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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.