We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.

A Fourier transform method for nonparametric estimation of multivariate volatility

Mancino, Maria Elvira;
2009

Abstract

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.
2009
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Continuous semi-martingale; Fourier transform; high frequency data; instantaneous co-volatility; nonparametric estimation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79787
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