Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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  • Xun Fa Lu
  • Kin Keung Lai
  • Liang Liang

Related Research Unit(s)


Original languageEnglish
Pages (from-to)333-357
Journal / PublicationAnnals of Operations Research
Issue number1
Online published17 May 2011
Publication statusPublished - Aug 2014


This paper combines copula functions with GARCH-type models to construct the conditional joint distribution, which is used to estimate Value-at-Risk (VaR) of an equally weighted portfolio comprising crude oil futures and natural gas futures in energy market. Both constant and time-varying copulas are applied to fit the dependence structure of the two assets returns. The findings show that the constant Student t copula is a good compromise for effectively fitting the dependence structure between crude oil futures and natural gas futures. Moreover, the skewed Student t distribution has a better fit than Normal and Student t distribution to the marginal distribution of each asset. Asymmetries and excess kurtosis are found in marginal distributions as well as in dependence. We estimate VaR of the underlying portfolio to be 95% and 99%, by using the Monte Carlo simulation. Then using backtesting, we compare the out-of-sample forecasting performances of VaR estimated by different models. © 2011 Springer Science+Business Media, LLC.

Research Area(s)

  • Backtesting, Copulas, Risk management, Time-varying models, Value-at-Risk