Fourier series method for measurement of multivariate volatilities
type: Item
instance of: scholarly article
title: Fourier series method for measurement of multivariate volatilities
zbMATH Open document ID: 1008.62091
author: Paul Malliavin
author: Maria Elvira Mancino
published in: Finance and Stochastics
publication date: 2002-11-21T00:00:00Z
review text: This article deals with a new method based on Fourier analysis to measure volatility under the hypothesis that all observed data \(u^{*}\) are driven by semi-martingales which have Itô's stochastic differential \(du^{j}=\sum_{i=1}^{d}\alpha_{i}^{j} dx^{i}+\beta^{j} dt\), where \(x^{*}\) are independent Brownian motions and \(\alpha_{*}^{*}, \beta^{*}\) are functions depending on time. The matrix \(\sum^{j,k}(t)=\sum_{i=1}^{d}\alpha_{i}^{j}(t)\alpha_{i}^{k}(t)\) is called volatility matrix. The proposed algorithm reconstructs the volatility as a function of time. This method, based on the integration of the time series, is more robust than the classical one, based on the quadratic variation formula, and is well suited to compute volatility for high frequency time series.
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 42B05
zbMATH DE Number: 1833867
zbMATH Keywords: Fourier series methods
zbMATH Keywords: multivariate volatilities
zbMATH Keywords: time series
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
full work available at URL: s780-002-8400-6
OpenAlex ID: W1984849251
DOI: 10.1007/S780-002-8400-6
description: scientific article; zbMATH DE number 1833867