On some models for value-at-risk

Philip L. H. YU, Wai Keung LI, Shusong JIN

Research output: Contribution to journalArticle

13 Citations (Scopus)


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) 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. Copyright © 2010 Taylor & Francis Group, LLC.
Original languageEnglish
Pages (from-to)622-641
JournalEconometric Reviews
Issue number5-6
Publication statusPublished - 2010


Value at risk
Risk measurement
Financial risk management
GARCH model
Statistical learning
Structural change
Generalized autoregressive conditional heteroscedasticity
Risk management
Risk model
Quantile regression
Market risk


Yu, P. L. H., Li, W. K., & Jin, S. (2010). On some models for value-at-risk. Econometric Reviews, 29(5-6), 622-641. doi: 10.1080/07474938.2010.481972


  • GARCH model
  • Mixtures
  • Threshold models
  • Value-at-risk