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The Stochastic Volatility in Mean Model

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  • Siem Jan Koopman

    ()
    (Vrije Universiteit Amsterdam)

  • Eugenie Hol Uspensky

    (University of Birmingham)

Abstract

In this paper we present an exact maximum likelihood treatment forthe estimation of a Stochastic Volatility in Mean(SVM) model based on Monte Carlo simulation methods. The SVM modelincorporates the unobserved volatility as anexplanatory variable in the mean equation. The same extension isdeveloped elsewhere for Autoregressive ConditionalHeteroskedastic (ARCH) models, known as the ARCH in Mean (ARCH-M)model. The estimation of ARCH models isrelatively easy compared with that of the Stochastic Volatility (SV)model. However, efficient Monte Carlo simulationmethods for SV models have been developed to overcome some of theseproblems. The details of modificationsrequired for estimating the volatility-in-mean effect are presentedin this paper together with a Monte Carlo study toinvestigate the small-sample properties of the SVM estimators. Takingthese developments of estimation methods intoaccount, we regard SV and SVM models as practical alternatives totheir ARCH counterparts and therefore it is ofinterest to study and compare the two classes of volatility models.We present an empirical study about theintertemporal relationship between stock index returns and theirvolatility for the United Kingdom, United States andJapan. This phenomenon has been discussed in the financial literaturebut has proved hard to find empirically; we findevidence of a negative but weak relationship.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 00-024/4.

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Date of creation: 30 Mar 2000
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Handle: RePEc:dgr:uvatin:20000024

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Web page: http://www.tinbergen.nl

Related research

Keywords: Forecasting; GARCH; Simulated maximum likelihood; Stochastic volatility; Stock indices;

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References

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  1. Diebold & Lopez, . "Modeling Volatility Dynamics," Home Pages, University of Pennsylvania _062, University of Pennsylvania.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Shephard, N. & Pitt, M.K., 1995. "Likelihood Analysis of Non-Gaussian Parameter-Driven Models," Economics Papers 108, Economics Group, Nuffield College, University of Oxford.
  5. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 19(1), pages 3-29, September.
  6. 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, Econometric Society, vol. 55(2), pages 391-407, March.
  7. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics, EconWPA 9610002, EconWPA.
  8. Poon, Ser-Huang & Taylor, Stephen J., 1992. "Stock returns and volatility: An empirical study of the UK stock market," Journal of Banking & Finance, Elsevier, Elsevier, vol. 16(1), pages 37-59, February.
  9. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, Elsevier, vol. 31(3), pages 281-318, June.
  10. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, Elsevier, vol. 19(2), pages 351-372, December.
  11. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 2(1), pages 107-160.
  12. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  13. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  14. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  15. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 69-87, January.
  16. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, Elsevier, vol. 87(2), pages 271-301, September.
  17. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(4), pages 429-34, October.
  18. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, Elsevier, vol. 64(1-2), pages 375-400.
  19. 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, Elsevier, vol. 52(1-2), pages 5-59.
  20. Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 16(3), pages 284-91, July.
  21. 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, Federal Reserve Bank of Minneapolis 157, Federal Reserve Bank of Minneapolis.
  22. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  23. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 4(2), pages 183-204.
  24. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 62(1), pages 3-56.
  25. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  26. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
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