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Theory & Methods: Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method

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  • John L. Knight
  • Stephen E. Satchell
  • Jun Yu

Abstract

The stochastic volatility model has no closed form for its likelihood and hence the maximum likelihood estimation method is difficult to implement. However, it can be shown that the model has a known characteristic function. As a consequence, the model is estimable via the empirical characteristic function. In this paper, the characteristic function of the model is derived and the estimation procedure is discussed. An application is considered for daily returns of Australian/New Zealand dollar exchange rate. Model checking suggests that the stochastic volatility model together with the empirical characteristic function estimates fit the data well.

Suggested Citation

  • John L. Knight & Stephen E. Satchell & Jun Yu, 2002. "Theory & Methods: Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(3), pages 319-335, September.
    • Handle: RePEc:bla:anzsta:v:44:y:2002:i:3:p:319-335
    DOI: 10.1111/1467-842X.00234
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    Cited by:

    1. Stojanović, Vladica S. & Popović, Biljana Č. & Milovanović, Gradimir V., 2016. "The Split-SV model," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 560-581.
    2. Taufer, Emanuele & Leonenko, Nikolai & Bee, Marco, 2011. "Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2525-2539, August.
    3. Dinghai Xu & John Knight & Tony S. Wirjanto, 2011. "Asymmetric Stochastic Conditional Duration Model--A Mixture-of-Normal Approach," Journal of Financial Econometrics, Oxford University Press, vol. 9(3), pages 469-488, Summer.
    4. Kotchoni, Rachidi, 2012. "Applications of the characteristic function-based continuum GMM in finance," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3599-3622.
    5. 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.
    6. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
    7. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    8. A. Hachicha & F. Hachicha, 2021. "Analysis of the bitcoin stock market indexes using comparative study of two models SV with MCMC algorithm," Review of Quantitative Finance and Accounting, Springer, vol. 56(2), pages 647-673, February.
    9. Maddalena Cavicchioli, 2017. "Estimation and asymptotic covariance matrix for stochastic volatility models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 437-452, August.
    10. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    11. Tore Selland Kleppe & Hans J. Skaug, 2008. "Building and Fitting Non‐Gaussian Latent Variable Models via the Moment‐Generating Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 664-676, December.
    12. Richard A. Davis & Thiago do Rêgo Sousa & Claudia Klüppelberg, 2021. "Indirect inference for time series using the empirical characteristic function and control variates," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 653-684, September.
    13. Dinghai Xu & John Knight, 2013. "Stochastic volatility model under a discrete mixture-of-normal specification," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 37(2), pages 216-239, April.
    14. Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008.
    15. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    16. Bruno Ebner & Bernhard Klar & Simos G. Meintanis, 2018. "Fourier inference for stochastic volatility models with heavy-tailed innovations," Statistical Papers, Springer, vol. 59(3), pages 1043-1060, September.

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