Value at Risk (VaR) Estimation: A New Extreme Value Approach for Risk Managers

Presented at 2012 FMA Asian Conference.[[abstract]]We propose a new approach for estimating value at risk (VaR). Our approach combines quasi-maximum-likelihood fitting of asymmetric conditional autoregressive range (ACARR) models to estimate the current volatility and classical extreme value theory (EVT) to estimate the tail of the innovation distribution of the ACARR model. Our approach reflects two stylized facts exhibited by most financial time series, namely stochastic volatility and the fat-tailedness of conditional distributions over short time horizons. Our approach presents two main advantages over the McNeil and Frey (2000) approach. First, the ACARR model (used in our approach) is an asymmetric model which treats the upward and downward movements of the asset price differently (asymmetrically), whereas the generalized autoregressive conditional heteroskedasticity (GARCH) model (used in the McNeil and Frey (2000) approach) is a symmetric model which ignores the asymmetric structure of the asset price. Second, as we use classical EVT to estimate the tail of the distribution of the residuals, we avoid dealing with the threshold issue in the modern EVT model. With the McNeil and Frey (2000) approach using modern EVT, the tail of the innovation distribution may be badly estimated. Using backtesting of historical time series data, we show that our approach gives better VaR estimates than the McNeil and Frey (2000) approach