Variance Reduction Technique for Estimating Value-at-Risk based on the Cross - Entropy  

作　　者：Mykhailo Pupashenko 

机构地区：[1]Department of Mathematics, University of Kaiserslautern, Erwin-Schroedinger-Srasse, Geb 48, 67663 Kaiserslautern, Germany

出　　处：《Journal of Mathematics and System Science》2014年第1期37-48,共12页数学和系统科学（英文版）

摘　　要：Value-at-Risk （VaR） estimation via Monte Carlo （MC） simulation is studied here. The variance reduction technique is proposed in order to speed up MC algorithm. The algorithm for estimating the probability of high portfolio losses （more general risk measure） based on the Cross - Entropy importance sampling is developed. This algorithm can easily be applied in any light- or heavy-tailed case without an extra adaptation. Besides, it does not loose in the performance in comparison to other known methods. A numerical study in both cases is performed and the variance reduction rate is compared with other known methods. The problem of VaR estimation using procedures for estimating the probability of high portfolio losses is also discussed.

关 键 词：VALUE-AT-RISK Monte Carlo simulation Cross - Entropy method variance reduction importance sampling stratifiedsampling. 

分 类 号：O212.1[理学—概率论与数理统计] U461.7[理学—数学]