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A Non-linear Filtering Approach to Stochastic Volatility Models with an Application to Daily Stock Returns

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  • Watanabe, Toshiaki

Abstract

This paper develops a new method for the analysis of stochastic volatility (SV) models. Since volatility is a latent variable in SV models, it is difficult to evaluate the exact likelihood. In this paper, a non-linear filter which yields the exact likelihood of SV models is employed. Solving a series of integrals in this filter by piecewise linear approximations with randomly chosen nodes produces the likelihood, which is maximized to obtain estimates of the SV parameters. A smoothing algorithm for volatility estimation is also constructed. Monte Carlo experiments show that the method performs well with respect to both parameter estimates and volatility estimates. We illustrate the method by analysing daily stock returns on the Tokyo Stock Exchange. Since the method can be applied to more general models, the SV model is extended so that several characteristics of daily stock returns are allowed, and this more general model is also estimated.

Suggested Citation

  • 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 101-121, March-Apr.
  • Handle: RePEc:jae:japmet:v:14:y:1999:i:2:p:101-21
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    File URL: http://qed.econ.queensu.ca:80/jae/1999-v14.2/
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    Cited by:

    1. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    2. Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.
    3. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    4. M. Hakan Eratalay, 2016. "Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 19-52, September.
    5. Jinghui Chen & Masahito Kobayashi & Michael McAleer, 2017. "Testing for volatility co-movement in bivariate stochastic volatility models," Documentos de Trabajo del ICAE 2017-10, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    6. Kobayashi, Masahito, 2009. "Testing for jumps in the stochastic volatility models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2597-2608.
    7. Chen, J. & Kobayashi, M. & McAleer, M.J., 2016. "Testing for a Common Volatility Process and Information Spillovers in Bivariate Financial Time Series Models," Econometric Institute Research Papers EI2016-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. repec:kap:compec:v:51:y:2018:i:3:d:10.1007_s10614-016-9628-6 is not listed on IDEAS
    9. Asai, Manabu, 2009. "Bayesian analysis of stochastic volatility models with mixture-of-normal distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2579-2596.
    10. T. R. Santos, 2018. "A Bayesian GED-Gamma stochastic volatility model for return data: a marginal likelihood approach," Papers 1809.01489, arXiv.org.
    11. Scott I. White & Adam E. Clements & Stan Hurn, 2004. "Discretised Non-Linear Filtering for Dynamic Latent Variable Models: with Application to Stochastic Volatility," Econometric Society 2004 Australasian Meetings 46, Econometric Society.
    12. Amir Atiya & Steve Wall, 2009. "An analytic approximation of the likelihood function for the Heston model volatility estimation problem," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 289-296.
    13. Čížek, Pavel, 2004. "(Non) Linear Regression Modeling," Papers 2004,11, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    14. Adam Clements & Scott White, 2005. "Non-linear filtering with state dependant transition probabilities: A threshold (size effect) SV model," School of Economics and Finance Discussion Papers and Working Papers Series 191, School of Economics and Finance, Queensland University of Technology.

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