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

Chunchou Wu

doi:10.4236/tel.2018.86078

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.

Highlights

There is no consistent approach for forecasting market risk
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
This paper has presented the empirical study on the performance of GARCH and CARR VaR models for CSI-300 spot and futures index

Summary

Introduction

There is no consistent approach for forecasting market risk. Value-at-Risk (VaR) has become a standard benchmark for measuring financial risk. Giot and Laurent [4] compare the performance of a daily ARCH type model with the performance of a model based on the daily realized volatility when the one-day-ahead VaR is to be computed. We aim to address the VaR topic by comparing the performance of a return-based daily GARCH model with the performance of a CARR model based on the daily range volatility model when the one-day-ahead VaR measure is to be calculated. Gerlach, Hwang and McAleer [19] use range-based quantile regression to predict the VaR They did not compare the performance for different volatility approaches.

VaR Estimation with GARCH and CARR Model

Data and Empirical Analysis

Findings

Conclusions