Nonparametric Methods for Volatility Density Estimation

Bert van Es (), Peter Spreij () and Harry van Zanten ()
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Bert van Es: Universiteit van Amsterdam, Korteweg-de Vries Institute for Mathematics
Peter Spreij: Universiteit van Amsterdam, Korteweg-de Vries Institute for Mathematics
Harry van Zanten: Eindhoven University of Technology, Department of Mathematics

Chapter Chapter 11 in Advanced Mathematical Methods for Finance, 2011, pp 293-312 from Springer

Abstract: 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.

Keywords: Stochastic volatility models; Deconvolution; Density estimation; Kernel estimator; Wavelets; Minimum contrast estimation; Mixing; 62G07; 62G08; 62M07; 62P20; 91G70 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18412-3_11

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DOI: 10.1007/978-3-642-18412-3_11

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