Multifractality and value-at-risk forecasting of exchange rates

• We model the high frequency VaR for EUR/USD returns.
• We use a modified version of the multifractal model of asset returns (MMAR).
• We study the out-of-sample forecasting performance of the MMAR model and two alternative models.
• Our dataset consists of 138,418 5-min round-the-clock observations of EUR/USD spot quotes and trading ticks.

This paper addresses market risk prediction for high frequency foreign exchange rates under nonlinear risk scaling behaviour. We use a modified version of the multifractal model of asset returns (MMAR) where trading time is represented by the series of volume ticks. Our dataset consists of 138,418 5-min round-the-clock observations of EUR/USD spot quotes and trading ticks during the period January 5, 2006 to December 31, 2007. Considering fat-tails, long-range dependence as well as scale inconsistency with the MMAR, we derive out-of-sample value-at-risk (VaR) forecasts and compare our approach to historical simulation as well as a benchmark GARCH(1,1) location-scale VaR model. Our findings underline that the multifractal properties in EUR/USD returns in fact have notable risk management implications. The MMAR approach is a parsimonious model which produces admissible VaR forecasts at the 12-h forecast horizon. For the daily horizon, the MMAR outperforms both alternatives based on conditional as well as unconditional coverage statistics.