Intraday FX Volatility-Curve Forecasting with Functional GARCH Approaches

Abstract

This paper seeks to forecast intraday volatility curves for major foreign exchange (FX) currencies using functional GARCH models. Intraday return curves are observed at a daily frequency, yet preserve the full high-frequency trading structure, enabling volatility analysis at the intraday level. We demonstrate that the USD/EUR, USD/GBP, and USD/JPY intraday return curves exhibit strong cross-dependence, while individually they are serially uncorrelated but display long-range conditional heteroskedasticity. Embedding cross-currency dependence via multi-level functional principal component analysis and adding intraday bid-ask spread curves as exogenous drivers significantly improves intraday and day-ahead volatility forecasts relative to functional and realised-volatility baselines. The precise volatility forecasts motivate the construction of intraday Value-at-Risk (VaR). An intraday risk management application highlights that predicted intraday VaR curves can help mitigate dramatic losses in intraday trading strategies, showcasing their practical economic benefits in FX markets.