IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

The stochastic volatility in mean model: empirical evidence from international stock markets

  • Siem Jan Koopman

    (Department of Econometrics, Free University Amsterdam, The Netherlands)

  • Eugenie Hol Uspensky

    (Department of Accounting and Finance, University of Birmingham, UK)

In this paper we present an exact maximum likelihood treatment for the estimation of a Stochastic Volatility in Mean (SVM) model based on Monte Carlo simulation methods. The SVM model incorporates the unobserved volatility as an explanatory variable in the mean equation. The same extension is developed elsewhere for Autoregressive Conditional Heteroscedastic (ARCH) models, known as the ARCH in Mean (ARCH-M) model. The estimation of ARCH models is relatively easy compared with that of the Stochastic Volatility (SV) model. However, efficient Monte Carlo simulation methods for SV models have been developed to overcome some of these problems. The details of modifications required for estimating the volatility-in-mean effect are presented in this paper together with a Monte Carlo study to investigate the finite sample properties of the SVM estimators. Taking these developments of estimation methods into account, we regard SV and SVM models as practical alternatives to their ARCH counterparts and therefore it is of interest to study and compare the two classes of volatility models. We present an empirical study of the intertemporal relationship between stock index returns and their volatility for the United Kingdom, the United States and Japan. This phenomenon has been discussed in the financial economic literature but has proved hard to find empirically. We provide evidence of a negative but weak relationship between returns and contemporaneous volatility which is indirect evidence of a positive relation between the expected components of the return and the volatility process. Copyright © 2002 John Wiley & Sons, Ltd.

If 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.

File URL: http://hdl.handle.net/10.1002/jae.652
File Function: Link to full text; subscription required
Download Restriction: no

File URL: http://qed.econ.queensu.ca:80/jae/2002-v17.6/
File Function: Supporting data files and programs
Download Restriction: no

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 17 (2002)
Issue (Month): 6 ()
Pages: 667-689

as
in new window

Handle: RePEc:jae:japmet:v:17:y:2002:i:6:p:667-689
Contact details of provider: Web page: http://www.interscience.wiley.com/jpages/0883-7252/

Order Information: Web: http://www3.interscience.wiley.com/jcatalog/subscribe.jsp?issn=0883-7252 Email:


References listed on IDEAS
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.:

as in new window
  1. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  2. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  3. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  4. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  5. Watanabe, Toshiaki, 1999. "A Non-linear Filtering Approach to Stochastic Volatility Models with an Application to Daily Stock Returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 101-21, March-Apr.
  6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  7. 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.
  8. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
  9. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
  10. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
  11. 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.
  12. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  13. 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.
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  15. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  16. 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.
  17. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  18. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  19. Francis X. Diebold & Jose A. Lopez, 1995. "Modeling volatility dynamics," Research Paper 9522, Federal Reserve Bank of New York.
  20. Chesney, Marc & Scott, Louis, 1989. "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(03), pages 267-284, September.
  21. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  22. 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.
  23. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  24. 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.
  25. Poon, Ser-Huang & Taylor, Stephen J., 1992. "Stock returns and volatility: An empirical study of the UK stock market," Journal of Banking & Finance, Elsevier, vol. 16(1), pages 37-59, February.
  26. 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.
  27. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
  28. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, March.
  29. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:jae:japmet:v:17:y:2002:i:6:p:667-689. 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: (Wiley-Blackwell Digital Licensing)

or (Christopher F. Baum)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.