A FOURIER TRANSFORM METHOD FOR NONPARAMETRIC ESTIMATION OF MULTIVARIATE VOLATILITY

• 成果类型: Article
• 署名作者: Malliavin, Paul; Mancino, Maria Elvira
• 署名单位: University of Florence
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS633
• 发表日期: 2009
• 页码: 1983-2010
• 关键词: High-frequency data; Market microstructure noise; INTEGRATED VOLATILITY; diffusion-coefficient; COVARIANCE ESTIMATION; models; sample; variance; feedback; prices

摘要

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous serni-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.