  In this paper we study time-consistent risk measures for returns that are
given by a GARCH(1,1) model. We present a construction of risk measures based
on their static counterparts that overcomes the lack of time-consistency. We
then study in detail our construction for the risk measures Value-at-Risk (VaR)
and Average Value-at-Risk (AVaR). While in the VaR case we can derive an
analytical formula for its time-consistent counterpart, in the AVaR case we
derive lower and upper bounds to its time-consistent version. Furthermore, we
incorporate techniques from Extreme Value Theory (EVT) to allow for a more
tail-geared statistical analysis of the corresponding risk measures. We
conclude with an application of our results to a data set of stock prices.
