Research grant Multi-period Conditional Distribution Functions for Heteroscedastic Models with Applications to VaR

Let (r_t)_t be a general GARCH(1G 1)-type process. We give explicit integral formula's for the probability densities of r_t+k conditional to given values of r_t,s_tG, where the latter denotes the variance. As an application, we study the extreme value asymptotics of r_t+k and of r_t+1 + ... + r_t+k. These are relevant for the estimation of Value at Risk and other measures of .financial risk in the context of GARCH-models.