2013/01/16 by Christa Cuchiero, Cuchiero, Christa, Josef Teichmann +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60F05 #60G48 #Applied mathematics #Central limit theorem #Covariance #Covariance function #Covariance intersection #Estimation of covariance matrices #Estimator #FOS: Mathematics #Financial Risk and Volatility Modeling #Fourier transform #Mathematical analysis #Mathematical optimization #Mathematics #Matérn covariance function #Monetary Policy and Economic Impact #Rational quadratic covariance function #Statistics #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #msc:60F05 #msc:60G48 #stat.TH
paper · pdf · doi:10.48550/arxiv.1301.3602
revised and slightly shortened final version
openalex publication_date 2013/01/16 · arxiv created 2014/06/20 · arxiv updated 2014/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a new non-parametric Fourier procedure to estimate the trajectory of the instantaneous covariance process (from discrete observations of a multidimensional price process) in the presence of jumps extending the seminal work Malliavin and Mancino~\citeMM:02, MM:09. Our approach relies on a modification of (classical) jump-robust estimators of integrated realized covariance to estimate the Fourier coefficients of the covariance trajectory. Using Fourier-Féjer inversion we reconstruct the path of the instantaneous covariance. We prove consistency and central limit theorem (CLT) and in particular that the asymptotic estimator variance is smaller by a factor 2/3 in comparison to classical local estimators. The procedure is robust enough to allow for an iteration and we can show theoretically and empirically how to estimate the integrated realized covariance of the instantaneous stochastic covariance process. We apply these techniques to robust calibration problems for multivariate modeling in finance, i.e., the selection of a pricing measure by using time series and derivatives' price information simultaneously.