The hierarchical-likelihood approach to autoregressive stochastic volatility models
AbstractMany volatility models used in financial research belong to a class of hierarchical generalized linear models with random effects in the dispersion. Therefore, the hierarchical-likelihood (h-likelihood) approach can be used. However, the dimension of the Hessian matrix is often large, so techniques of sparse matrix computation are useful to speed up the procedure of computing the inverse matrix. Using numerical studies we show that the h-likelihood approach gives better long-term prediction for volatility than the existing MCMC method, while the MCMC method gives better short-term prediction. We show that the h-likelihood approach gives comparable estimations of fixed parameters to those of existing methods.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 55 (2011)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
Autoregressive stochastic volatility model Hierarchical generalized linear model Hierarchical likelihood Sparse matrix computation Prediction;
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.:
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996.
"Stochastic Volatility: Likelihood Inference And Comparison With Arch Models,"
- Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
- Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
- Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
- Stephen Pollock, 2002.
"Recursive Estimation in Econometrics,"
462, Queen Mary, University of London, School of Economics and Finance.
- Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
- Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
- Ruiz, Esther, 1994.
"Quasi-Maximum Likelihood estimation of Stochastic Volatility models,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/4786, Universidad Carlos III de Madrid.
- Ruiz, Esther, 1994. "Quasi-maximum likelihood estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 63(1), pages 289-306, July.
- Renate Meyer & David A. Fournier & Andreas Berg, 2003. "Stochastic volatility: Bayesian computation using automatic differentiation and the extended Kalman filter," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 408-420, December.
- Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
- Renate Meyer & Jun Yu, 2000. "BUGS for a Bayesian analysis of stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 198-215.
- Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
- 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.
- 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.
- 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.
- 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.
- 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.
- Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.