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Stimulated Maximum Likelihood Estimation of Continuous Time Stochastic Volatility Models

Author

Listed:
  • Tore Selland KLEPPE

    () (Department of Mathematics, University of Bergen)

  • Jun YU

    () (School of Economics, Singapore Management University)

  • Hans J. SKAUG

    () (University of Bergen)

Abstract

In this paper we develop and implement a method for maximum simulated likelihood estimation of the continuous time stochastic volatility model with the constant elasticity of volatility. The approach do not require observations on option prices nor volatility. To integrate out latent volatility from the joint density of return and volatility, a modified efficient importance sampling technique is used after the continuous time model is approximated using the Euler-Maruyama scheme. The Monte Carlo studies show that the method works well and the empirical applications illustrate usefulness of the method. Empirical results provide strong evidence against the Heston model.

Suggested Citation

  • Tore Selland KLEPPE & Jun YU & Hans J. SKAUG, 2009. "Stimulated Maximum Likelihood Estimation of Continuous Time Stochastic Volatility Models," Working Papers 20-2009, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:20-2009
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    References listed on IDEAS

    as
    1. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
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    3. Durham, Garland B., 2006. "Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models," Journal of Econometrics, Elsevier, vol. 133(1), pages 273-305, July.
    4. Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.
    5. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    6. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    7. Bauwens, L. & Galli, F., 2009. "Efficient importance sampling for ML estimation of SCD models," Computational Statistics & Data Analysis, Elsevier, pages 1974-1992.
    8. Kleppe, Tore Selland & Skaug, Hans Julius, 2012. "Fitting general stochastic volatility models using Laplace accelerated sequential importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3105-3119.
    9. Hiroyuki Kawakatsu, 2007. "Numerical integration-based Gaussian mixture filters for maximum likelihood estimation of asymmetric stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 342-358, July.
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    More about this item

    Keywords

    Efficient importance sampler; Constant elasticity of volatility;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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