A high-frequency approach to VaR measures and forecasts based on the HAR-QREG model with jumps

The occurrence of extreme events has brought tremendous impact to stock markets, and the accuracy of measuring and forecasting value at risk (VaR) has important theoretical and practical value for the risk management of stock markets. This paper proposes a heterogeneous auto-regression quantile regression (HAR-QREG) model based on 5-min high frequency data and incorporating positive and negative jumps to explore the heterogeneity of different volatility components on returns under different market states and to make sliding forecasting of VaR. The results show that: (1) in the conditional quantile tail of returns, short-term daily and medium-term weekly volatility have a greater impact on returns than long-term monthly volatility in the Chinese stock market. (2) Volatility of different maturities has a significantly greater impact on returns in bear markets than in oscillating and bull markets. (3) There is heterogeneity in the impact of jump volatility on returns across different market states, with a greater impact in bear and bull markets, but the degree of impact decreases as the duration lengthens. Furthermore, the model has better results for out-of-sample VaR forecasting.