Statistical Learning of Value-at-Risk and Expected Shortfall

2022/09/14 by David Barrera, S Crépey, Barrera, D +7 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (stat.ML) #Monetary Policy and Economic Impact #Risk and Portfolio Optimization #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2209.06476

openalex publication_date 2022/09/14 · openalex created_date 2022/09/15 · openalex updated_date 2026/07/28

Abstract

We propose a non-asymptotic convergence analysis of a two-step approach to learn a conditional value-at-risk (VaR) and a conditional expected shortfall (ES) using Rademacher bounds, in a non-parametric setup allowing for heavy-tails on the financial loss. Our approach for the VaR is extended to the problem of learning at once multiple VaRs corresponding to different quantile levels. This results in efficient learning schemes based on neural network quantile and least-squares regressions. An a posteriori Monte Carlo procedure is introduced to estimate distances to the ground-truth VaR and ES. This is illustrated by numerical experiments in a Student-t toy model and a financial case study where the objective is to learn a dynamic initial margin.

Citations

• Quantile regression for longitudinal data
• Quantile regression with deep ReLU Networks: Estimators and minimax rates

Cited by

• An Explicit Scheme for Pathwise XVA Computations

Related

• Estimating Value at Risk and Expected Shortfall: A Brief Review and Some New Developments
• Statistical Learning with Conditional Value at Risk
• A Semi-parametric Realized Joint Value-at-Risk and Expected Shortfall Regression Framework
• Deep Empirical Risk Minimization in finance: looking into the future
• Quantile Convolutional Neural Networks for Value at Risk Forecasting