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

## TL;DR

This paper studies the probability of large deviations in factor models with heavy-tailed distributions, introduces an efficient estimation method, and validates it through simulations, improving over traditional Monte Carlo techniques.

## Contribution

It provides a new asymptotic analysis for large deviations in heavy-tailed factor models and develops an efficient estimation method outperforming crude Monte Carlo.

## Key findings

- The proposed estimator significantly reduces variance compared to Monte Carlo.
- Empirical validation confirms the theoretical efficiency gains.
- The method is implemented in the Betta software package.

## Abstract

We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{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 \texttt{Betta} package.