Measuring and Comparing the Value-at-Risk Using GARCH and CARsR Models for CSI 300 Index

Abstract

This article is the first to provide a detailed method for range-based CARR model to estimate the VaR and its out-of-sample prediction. In this paper, we use GARCH and CARR volatility models to compare the VaR’s out-of-sample forecasting performance. Using the historical simulation method as benchmark for VaR estimation, we found that the historical simulation approach for VaR measurement is more conservative than GARCH and CARR methods. The mean violation rate for the CARR VaRs is lower than that of the GARCH VaRs. Meanwhile, the CARR VaR is able to deliver lower required capital levels without producing bigger violations. This paper argued that the CARR VaR valuation approach is suitable as an internal model method for financial institution in VaR forecasting.