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Finance and Stochastics

, 14:49 | Cite as

Nonparametric estimation for a stochastic volatility model

  • F. Comte
  • V. Genon-Catalot
  • Y. Rozenholc
Article

Abstract

Consider discrete-time observations (X δ )1≤n+1 of the process X satisfying \(dX_{t}=\sqrt{V_{t}}dB_{t}\) , with V a one-dimensional positive diffusion process independent of the Brownian motion B. For both the drift and the diffusion coefficient of the unobserved diffusion V, we propose nonparametric least square estimators, and provide bounds for their risk. Estimators are chosen among a collection of functions belonging to a finite-dimensional space whose dimension is selected by a data driven procedure. Implementation on simulated data illustrates how the method works.

Keywords

Diffusion coefficient Drift Mean square estimator Model selection Nonparametric estimation Penalized contrast Stochastic volatility 

Mathematics Subject Classification (2000)

62G08 62M05 62P05 

JEL Classification

C14 C87 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.MAP5 UMR 8145Université Paris DescartesParis cedex 06France

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