41446328917 (Phone)
41446321914 (Fax)
HOME PAGE: http://www.er.ethz.ch/
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