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Nonparametric Methods for Volatility Density Estimation

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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.

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Mathematics Subject Classification (2010)

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Correspondence to Peter Spreij .

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van Es, B., Spreij, P., van Zanten, H. (2011). Nonparametric Methods for Volatility Density Estimation. In: Di Nunno, G., Øksendal, B. (eds) Advanced Mathematical Methods for Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18412-3_11

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