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The hierarchical-likelihood approach to autoregressive stochastic volatility models

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  • Lee, Woojoo
  • Lim, Johan
  • Lee, Youngjo
  • del Castillo, Joan
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    Abstract

    Many volatility models used in financial research belong to a class of hierarchical generalized linear models with random effects in the dispersion. Therefore, the hierarchical-likelihood (h-likelihood) approach can be used. However, the dimension of the Hessian matrix is often large, so techniques of sparse matrix computation are useful to speed up the procedure of computing the inverse matrix. Using numerical studies we show that the h-likelihood approach gives better long-term prediction for volatility than the existing MCMC method, while the MCMC method gives better short-term prediction. We show that the h-likelihood approach gives comparable estimations of fixed parameters to those of existing methods.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 1 (January)
    Pages: 248-260

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:248-260

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Autoregressive stochastic volatility model Hierarchical generalized linear model Hierarchical likelihood Sparse matrix computation Prediction;

    References

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    1. Pollock, D. S. G., 2003. "Recursive estimation in econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 37-75, October.
    2. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    3. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
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    12. Renate Meyer & Jun Yu, 2000. "BUGS for a Bayesian analysis of stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 198-215.
    13. Renate Meyer & David A. Fournier & Andreas Berg, 2003. "Stochastic volatility: Bayesian computation using automatic differentiation and the extended Kalman filter," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 408-420, December.
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    Cited by:
    1. Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.

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