QMC Method With Variance Reduction Techniques For Estimating Hedging Portfolio’s VaR And CVaR

Risk is defined as the uncertainty of future results.Measuring financial market risk is measuring loss resulting from unfavorable change.Value-at-Risk(VaR)and Conditional Value-at-Risk(CVaR)are popular in financial risk management.There are so many research to calculate VaR using MC and parametric methods,QMC method is an improvement of MC methodby using deterministic sequences.Depending on the Black-Scholes model,this article will mainly try to get VaR and CVaR using Monte Carlo and Quasi Monte Carlo(QMC)methods.And considering the fact that losses surpass VaR are rare events,this paper takes advantage of importance sampling to increase efficiency.Meantime,using PCA decomposition method to overcome the poor quality of low-discrepancy points in high dimensions.This paper mainly discuss the VaR of hedging portfolio that contains 50 futures contract and 20 spot commodities using the method we referred,and in order to compare,this paper talks about independent and dependent condition respectively.Based on this,using likelihood ratio test to confirm the practical application of QMC method.The result indicate that the method is more efficient than traditional MC method,and this result can reflect most of the actual losses.