Estimation of Stochastic Volatility Models by Nonparametric Filtering
AbstractA two-step estimation method of stochastic volatility models is proposed: In the first step, we estimate the (unobserved) instantaneous volatility process using the estimator of Kristensen (2010, Econometric Theory 26). In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and we give theoretical results for both. The resulting estimators of the drift and diffusion terms of the volatility model will carry additional biases and variances due to the first-step estimation, but under regularity conditions these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties of the proposed estimators.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-67.
Date of creation: 10 Jan 2010
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Realized spot volatility; stochastic volatility; kernel estimation; nonparametric; semiparametric;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-10-23 (All new papers)
- NEP-ECM-2010-10-23 (Econometrics)
- NEP-ETS-2010-10-23 (Econometric Time Series)
- NEP-ORE-2010-10-23 (Operations Research)
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- Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
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- Dennis Kristensen & Andrew Ang, 2009. "Testing Conditional Factor Models," CREATES Research Papers 2009-09, School of Economics and Management, University of Aarhus.
- Andrew Ang & Dennis Kristensen, 2011. "Testing Conditional Factor Models," NBER Working Papers 17561, National Bureau of Economic Research, Inc.
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