Data Driven Value-at-Risk Forecasting Using a SVR-GARCH-KDE Hybrid

Abstract

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. 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 and adapts for a wide class of tail events. 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 forecasts are produced for different financial indices. Model evaluation using a likelihood ratio based test framework for interval forecasts indicates that the SVR-GARCH-KDE hybrid performs competitive to benchmark models. Especially models that are coupled with a normal distribution are systematically outperformed.

Keywords: Value-at-Risk, Support Vector Regression, Kernel Density Estimation, GARCH