Statistical Modelling 2 (2002), 103–122
Improving Financial Risk Assessment Through Dependency
Beatriz Vaz de Melo Mendes,
Department of Statistics,
Federal University at Rio de Janeiro,
Rio de Janeiro, 22221-080, RJ
Brazil
e-mail: rbeatriz@im.ufrj.br or
bmendes@visualnet.com.br
Alba Regina Moretti,
Department of Mathematics,
Federal University at S. J. Del Rey
Brazil
e-mail: amoretti@dme.ufrj.br
Abstract:
Understanding
dependency between financial markets is crucial when measuring globally
integrated exposures to risk. To this end the first step may be the
investigation of the joint behavior of their most representative indexes. We
fit by parametric and non parametric methods bivariate extreme value models on
the componentwise maxima and minima computed monthly from several pairs of
indexes representing the North American, the Latin American, and the Emerging
markets. We analyze the role of the asymmetric models, finding which market
drives the dependency, and express the degrees of dependence using measures of
linear and nonlinear dependency such as the linear correlation coefficient \rho
and the measure \tau based on the dependence function. We discuss the
interpretation of \tau as a conditional probability that a crash occurs in a
market given that a catastrophic event has occurred in some other market.
We assess risks by computing probabilities associated with joint extreme events
and by computing joint risk measures. We show empirically that the joint
Value-at-Risk may be severely under estimated if independence is assumed
between markets. To take into account the clustering of extreme events we
compute the bivariate extremal index and incorporate this information in the
analysis.
Keywords:
Bivariate extreme value models; extremal index; risk measures
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