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Two-step methods in VaR prediction and the importance of fat tails. (English) Zbl 1398.91683
Summary: This paper proposes a two-step methodology for value-at-risk prediction. The first step involves estimation of a GARCH model using quasi-maximum likelihood estimation and the second step uses model filtered returns with the skewed \(t\) distribution of A. Azzalini and A. Capitanio [J. R. Stat. Soc. B. 65, No. 2, 367–389 (2003; doi:10.1111/1467-9868.00391)]. The predictive performance of this method is compared to the single-step joint estimation of the same data generating process, to the well-known GARCH-EVT model and to a comprehensive set of other market risk models. Backtesting results show that the proposed two-step method outperforms most benchmarks including the classical joint estimation method of same data generating process and it performs competitively with respect to the GARCH-EVT model. This paper recommends two robust models to risk managers of emerging market stock portfolios. Both models are estimated in two steps: the GJR-GARCH-EVT model and the two-step GARCH-St model proposed in this study.

MSC:
91G70 Statistical methods; risk measures
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G70 Extreme value theory; extremal stochastic processes
Software:
ismev; QRM
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