Range-based models in estimating value-at-risk (VaR)

Abstract

This paper introduces new methods of estimating Value-at-Risk (VaR) using range-based GARCH (general autoregressive conditional heteroskedasticity) models. These models, which could be based on either the Parkinson range or the Garman-Klass range, are applied to ten stock market indices of selected countries in the Asia-Pacific region. The results are compared using the traditional methods such as the econometric method based on the autoregressive moving average (ARMA)-GARCH models and RiskMetricsTM. The performance of the different models is assessed using the out-ofsample VaR forecasts. Series of likelihood ratio (LR) tests—namely, LR of unconditional coverage (LRuc), LR of independence (LRind), and LR of conditional coverage (LRcc)—are performed for comparison. The result of the assessment shows that the model based on the Parkinson range GARCH (1,1) with Student’s t distribution, is the best-performing model on the ten stock market indices. It has a failure rate, defined as the percentage of actual return that is smaller than the one-step-ahead VaR forecast, of zero in nine out of ten stock market indices. This paper finds that range-based GARCH models are good alternatives in modeling volatility and in estimating VaR.

JEL classification: C01, C13