Statistical Learning of Value-at-Risk and Expected Shortfall

D Barrera, S Crépey, E Gobet, Hoang-Dung Nguyen and B Saadeddine
Additional contact information
D Barrera: UNIANDES - Universidad de los Andes [Bogota]
S Crépey: LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité, UPCité - Université Paris Cité
E Gobet: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, X - École polytechnique - IP Paris - Institut Polytechnique de Paris, Université Paris-Saclay
Hoang-Dung Nguyen: LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité, UPCité - Université Paris Cité, Natixis
B Saadeddine: UEVE - Université d'Évry-Val-d'Essonne, Crédit Agricole

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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.

Keywords: value-at-risk; expected shortfall; quantile regression; quantile crossings; neural networks; numerical finance; 62G32; 62L20; 62M45; 91G60; 91G70 (search for similar items in EconPapers)
Date: 2024-09-18
New Economics Papers: this item is included in nep-big and nep-rmg
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