Abstract:

A question of common interest is how to evaluate multiple period Value at Risk
in heteroscedastic models like GARCH(1, 1). For example, in the context of the
Basle agreement, how to the estimate the 10-day 99% VaR on the basis of a GARCH
model for the daily returns. We discuss some approaches to this question, both
numerical and theoretical. We will in particular study ways to quantify the
intertemporal dependence structure in a GARCH(1, 1 ), by introducing and
evaluating suitably defined tail dependence functions and coefficients, which
are a variant on the usual coefficient of (lower) tail dependence.