Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models
Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression. In this paper we propose a characteristic function-based estimation method for non-Gaussian Ornstein-Uhlenbeck-based stochastic volatility models. After deriving explicit expressions of the characteristic functions for various cases of interest we analyze the asymptotic properties of the estimators and evaluate their performance by means of a simulation experiment. Finally, a real-data application shows that the superposition of two Ornstein-Uhlenbeck processes gives a good approximation to the dependence structure of the process.
|Date of creation:||Oct 2009|
|Date of revision:||02 Dec 2009|
|Contact details of provider:|| Postal: |
Web page: http://www.unitn.it/disa
More information through EDIRC
|Order Information:|| Postal: DISA Università degli Studi di Trento via Inama, 5 I-38122 Trento TN Italy|
Web: http://www.unitn.it/disa Email:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Todorov, Viktor & Tauchen, George, 2006. "Simulation Methods for Levy-Driven Continuous-Time Autoregressive Moving Average (CARMA) Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 455-469, October.
- Taufer, Emanuele & Leonenko, Nikolai, 2009.
"Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution,"
Computational Statistics & Data Analysis,
Elsevier, vol. 53(6), pages 2427-2437, April.
- Emanuele Taufer & Nikolai Leonenko, 2007. "Simulation of Lévy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Quaderni DISA 123, Department of Computer and Management Sciences, University of Trento, Italy, revised 23 May 2007.
- Griffin, Jim & Steel, Mark F.J., 2008.
"Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes,"
11071, University Library of Munich, Germany.
- Griffin, J.E. & Steel, M.F.J., 2010. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2594-2608, November.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Knight, John L. & Yu, Jun, 2002. "Empirical Characteristic Function In Time Series Estimation," Econometric Theory, Cambridge University Press, vol. 18(03), pages 691-721, June.
- Geurt Jongbloed & Frank H. Van Der Meulen, 2006. "Parametric Estimation for Subordinators and Induced OU Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 825-847.
- Ole E. Barndorff-Nielsen, 2003. "Integrated OU Processes and Non-Gaussian OU-based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 277-295.
- T.W. Epps, 2005. "Tests for location-scale families based on the empirical characteristic function," Metrika, Springer, vol. 62(1), pages 99-114, 09.
- Matthew P. S. Gander & David A. Stephens, 2007. "Simulation and inference for stochastic volatility models driven by Lévy processes," Biometrika, Biometrika Trust, vol. 94(3), pages 627-646.
- Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
- Jun Yu, 2004. "Empirical Characteristic Function Estimation and Its Applications," Econometric Reviews, Taylor & Francis Journals, vol. 23(2), pages 93-123.
- Griffin, J.E. & Steel, M.F.J., 2006.
"Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility,"
Journal of Econometrics,
Elsevier, vol. 134(2), pages 605-644, October.
- James E. Griffin & Mark F.J. Steel, 2002. "Inference With Non-Gaussian Ornstein-Uhlenbeck Processes for Stochastic Volatility," Econometrics 0201002, EconWPA, revised 04 Apr 2003.
- John L. Knight & Stephen E. Satchell & Jun Yu, 2002. "Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(3), pages 319-335, 09.
- Ole E. Barndorff-Nielsen & Shephard, 2002.
"Econometric analysis of realized volatility and its use in estimating stochastic volatility models,"
Journal of the Royal Statistical Society Series B,
Royal Statistical Society, vol. 64(2), pages 253-280.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
- Michael Sørensen, 2000. "Prediction-based estimating functions," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 123-147.
- Gareth O. Roberts & Omiros Papaspiliopoulos & Petros Dellaportas, 2004. "Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 369-393.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- Jiang, George J & Knight, John L, 2002. "Estimation of Continuous-Time Processes via the Empirical Characteristic Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 198-212, April.
When requesting a correction, please mention this item's handle: RePEc:trt:disawp:0907. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Roberto Gabriele)
If references are entirely missing, you can add them using this form.