Conditional Range Model

Value at risk (VaR) is a single, summary, statistical measure of possible asset losses. This paper explores the various VaR models that were proposed with different characteristics of financial data. Above all, we introduce the idea of dynamical range process to the VaR estimation. Accordingly, the Conditional Autoregressive Range (CARR) model proposed by Chou (2005) is used for the estimation of volatility process for single asset and extended to the modification of Engle’s (2002) DCC model for a portfolio. Then the range-based VaR model is constructed. Our method can be applied to measure the VaR for single assets and for portfolios. Using empirical data of the stock indices of S&P 500 composite and the ten-year Treasury bond, we find that the range-based model with theory of extreme value have salient evaluation performance than other alternatives, such as the conventional return-based models in the estimation of VaR