Multi-period risk assesment in GARCH models
Professor Raymond Brummelhuis Department of Mathematics and Statistics, Birkbeck College, London

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.