Skip to Main content Skip to Navigation
Journal articles

Computation of VaR and CVaR using stochastic approximations and unconstrained importance sampling.

Abstract : Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are two risk measures which are widely used in the practice of risk management. This paper deals with the problem of computing both VaR and CVaR using stochastic approximation (with decreasing steps): we propose a first Robbins-Monro procedure based on Rockaffelar-Uryasev's identity for the CVaR. The convergence rate of this algorithm to its target satisfies a Gaussian Central Limit Theorem. As a second step, in order to speed up the initial procedure, we propose a recursive importance sampling (I.S.) procedure which induces a significant variance reduction of both VaR and CVaR procedures. This idea, which goes back to the seminal paper of B. Arouna, follows a new approach introduced by V. Lemaire and G. Pagès. Finally, we consider a deterministic moving risk level to speed up the initialization phase of the algorithm. We prove that the convergence rate of the resulting procedure is ruled by a Central Limit Theorem with minimal variance and its efficiency is illustrated by considering several typical energy portfolios.
Document type :
Journal articles
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00348098
Contributor : Noufel Frikha <>
Submitted on : Friday, December 3, 2010 - 11:57:23 AM
Last modification on : Monday, December 14, 2020 - 9:43:31 AM
Long-term archiving on: : Friday, March 4, 2011 - 2:41:03 AM

Files

VaRCVaR.pdf
Files produced by the author(s)

Identifiers

Citation

Olivier Bardou, Noufel Frikha, G. Pagès. Computation of VaR and CVaR using stochastic approximations and unconstrained importance sampling.. Monte Carlo Methods and Applications, De Gruyter, 2009, 15 (3), pp.173-210. ⟨10.1515/MCMA.2009.011⟩. ⟨hal-00348098v5⟩

Share

Metrics

Record views

553

Files downloads

3296