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Simulated Maximum Likelihood Estimation of Continuous Time Stochastic Volatility Models

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Author Info

  • Tore Selland Kleppe

    (University of Bergen)

  • Hans J. Skaug

    (University of Bergen)

  • Jun Yu

    (Sim Kee Boon Institute for Financial Economics, Singapore Management University)

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 modi ed ecient 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.

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File URL: http://www.smu.edu.sg/institutes/skbife/downloads/CoFiE/Working%20Papers/Simulated%20Maximum%20Likelihood%20Estimation%20of%20Continuous%20Time%20Stochastic%20Volatility%20Models.pdf
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Bibliographic Info

Paper provided by Sim Kee Boon Institute for Financial Economics in its series Working Papers with number CoFie-09-2009.

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Length: 19 Pages
Date of creation: Jun 2009
Date of revision:
Publication status: Published in SMU-SKBI CoFie Working Paper
Handle: RePEc:skb:wpaper:cofie-09-2009

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Keywords: Efficient importance sampler; Constant elasticity of volatility;

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  1. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Working Papers 13-2004, Singapore Management University, School of Economics.
  2. BAUWENS, Luc & GALLI, Fausto, . "Efficient importance sampling for ML estimation of SCD models," CORE Discussion Papers RP -2088, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
  4. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  5. 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.
  6. 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, 07.
  7. 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.
  8. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
  9. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  11. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Papers 321, University of Pittsburgh, Department of Economics, revised Jan 2007.
  12. 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.
  13. Liesenfeld, Roman & Richard, Jean-François, 2004. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Economics Working Papers 2004,12, Christian-Albrechts-University of Kiel, Department of Economics.
  14. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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