Abstract
We investigate Value-at-Risk (VaR) estimates based on extreme value theory (EVT) models combined with time varying parametric copulas against competing parametric approaches accounting for dynamic conditional correlations feasible to higher order portfolios. Tails of the return distributions are modeled via Generalized Pareto Distribution (GPD) applied to GARCH filtered residuals to capture excess returns, linked via constant and time varying copulas. Drawing on this EVT-GARCH-Copula, we evaluate portfolios consisting of German Stocks, market indices and FX-rates. However, the empirical results support the dynamic EVT-GARCH-Copula approach, as 99 % VaR forecasts clearly outperform parametric estimates stemming from competing dependency approaches.
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- 1.
Due to the explicit separation between dependency structure and the modeling of univariate marginal distributions, semi-parametric GP distribution is additionally applied to the return series.
- 2.
In this survey, observations below \(\alpha =10~\%\) are modeled via GPD.
- 3.
This approach is also known as inference for the margins (IFM).
- 4.
For 99 % VaR forecasts, the Basel II document allows for 4 misspecifications within 250 days.
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© 2014 Springer International Publishing Switzerland
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Berger, T. (2014). Financial Crisis, VaR Forecasts and the Performance of Time Varying EVT-Copulas. In: Helber, S., et al. Operations Research Proceedings 2012. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-00795-3_6
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DOI: https://doi.org/10.1007/978-3-319-00795-3_6
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