  Appropriate risk management is crucial to ensure the competitiveness of
financial institutions and the stability of the economy. One widely used
financial risk measure is Value-at-Risk (VaR). VaR estimates based on linear
and parametric models can lead to biased results or even underestimation of
risk due to time varying volatility, skewness and leptokurtosis of financial
return series. The paper proposes a nonlinear and nonparametric framework to
forecast VaR that is motivated by overcoming the disadvantages of parametric
models with a purely data driven approach. Mean and volatility are modeled via
support vector regression (SVR) where the volatility model is motivated by the
standard generalized autoregressive conditional heteroscedasticity (GARCH)
formulation. Based on this, VaR is derived by applying kernel density
estimation (KDE). This approach allows for flexible tail shapes of the profit
and loss distribution, adapts for a wide class of tail events and is able to
capture complex structures regarding mean and volatility.
  The SVR-GARCH-KDE hybrid is compared to standard, exponential and threshold
GARCH models coupled with different error distributions. To examine the
performance in different markets, one-day-ahead and ten-days-ahead forecasts
are produced for different financial indices. Model evaluation using a
likelihood ratio based test framework for interval forecasts and a test for
superior predictive ability indicates that the SVR-GARCH-KDE hybrid performs
competitive to benchmark models and reduces potential losses especially for
ten-days-ahead forecasts significantly. Especially models that are coupled with
a normal distribution are systematically outperformed.

Statistical Finance