Samuel Y. M. Ze-To^*

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Department of Finance and Decision Sciences, Hong Kong Baptist University, Hong Kong, China.
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Abstract: This study develops a new conditional extreme value theory-based model (EVT) combined with the NIG + Jump model to forecast extreme risks. This paper utilizes the NIG + Jump model to asymmetrically feedback the past realization of jump innovation to the future volatility of the return distribution and uses the EVT to model the tail distribution of the NIG + Jump-processed residuals. The model is compared to the GARCH-t model and NIG + Jump model to evaluate its performance in estimating extreme losses in three major market crashes and crises. The results show that the conditional EVT-NIG + Jump model outperforms the GARCH and GARCH-t models in depicting the non-normality and in pro- viding accurate VaR forecasts in the in-sample and out-sample tests. The EVT-NIG + Jump model, which can measure the volatility of extreme price movement in capital markets due to unexpected events, enhances the EVT-based model for measuring the tail risk.

Keywords: Value-at-Risk; Extreme Value Theory; Jump; NIG

Cite this paper: S. Ze-To, "Crisis, Value at Risk and Conditional Extreme Value Theory via the NIG + Jump Model," Journal of Mathematical Finance, Vol. 2 No. 3, 2012, pp. 225-237. doi: 10.4236/jmf.2012.23025.

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