Value at risk estimation by quantile regression and kernel estimator

Abstract

Risk management has attracted a great deal of attention, and Value at Risk (VaR) has emerged as a particularly popular and important measure for detecting the market risk of financial assets. The quantile regression method can generate VaR estimates without distributional assumptions; however, empirical evidence has shown the approach to be ineffective at evaluating the real level of downside risk in out-of-sample examination. This paper proposes a process in VaR estimation with methods of quantile regression and kernel estimator which applies the nonparametric technique with extreme quantile forecasts to realize a tail distribution and locate the VaR estimates. Empirical application of worldwide stock indices with 29 years of data is conducted and confirms the proposed approach outperforms others and provides highly reliable estimates.