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June 2003 Nonparametric volatility density estimation
Bert Van Es, Peter Spreij, Harry Van Zanten
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Bernoulli 9(3): 451-465 (June 2003). DOI: 10.3150/bj/1065444813


We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We assume that we observe the process at discrete instants in time. The sampling times will be equidistant with vanishing distance. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared processes is proposed to estimate the volatility density. An expansion of the bias and a bound on the variance are derived.


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Bert Van Es. Peter Spreij. Harry Van Zanten. "Nonparametric volatility density estimation." Bernoulli 9 (3) 451 - 465, June 2003.


Published: June 2003
First available in Project Euclid: 6 October 2003

zbMATH: 1044.62037
MathSciNet: MR1997492
Digital Object Identifier: 10.3150/bj/1065444813

Keywords: Deconvolution , Density estimation , Kernel estimator , Mixing , stochastic volatility models

Rights: Copyright © 2003 Bernoulli Society for Mathematical Statistics and Probability

Vol.9 • No. 3 • June 2003
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