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

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Author Info
Siem Jan Koopman (Department of Econometrics, Free University Amsterdam, The Netherlands)
Eugenie Hol Uspensky (Department of Accounting and Finance, University of Birmingham, UK)

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Abstract

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.

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File URL: http://hdl.handle.net/10.1002/jae.652
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 17 (2002)
Issue (Month): 6 ()
Pages: 667-689
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Handle: RePEc:jae:japmet:v:17:y:2002:i:6:p:667-689

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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.:
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  13. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(1), pages 1-42.
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  14. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 5(2), pages 199-242. [Downloadable!] (restricted)
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    • 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. [Downloadable!] (restricted)
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  21. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400. [Downloadable!] (restricted)
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  23. 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.
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Cited by:
(explanations, 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.)

  1. Manabu Asai & Michael McAleer, 2005. "Asymmetric Multivariate Stochastic Volatility," DEA Working Papers 12, Universitat de les Illes Balears, Departament d'Economía Aplicada. [Downloadable!]
  2. María García Centeno & Román Mínguez Salido, 2009. "Estimation of Asymmetric Stochastic Volatility Models for Stock-Exchange Index Returns," International Advances in Economic Research, Springer, vol. 15(1), pages 71-87, February. [Downloadable!] (restricted)
  3. S. Bordignon & D. Raggi, 2008. "Volatility, Jumps and Predictability of Returns: a Sequential Analysis," Working Papers 636, Dipartimento Scienze Economiche, Universita' di Bologna. [Downloadable!]
  4. Martin M. Andreasen, 2009. "Stochastic Volatility and DSGE Models," CREATES Research Papers 2009-29, School of Economics and Management, University of Aarhus. [Downloadable!]
  5. Carmen Broto & Esther Ruiz, 2002. "Estimation Methods For Stochastic Volatility Models: A Survey," Statistics and Econometrics Working Papers ws025414, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
    Other versions:
  6. Eugenie Hol & Siem Jan Koopman, 2000. "Forecasting the Variability of Stock Index Returns with Stochastic Volatility Models and Implied Volatility," Tinbergen Institute Discussion Papers 00-104/4, Tinbergen Institute. [Downloadable!]
  7. Tim Bollerslev & Hao Zhou, 2003. "Volatility puzzles: a unified framework for gauging return-volatility regressions," Finance and Economics Discussion Series 2003-40, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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