Data driven value-at-risk forecasting using a SVR-GARCH-KDE hybrid

TL;DR

This paper introduces a nonlinear, data-driven framework combining support vector regression, GARCH, and kernel density estimation to improve VaR forecasting accuracy by capturing complex market behaviors and tail risks.

Contribution

It proposes a novel hybrid model that overcomes parametric model limitations, providing flexible, adaptive VaR forecasts for financial risk management.

Findings

SVR-GARCH-KDE outperforms benchmark models in risk prediction.

The hybrid model significantly reduces potential losses in ten-day forecasts.

Models with non-normal distributions outperform those with normal assumptions.

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 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.