  We study large deviation probabilities for a sum of dependent random
variables from a heavy-tailed factor model, assuming that the components are
regularly varying. We identify conditions where both the factor and the
idiosyncratic terms contribute to the behaviour of the tail-probability of the
sum. A simple conditional Monte Carlo algorithm is also provided together with
a comparison between the simulations and the large deviation approximation. We
also study large deviation probabilities for stochastic processes with factor
structure. The processes involved are assumed to be Levy processes with
regularly varying jump measures. Based on the results of the first part of the
paper, we show that large deviations on a finite time interval are due to one
large jump that can come from either the factor or the idiosyncratic part of
the process.
