Large Deviations for Heavy-Tailed Factor Models

TL;DR

This paper investigates large deviation probabilities in heavy-tailed factor models, analyzing the contributions of factors and idiosyncratic components, and extends results to Levy processes with large jumps.

Contribution

It identifies conditions under which both factor and idiosyncratic terms influence tail behavior and introduces a Monte Carlo algorithm for estimation.

Findings

Both factor and idiosyncratic components can dominate tail probabilities.

Large deviations are primarily caused by a single large jump from either component.

The Monte Carlo method effectively approximates large deviation probabilities.

Abstract

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.