A Multilevel Stochastic Approximation Algorithm for Value-at-Risk and Expected Shortfall Estimation - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

A Multilevel Stochastic Approximation Algorithm for Value-at-Risk and Expected Shortfall Estimation

Résumé

We propose a multilevel stochastic approximation (MLSA) scheme for the computation of the Value-at-Risk (VaR) and the Expected Shortfall (ES) of a financial loss, which can only be computed via simulations conditional on the realization of future risk factors. Thus, the problem of estimating its VaR and ES is nested in nature and can be viewed as an instance of a stochastic approximation problem with biased innovation. In this framework, for a prescribed accuracy ε, the optimal complexity of a standard stochastic approximation algorithm is shown to be of order ε −3. To estimate the VaR, our MLSA algorithm attains an optimal complexity of order ε −2−δ , where δ < 1 is some parameter depending on the integrability degree of the loss, while to estimate the ES, it achieves an optimal complexity of order ε −2 |ln ε| 2. Numerical studies of the joint evolution of the error rate and the execution time demonstrate how our MLSA algorithm regains a significant amount of the lost performance due to the nested nature of the problem.
Fichier principal
Vignette du fichier
MLSA_VaR_ES.pdf (812.38 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04037328 , version 1 (22-03-2023)

Identifiants

  • HAL Id : hal-04037328 , version 1

Citer

Stéphane Crépey, Noufel Frikha, Azar Louzi. A Multilevel Stochastic Approximation Algorithm for Value-at-Risk and Expected Shortfall Estimation. 2023. ⟨hal-04037328⟩
238 Consultations
59 Téléchargements

Partager

Gmail Facebook X LinkedIn More