Large Deviations of Factor Models with Regularly-Varying Tails: Asymptotics and Efficient Estimation

We analyze the $\mathit{\text{Large}}\mathit{\text{Deviation}}\mathit{\text{Probability}}\mathit{\text{(LDP)}}$ of linear factor models generated from non-identically distributed components with $\mathit{\text{regularly-varying}}$ tails, a large subclass of heavy tailed distributions. An efficient sampling method for LDP estimation of this class is introduced and theoretically shown to exponentially outperform the crude Monte-Carlo estimator, in terms of the coverage probability and the confidence interval’s length. The theoretical results are empirically validated through stochastic simulations on independent non-identically Pareto distributed factors. The proposed estimator is available as part of a more comprehensive $\mathtt{\text{Betta}}$ package.