Realized Quantiles^*

This article proposes a simple approach to estimate quantiles of daily financial returns directly from high-frequency data. We denote the resulting estimator as realized quantile (RQ) and use it forecast tail risk measures, such Value at Risk (VaR) Expected Shortfall (ES). The RQ is built on assumption that logarithm prices are subordinated self-similar processes in intrinsic time. time dimension stochastically transforms clock order capture real “heartbeat” markets accordance with their trading activity and/or riskiness. self-similarity allows compute by simply scaling up intraday counterparts, while subordination technique can easily accommodate numerous empirical features returns, volatility persistence fat-tailedness. Our method, which flexible assumption, implement exploits rich information content data another perspective than classical In comprehensive exercise, we show our forecasts VaR ES more accurate ones large set up-to-date comparative models, for both, stocks foreign exchange rates.