How to mitigate the impact of inappropriate distributional settings when the parametric value-at-risk approach is used.

*(English)*Zbl 1294.91198Summary: This study utilizes four types of model, which are composed of two volatility specifications (generalized autoregressive conditional heteroskedasticity – GARCH – and autoregressive jump intensity – ARJI) and two value-at-risk (VaR) approaches (parametric and semi-parametric) with three return distribution settings (normal, GED and SGED), to explore, under the same return distribution settings and GARCH-based models as the benchmark, which variance specification and which VaR approach can enhance the VaR performance of GARCH-based models through assessments of accuracy, and further investigate approaches to mitigating the impact of inappropriate distributional settings that may cause misestimation of the parametric approach to VaR via a range of statistics. Empirical results show that, with regard to a long position, especially for the filter historical simulation (FHS) approach, both the variance specification of the ARJI approach and the FHS VaR approach can not only improve the VaR forecasting performance of GARCH-based models but also significantly reduce the influence of inappropriate return distribution settings on the VaR estimate of GARCH-based models. Moreover, FHS-ARJI-based models seem to be superior to FHS-GARCH-based models, but less significantly so than for the other groups competing above. As to short positions, both ARJI-based models and GARCH-based models seem to have similar VaR performance whereas FHS-GARCH-based models are superior to both GARCH-based models and ARJI-based models. In addition, the other three types of model (ARJI, FHS-GARCH and FHS-ARJI) can reduce more effectively the impact of incorrect return distribution specifications of GARCH-based models as compared with the case of a long position. Finally, within the same type of model, the SGED has just about the best performance among these three distribution specifications for a long position, whereas these phenomena seem to be less significant for a short position. Additionally, the VaR forecasting performance of a short position is less significantly affected by return distribution specifications, volatility specifications or VaR approaches as compared with that of a long position.

##### MSC:

91G70 | Statistical methods; risk measures |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

##### Keywords:

value at risk (VaR); autoregressive jump intensity (ARJI); skewed generalized error distribution; filter historical simulation; parametric approach##### Software:

RiskMetrics
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