Nonparametric estimation for a stochastic volatility model
Abstract
Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ 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 theirrisk. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2007
- DOI:
- 10.48550/arXiv.0712.3735
- arXiv:
- arXiv:0712.3735
- Bibcode:
- 2007arXiv0712.3735C
- Keywords:
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- Statistics - Methodology;
- Mathematics - Statistics