Abstract
Consider discrete-time observations (X ℓ δ )1≤ℓ≤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.
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Comte, F., Genon-Catalot, V. & Rozenholc, Y. Nonparametric estimation for a stochastic volatility model. Finance Stoch 14, 49–80 (2010). https://doi.org/10.1007/s00780-009-0094-z
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DOI: https://doi.org/10.1007/s00780-009-0094-z
Keywords
- Diffusion coefficient
- Drift
- Mean square estimator
- Model selection
- Nonparametric estimation
- Penalized contrast
- Stochastic volatility