On Some Models for Value-At-Risk

Abstract

The idea of statistical learning can be applied in financial risk management. In recent years, value-at-risk (VaR) has become the standard tool for market risk measurement and management. For better VaR estimation, Engle and Manganelli (2004 Engle , R. , Manganelli , S. ( 2004 ). CAViaR: Conditional value at risk by regression quantiles . Journal of Business & Economic Statistics 22 : 367 – 381 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) introduced the conditional autoregressive value-at-risk (CAViaR) model to estimate the VaR directly by quantile regression. To entertain the nonlinearity and structural change in the VaR, we extend the CAViaR idea using two approaches: the threshold GARCH (TGARCH) and the mixture-GARCH models. The estimation method of these models are proposed. Our models should possess all the advantages of the CAViaR model and enhance the nonlinear structure. The methods are applied to the S&P500, Hang Seng, Nikkei and Nasdaq indices to illustrate our models.

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