Estimating value at risk with higher order moments: a semiparametric approach

The present paper develops a semiparametric procedure to estimate value at risk (VaR) by Estimating Function approach. In such framework, the features of higher order moments exhibited in the stock market returns are explicitly considered. And more importantly, these features are taken into account by a non-parametric approach, which is significantly different from the parametric model. The empirical work compares the performance of such method with traditional Quasi-MLE when estimating VaR based on daily returns from indices of Shanghai stock market, S&P 500 and FTSE 100 during the past ten years. The results show strongly positive evidence on the success of our semiparametric procedure and failure of QMLE when estimating VaR. And thus the findings imply further the importance of higher moments in modeling the tails of returns distribution. Since the implication is non-parametric, it does not depend on any definite specification of returns conditional distribution.