Fourier volatility forecasting with high-frequency data and microstructure noise

Abstract

We study the forecasting performance of the Fourier volatility estimator in the presence of microstructure noise. Analytical comparison and simulation studies indicate that the Fourier estimator significantly outperforms realized volatility-type estimators, particularly for high-frequency data and when the noise component is relevant. We show that the Fourier estimator generally exhibits better performance, even compared with methods specifically designed to handle market microstructure contamination.

Keywords:

• Monte Carlo methods
• Wavelets in finance
• Mathematical finance
• GARCH models
• Derivatives pricing; Financial engineering
• Numerical methods for option pricing

Notes

†The noise return moments may depend on the sampling frequency. Here we consider the simplified case where the microstructure noise displays an MA(1) structure with a negative first-order autocorrelation. This assumption is typically justified by bid–ask bounce effects (Roll 1984) and seems to be realistic in decentralized markets where trades arrive in a random fashion, e.g. the foreign exchange market (Bai et al. 2005). The hypothesis that u(s) is independent of the true return process is discussed by Hansen and Lunde (2006): it turns out that the independence assumption is not too damaging statistically when we analyse data in tick traded stocks recorded every minute.