IDEAS home Printed from https://ideas.repec.org/a/jae/japmet/v14y1999i2p101-21.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://qed.econ.queensu.ca:80/jae/1999-v14.2/
    File Function: Supporting data files and programs
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Junji Shimada & Yoshihiko Tsukuda, 2004. "Estimation of Stochastic Volatility Models : An Approximation to the Nonlinear State Space," Econometric Society 2004 Far Eastern Meetings 611, Econometric Society.
    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. 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.
    4. Kobayashi, Masahito, 2009. "Testing for jumps in the stochastic volatility models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2597-2608.
    5. 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.
    6. Miroslav Šimandl & Tomáš Soukup, 2002. "Simulation Monte Carlo methods in extended stochastic volatility models," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 109-117, April.
    7. Yi-Hsien Wang, 2009. "Using neural network to forecast stock index option price: a new hybrid GARCH approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(5), pages 833-843, September.
    8. 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.
    9. Panayotis G. Michaelides & Efthymios G. Tsionas & Angelos T. Vouldis & Konstantinos N. Konstantakis & Panagiotis Patrinos, 2018. "A Semi-Parametric Non-linear Neural Network Filter: Theory and Empirical Evidence," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 637-675, March.
    10. 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.
    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. Takada, Teruko, 2009. "Simulated minimum Hellinger distance estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2390-2403, April.
    13. 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.
    14. 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.
    15. Adam Clements & Stan Hurn & Scott White, 2006. "Estimating Stochastic Volatility Models Using a Discrete Non-linear Filter. Working paper #3," NCER Working Paper Series 3, National Centre for Econometric Research.
    16. 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.
    17. 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.
    18. 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.
    19. T. R. Santos, 2018. "A Bayesian GED-Gamma stochastic volatility model for return data: a marginal likelihood approach," Papers 1809.01489, arXiv.org.
    20. Manabu Asai, 2005. "Comparison of MCMC Methods for Estimating Stochastic Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 25(3), pages 281-301, June.
    21. Čížek, Pavel, 2004. "(Non) Linear Regression Modeling," Papers 2004,11, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    22. F. Cacace & A. Germani & M. Papi, 2019. "On parameter estimation of Heston’s stochastic volatility model: a polynomial filtering method," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 503-525, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jae:japmet:v:14:y:1999:i:2:p:101-21. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    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 (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0883-7252/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.