Bernoulli

  • Bernoulli
  • Volume 9, Number 3 (2003), 451-465.

Nonparametric volatility density estimation

Bert Van Es, Peter Spreij, and Harry Van Zanten

Full-text: Open access

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.

Article information

Source
Bernoulli Volume 9, Number 3 (2003), 451-465.

Dates
First available in Project Euclid: 6 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.bj/1065444813

Digital Object Identifier
doi:10.3150/bj/1065444813

Mathematical Reviews number (MathSciNet)
MR1997492

Zentralblatt MATH identifier
1044.62037

Keywords
deconvolution density estimation kernel estimator mixing stochastic volatility models

Citation

Van Es, Bert; Spreij, Peter; Van Zanten, Harry. Nonparametric volatility density estimation. Bernoulli 9 (2003), no. 3, 451--465. doi:10.3150/bj/1065444813. https://projecteuclid.org/euclid.bj/1065444813


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