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Nonparametric Methods for Volatility Density Estimation

In: Advanced Mathematical Methods for Finance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Bert van Es & Peter Spreij & Harry van Zanten, 2011. "Nonparametric Methods for Volatility Density Estimation," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 293-312, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18412-3_11
    DOI: 10.1007/978-3-642-18412-3_11
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