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Penalized Projection Estimator for Volatility Density

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  • F. COMTE
  • V. GENON‐CATALOT

Abstract

. In this paper, we consider a stochastic volatility model (Yt, Vt), where the volatility (Vt) is a positive stationary Markov process. We assume that (lnVt) admits a stationary density f that we want to estimate. Only the price process Yt is observed at n discrete times with regular sampling interval Δ. We propose a non‐parametric estimator for f obtained by a penalized projection method. Under mixing assumptions on (Vt), we derive bounds for the quadratic risk of the estimator. Assuming that Δ=Δn tends to 0 while the number of observations and the length of the observation time tend to infinity, we discuss the rate of convergence of the risk. Examples of models included in this framework are given.

Suggested Citation

  • F. Comte & V. Genon‐Catalot, 2006. "Penalized Projection Estimator for Volatility Density," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 875-893, December.
    • Handle: RePEc:bla:scjsta:v:33:y:2006:i:4:p:875-893
    DOI: 10.1111/j.1467-9469.2006.00519.x
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    Cited by:

    1. Van Es, Bert & Spreij, Peter, 2011. "Estimation of a multivariate stochastic volatility density by kernel deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 683-697, March.
    2. Yang Zu, 2015. "A Note on the Asymptotic Normality of the Kernel Deconvolution Density Estimator with Logarithmic Chi-Square Noise," Econometrics, MDPI, vol. 3(3), pages 1-16, July.
    3. Comte, F. & Genon-Catalot, V. & Rozenholc, Y., 2009. "Nonparametric adaptive estimation for integrated diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 811-834, March.

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