KAEA-VSS: Empirical Macro-Finance seminar (Dec 17, 2020)

Presenter: Donggyu Kim (KAIST) (https://sites.google.com/site/donggyukim0329/)

Title: Dynamic Realized Quantile Regression Models

Abstract:

Quantile regression models are widely used in the modern risk management. To capture quantile dynamics of stock returns, we often employ low-frequency information such as squared stock returns. However, in the high-frequency literature, it is well-studied that incorporating the high-frequency information such as realized volatility and realized quantile helps to account for low-frequency market dynamics. In this paper, to harness the high-frequency information in the daily conditional quantile estimation, we introduce a novel quantile regression model which has high-frequency explanatory variables such as realized volatility and realized quantile. For example, we model the conditional standard deviation as some realized GARCH model and use the conditional standard deviation, realized volatility, realized quantile, and absolute overnight return as innovations in dynamic quantile models. To estimate the conditional quantile parameters, we suggest a two-step estimation procedure. In the first step, we apply the famous quasi-maximum likelihood estimation procedure with the realized volatility as the volatility proxy to estimating conditional standard deviation parameters. In the second step, we use quantile regression estimation procedure with the estimated conditional standard deviation in the first step. Then we establish the asymptotic properties of the proposed estimators. Finally, we apply the proposed methodology to calculating the value at risk (VaR) of the S&P500 stock index and compare its performance with competitors.