Forecasting Value at Risk via Intra-day Return Curves

Methods for incorporating high resolution intra-day asset price data into risk forecasts are being developed at an increasing pace. Existing methods, such as those based on realized volatility, rely primarily on reducing the observed intra-day price fluctuations to simple scalar summaries. In this paper, we propose several methods that incorporate full intra-day price information as functional data objects in order to forecast Value at Risk (VaR). The methods we consider are based on the recently proposed functional GARCH models and a new functional linear quantile regression model. In addition to providing daily VaR forecasts, these methods can also be used to forecast intra-day VaR curves, which we develop and study along with companion backtests to evaluate the quality of such intra-day risk measures. Using high-frequency trading data from equity and foreign exchange markets, we first forecast 1-day-ahead daily and intra-day VaR by applying the proposed methods and a host of benchmark models. Empirical evidence suggests that the functional GARCH models estimated from over-night cumulative intra-day return curves exhibit competitive performance relative to benchmark models in daily risk management, and produce valid intra-day VaR curves.