Simulated maximum likelihood for general stochastic volatility models: a change of variable approach
AbstractMaximum likelihood has proved to be a valuable tool for fitting the log-normal stochastic volatility model to financial returns time series. Using a sequential change of variable framework, we are able to cast more general stochastic volatility models into a form appropriate for importance samplers based on the Laplace approximation. We apply the methodology to two example models, showing that efficient importance samplers can be constructed even for highly non-Gaussian latent processes such as square-root diffusions.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 12022.
Date of creation: 10 Jul 2008
Date of revision:
Change of Variable; Heston Model; Laplace Importance Sampler; Simulated Maximum Likelihood; Stochastic Volatility;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-12-14 (All new papers)
- NEP-ECM-2008-12-14 (Econometrics)
- NEP-ETS-2008-12-14 (Econometric Time Series)
- NEP-ORE-2008-12-14 (Operations Research)
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.:
- Durham, Garland B., 2006. "Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models," Journal of Econometrics, Elsevier, vol. 133(1), pages 273-305, July.
- Durham, Garland B., 2007. "SV mixture models with application to S&P 500 index returns," Journal of Financial Economics, Elsevier, vol. 85(3), pages 822-856, September.
- Skaug, Hans J. & Fournier, David A., 2006. "Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 699-709, November.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
- Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994.
"Multivariate Stochastic Variance Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Tom Doan, . "RATS programs to estimate multivariate stochastic volatility models," Statistical Software Components RTZ00093, Boston College Department of Economics.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1995. "Multivariate Stochastic Variance Models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4783, Universidad Carlos III de Madrid.
- Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
- Roman Liesenfeld & Jean-Francois Richard, 2006.
"Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models,"
Taylor and Francis Journals, vol. 25(2-3), pages 335-360.
- Liesenfeld, Roman & Richard, Jean-François, 2004. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Economics Working Papers 2004,12, Christian-Albrechts-University of Kiel, Department of Economics.
- Jean-Francois Richard & Roman Liesenfeld, 2007. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Working Papers 322, University of Pittsburgh, Department of Economics, revised Jan 2004.
- Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
- G Sandmann & Siem Jan Koopman, 1996. "Maximum Likelihood Estimation of Stochastic Volatility Models," FMG Discussion Papers dp248, Financial Markets Group.
- Richard, Jean-Francois & Zhang, Wei, 2007.
"Efficient high-dimensional importance sampling,"
Journal of Econometrics,
Elsevier, vol. 141(2), pages 1385-1411, December.
- Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
- Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
- B. Nielsen & N. Shephard, 2003.
"Likelihood analysis of a first-order autoregressive model with exponential innovations,"
Journal of Time Series Analysis,
Wiley Blackwell, vol. 24(3), pages 337-344, 05.
- Bent Nielsen & Neil Shephard, 1999. "Likelihood Anlaysis of a First Order Autoregressive Model with Exponential Innovations," Economics Series Working Papers 1999-W08, University of Oxford, Department of Economics.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.