Estimation Of Exponential Power Mixture Model And Its Application To The VaR Measurement

In the process of interest rate liberalization,Shanghai Interbank Offered Rate(SHIBOR)is gradually linked to the asset pricing.It makes financial institutions pay more and more attention to the risk management of SHIBOR.As an important tool of risk management,Value at Risk(VaR)can be calculated by estimating the distribution of asset return based on mixture model.Exponential Power mixture model,compared to other mixture models,is more general and can handle more situations.It can also capture leptokurtosis well.The commonly used Gaussian mixture model is a special case of Exponential Power mixture model.This paper mainly studies model selection and estimation for exponential power mixture model,and its application in measuring VaR of SHIBOR.A penalized likelihood method is proposed to select the components of the model and estimate parameters simultaneously.This method can shrink mixing probabilities in the mixture model to zero to delete the corresponding components.This paper also relaxes the assumption in existing method that each component has zero mean.A modified EM algorithm is proposed to solve the maximization problem of the proposed penalized likelihood function.In addition,Monte Carlo simulations are conducted to evaluate the performance of the proposed method.It is found that the proposed method is comparable with the penalized Gaussian mixture model method when the underlying model is Gaussian mixture model.They both have 95%correctly estimation rate of the number of model components.When the underlying model is Exponential Power mixture model,the proposed method outperforms others with both higher correctly estimation rate of component numbers,and the proposed method has high accuracy in the estimation of parameters.The proposed method is applied to fit the distribution of SHIBOR yield,and its VaR is then calculated based on the estimated distribution.Compared with the penalized Gaussian mixture model method,the proposed method selects much less number of components.The fitted VaR by the proposed method has no significant difference in the failure rate compared to its theoretical value.The failure rate of predicted VaR is the closest to the corresponding confidence level compared with other methods.Therefore the proposed method has better performance in both fitting and predicting VaR.