Nonparametric methods for volatility density estimation

Bert Es, van, P.J.C. Spreij, J.H. Zanten, van

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

824 Citations (Scopus)

Abstract

Stochastic volatility modeling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on discretely sampled continuous-time processes and discrete-time models will be discussed. The key insight for the analysis is a transformation of the volatility density estimation problem to a deconvolution model for which standard methods exist. Three types of nonparametric density estimators are reviewed: the Fourier-type deconvolution kernel density estimator, a wavelet deconvolution density estimator, and a penalized projection estimator. The performance of these estimators will be compared.
Original languageEnglish
Title of host publicationAMaMeF: Advanced Mathematical Methods in Finance
EditorsG. Di Nunno, B. Oksendal
Place of PublicationBerlin
PublisherSpringer
Pages293-312
ISBN (Print)978-3-642-18411-6
DOIs
Publication statusPublished - 2011

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