Likelihood-based estimation and specification analysis of one- and two-factor SV models with leverage effects
Techniques for simulated maximum likelihood (SML) estimation, filtering, and assessing the fit of stochastic volatility models are examined. Both one- and two-factor models (with leverage effects) are considered. The techniques are computationally efficient, robust, straightforward to implement, and easy to adapt to new models. Using these techniques, it is possible to estimate single-factor models over data sets of several thousand observations in several seconds. The computational efficiency of the techniques means that Monte Carlo studies assessing both the small sample statistical properties as well as the numerical properties of the estimators are easy to do. Such studies are important for all simulation estimators, including simulation-based Bayesian and method of moments estimators. The application looks at S\&P 500 index returns. Even the simple single-factor models adequately capture the dynamics of volatility; the problem is to get the shape of the returns distribution right. Although including a second volatility factor improves the fit over the basic single-factor models, a new formulation of the SV-t model (a single factor model, but with $t$ rather than normal errors in the observation equation) provides the best fit. However, all the models considered fail in a similar manner: they are unable to capture the left tail of the distribution. Fitting this part of the distribution is important for option-pricing and risk management. Although it may be possible to come up with ad hoc parametric models that fit particular data series and sample periods, a promising alternative might be to look at single-factor models with flexible forms for the error distributions
|Date of creation:||11 Aug 2004|
|Date of revision:|
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
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.:
- Gallant, A. Ronald & Tauchen, George, 1996.
"Which Moments to Match?,"
Cambridge University Press, vol. 12(04), pages 657-681, October.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
- 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.
- Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
- Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
- Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994.
"Bayesian Analysis of Stochastic Volatility Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 12(4), pages 371-89, October.
- Tom Doan, . "RATS programs to replicate Jacquier, Polson, Rossi (1994) stochastic volatility," Statistical Software Components RTZ00105, Boston College Department of Economics.
- Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003.
"Alternative models for stock price dynamics,"
Journal of Econometrics,
Elsevier, vol. 116(1-2), pages 225-257.
- Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
- Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics.
- Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-91, April.
- Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
- repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
- Neil Shephard, 2005.
Economics Series Working Papers
2005-W17, University of Oxford, Department of Economics.
- Shephard, N. & Pitt, M.K., 1995.
"Likelihood Analysis of Non-Gaussian Parameter-Driven Models,"
108, Economics Group, Nuffield College, University of Oxford.
- Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
- Gallant, A. Ronald & Hsu, Chien-Te & Tauchen, George, 2000.
"Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance,"
00-04, Duke University, Department of Economics.
- A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999. "Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 617-631, November.
- Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
- Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
- Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 284-91, July.
When requesting a correction, please mention this item's handle: RePEc:ecm:nasm04:294. 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: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.