Conditional quantile analysis for realized GARCH models

Abstract

This article introduces a novel quantile approach to harness the high‐frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized generalized autoregressive conditional heteroskedasticity (GARCH) model and employ conditional standard deviation, realized volatility, realized quantile, and absolute overnight return as innovations in the proposed dynamic quantile models. We devise a two‐step estimation procedure to estimate the conditional quantile parameters. The first step applies a quasi‐maximum likelihood estimation procedure, with the realized volatility as a proxy for the volatility proxy, to estimate the conditional standard deviation parameters. The second step utilizes a quantile regression estimation procedure with the estimated conditional standard deviation in the first step. Asymptotic theory is established for the proposed estimation methods, and a simulation study is conducted to check their finite‐sample performance. Finally, we apply the proposed methodology to calculate the value at risk of 20 individual assets and compare its performance with existing competitors.