Expected Shortfall LASSO

TL;DR

This paper introduces a new high-dimensional estimator for Expected Shortfall using an $ ext{L}_1$ penalty, suitable for heavy-tailed time-series data, with theoretical guarantees and empirical validation showing improved performance over benchmarks.

Contribution

It develops a novel $ ext{L}_1$-penalized estimator for ES in high-dimensional settings, providing nonasymptotic error bounds and applicability to heavy-tailed data.

Findings

Estimator performs well with heavy-tailed data.

Nonlinear models outperform benchmarks.

Model complexity can grow with sample size.

Abstract

We propose an $\ell_1$-penalized estimator for high-dimensional models of Expected Shortfall (ES). The estimator is obtained as the solution to a least-squares problem for an auxiliary dependent variable, which is defined as a transformation of the dependent variable and a pre-estimated tail quantile. Leveraging a sparsity condition, we derive a nonasymptotic bound on the prediction and estimator errors of the ES estimator, accounting for the estimation error in the dependent variable, and provide conditions under which the estimator is consistent. Our estimator is applicable to heavy-tailed time-series data and we find that the amount of parameters in the model may grow with the sample size at a rate that depends on the dependence and heavy-tailedness in the data. In an empirical application, we consider the systemic risk measure CoES and consider a set of regressors that consists of nonlinear transformations of a set of state variables. We find that the nonlinear model outperforms an unpenalized and untransformed benchmark considerably.