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

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

2008-12-17

arxiv.org/abs/0812.3381v5

Economy

Quantitative Finance

Computational Finance

Scientific paper

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. Pag\`es. 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.

Affiliated with

Also associated with

No associations

Rating

Computation of VaR and CVaR using stochastic approximations and unconstrained importance sampling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Computation of VaR and CVaR using stochastic approximations and unconstrained importance sampling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computation of VaR and CVaR using stochastic approximations and unconstrained importance sampling will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-172114