文章基本信息

标题：A Hybrid Importance Sampling Algorithm for Estimating VaR under the Jump Diffusion Model
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作者：Tian-Shyr Dai ; Li-Min Liu
期刊名称：Journal of Software Engineering and Applications
印刷版ISSN：1945-3116
电子版ISSN：1945-3124
出版年度：2009
卷号：2
期号：4
页码：301-307
DOI：10.4236/jsea.2009.24039
出版社：Scientific Research Publishing
摘要：Value at Risk (VaR) is an important tool for estimating the risk of a financial portfolio under significant loss. Although Monte Carlo simulation is a powerful tool for estimating VaR, it is quite inefficient since the event of significant loss is usually rare. Previous studies suggest that the performance of the Monte Carlo simulation can be improved by impor-tance sampling if the market returns follow the normality or the distributions. The first contribution of our paper is to extend the importance sampling method for dealing with jump-diffusion market returns, which can more precisely model the phenomenon of high peaks, heavy tails, and jumps of market returns mentioned in numerous empirical study papers. This paper also points out that for portfolios of which the huge loss is triggered by significantly distinct events, naively applying importance sampling method can result in poor performance. The second contribution of our paper is to develop the hybrid importance sampling method for the aforementioned problem. Our method decomposes a Monte Carlo simulation into sub simulations, and each sub simulation focuses only on one huge loss event. Thus the perform-ance for each sub simulation is improved by importance sampling method, and overall performance is optimized by determining the allotment of samples to each sub simulation by Lagrange’s multiplier. Numerical experiments are given to verify the superiority of our method.
关键词：Hybrid Importance Sampling; VaR; Straddle Options; Jump Diffusion Process