Abstract
Financial asset returns are known to be conditionally heteroskedastic and generally non-normally distributed, fat-tailed and often skewed. These features must be taken into account to produce accurate forecasts of Value-at-Risk (VaR). We provide a comprehensive look at the problem by considering the impact that different distributional assumptions have on the accuracy of both univariate and multivariate GARCH models in out-of-sample VaR prediction. The set of analyzed distributions comprises the normal, Student, Multivariate Exponential Power and their corresponding skewed counterparts. The accuracy of the VaR forecasts is assessed by implementing standard statistical backtesting procedures used to rank the different specifications. The results show the importance of allowing for heavy-tails and skewness in the distributional assumption with the skew-Student outperforming the others across all tests and confidence levels.
Highlights
Value-at-Risk (VaR) is a quantitative tool used to measure the maximum potential loss in value of a portfolio of assets over a defined period for a given probability
Model proposed by Krause and Paolella [16], as the authors developed an extremely fast method for parameter estimation that is found to outperform highly competitive models and can be compared to ours 2. Both univariate and multivariate models are estimated employing the aforementioned set of distributional assumptions and their accuracy in producing out-of-sample VaR forecasts is assessed by means of statistical backtesting procedures
Our results show that allowing for heavy-tails and skewness produces the most accurate VaR forecasts in both the univariate and multivariate setups
Summary
Value-at-Risk (VaR) is a quantitative tool used to measure the maximum potential loss in value of a portfolio of assets over a defined period for a given probability. Within the univariate framework the most complete study of VaR prediction methods is provided by Kuester et al [7] who compare fully parametric models with VaR constructed using historical simulation, extreme-value theory and quantile regression Their results show that considerable improvement over normality is achieved when using innovation distributions that allow for skewness and fat tails. Within the univariate scenario we consider the NCT-APARCH model proposed by Krause and Paolella [16], as the authors developed an extremely fast method for parameter estimation that is found to outperform highly competitive models and can be compared to ours 2 Both univariate and multivariate models are estimated employing the aforementioned set of distributional assumptions and their accuracy in producing out-of-sample VaR forecasts is assessed by means of statistical backtesting procedures.
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