High-Frequency Risk Measures.

Summary This paper proposes intraday High Frequency Risk (HFR) measures for market risk in the case of irregularly spaced high-frequency data. In this context, we distinguish three concepts of value-at-risk (VaR): the total VaR, the marginal (or per-time-unit) VaR, and the instantaneous VaR. Since the market risk is obviously related to the duration between two consecutive trades, these measures are completed with a duration risk measure, i.e., the time-at-risk (TaR). We propose a forecasting procedure for VaR and TaR for each trade or other market microstructure event. We perform a backtesting procedure specifically designed to assess the validity of the VaR and TaR forecasts on irregularly spaced data. The performance of the HFR measure is illustrated in an empirical application for two stocks (Bank of America and Microsoft) and an exchange-traded fund (ETF) based on Standard and Poor's (the S&P) 500 index. We show that the intraday HFR forecasts accurately capture the volatility and duration dynamics for these three assets.