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Application for Shenzhen composite index of the three-parameter generalized Pareto distribution to estimate VaR

Zhao Xu, Cheng Weihu, Zhang Qingnan, Zhang Yang


Value at Risk (VaR) estimation plays an important role in risk management and becomes the universally accepted risk standard for financial market. The generalized Pareto distribution is effective tool using excesses over a high threshold to estimate VaR, building an effective risk protection program to reduce economic loss. The parameters of the three-parameter generalized Pareto distribution were estimated using the methods of moments (MOM) and probability weighted moments (PWM) methods for Monte Carlo generated samples. The performance of these estimators was statistically compared. Simulation studies show that the PWM performs well compared to the MOM. Therefore, the PWM method is applied in Chinese stock market to estimate VaR and gives evidence of good performances.


three-parameter generalized Pareto distribution, methods of moments, probability weighted moments, threshold, Value at Risk.

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