Instantaneous volatility estimation by nonparametric fourier transform methods

Abstract

Malliavin and Mancino (2009) proposed a nonparametric Fourier transform method to estimate the instantaneous volatility under the assumption that the underlying asset price process is a semi-martingale. Based on this theoretical result, this chapter first conducts some simulation tests to justify the effectiveness of the Fourier transform method. Two correction schemes are proposed to improve the accuracy of volatility estimation. By means of these Fourier transform methods, some documented phenomena such as volatility daily effect and multiple risk factors of volatility can be observed. Then, a linear hypothesis between the instantaneous volatility and VIX derived from Zhang and Zhu (2006) is investigated. We extend their result and adopt a general linear test for empirical analysis.