QMC Method With Variance Reduction Techniques For Estimating VaR And CVaR

Value-at-Risk(VaR)and Conditional Value-at-Risk(CVaR)are popular riskmeasures in recent years. This paper uses quasi-Monte Carlo(QMC)method to cal-culate VaR and CVaR of porfolios under Black-Scholes model. Due to some rare eventsarising from estimating VaR and CVaR, this paper takes advantage of importance sam-pling to increase calculation efciency. In order to overcome the poor quality of low dis-crepancy points in the higher dimension projections, this paper uses PCA decompositionfor the covariance matrix, which could reduce the efective dimension. The numerical ex-periments demonstrate that QMC method in combination with PCA decomposition andimportance sampling leads to large variance reduction, implying that better efciency canbe achieved.