Nonparametric volatility density estimation

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

doi:10.3150/bj/1065444813

Nonparametric volatility density estimation

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

Research output: Contribution to journal › Article › Academic › peer-review

17 Citations (Scopus)

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Abstract

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.

Original language	English
Pages (from-to)	451-465
Journal	Bernoulli
Volume	9
Issue number	3
DOIs	https://doi.org/10.3150/bj/1065444813
Publication status	Published - 2003

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title = "Nonparametric volatility density estimation",

abstract = "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.",

author = "{Es, van}, Bert and P.J.C. Spreij and {Zanten, van}, J.H.",

year = "2003",

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T1 - Nonparametric volatility density estimation

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AU - Spreij, P.J.C.

AU - Zanten, van, J.H.

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N2 - 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.

AB - 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.

U2 - 10.3150/bj/1065444813

DO - 10.3150/bj/1065444813

M3 - Article

SN - 1350-7265

VL - 9

SP - 451

EP - 465

JO - Bernoulli

JF - Bernoulli

IS - 3

ER -

Nonparametric volatility density estimation

Abstract

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