Abstract
The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk.
Highlights
The relevance of the estimation of time varying volatility in financial economics has been recognized for a long time but the recent availability of high-frequency financial data has given an enormous impulse to its investigation and application
We show how to optimize the asymptotic variance through a suitable choice of ratio of the observation number to the number of the Fourier frequencies
We stress that with this choice of c the Fourier estimator has the same rate of convergence and asymptotic variance of the Fejer kernel-based realized spot volatility considered in Refs. [34, 40]
Summary
The relevance of the estimation of time varying volatility in financial economics has been recognized for a long time but the recent availability of high-frequency financial data has given an enormous impulse to its investigation and application. Instantaneous volatility estimation from high frequency data was first proposed in Ref. The Fourier method reconstructs the instantaneous volatility as a series expansion with coefficients gathered from the Fourier coefficients of the price variation For this reason it is based on the integration of the time series of returns rather than on its differentiation. We show how to optimize the asymptotic variance through a suitable choice of ratio of the observation number to the number of the Fourier frequencies These frequencies are those to be used in the Fejer series to reconstruct the volatility process. Most spot volatility estimators, especially the methods based on the quadratic variation formula, are defined as pointwise estimators; their adjustment parameters are tuned to work well only at a specific point in time.
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