Penalized Projection Estimator for Volatility Density

Authors: COMTE, F.; GENON-CATALOT, V.

Source: Scandinavian Journal of Statistics, Volume 33, Number 4, December 2006 , pp. 875-893(19)

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Abstract:

In this paper, we consider a stochastic volatility model (Y_t, V_t), where the volatility (V_t) is a positive stationary Markov process. We assume that (lnV_t) admits a stationary density f that we want to estimate. Only the price process Y_t 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 (V_t), we derive bounds for the quadratic risk of the estimator. Assuming that Δ=Δ_n 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.

Keywords: adaptive estimation; density deconvolution; diffusion processes; penalized projection estimator; stochastic volatility

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9469.2006.00519.x

Affiliations: 1: MAP5, UMR CNRS 8145, Université Paris V-René Descartes

Publication date: 2006-12-01