Measuring financial risk with generalized asymmetric least squares regression

This paper proposes a generalized asymmetric least squares regression method to estimate Value-at-risk and expected shortfall. By solving an asymmetric least squares regression in a Reproducing Kernel Hilbert Space, the method achieves nonlinear prediction power, while making no assumption on the underlying probability distributions. Two toy datasets are used to demonstrate its nonlinear prediction power. The empirical results on the S&P 500 stock index obviously show that the method is superior to other four benchmark methods. © 2011 Elsevier B.V. All rights reserved.