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Estimating Stochastic Volatility Models Using Daily Returns and Realized Volatility Simultaneously

  • Makoto Takahashi

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

  • Toshiaki Watanabe

    (Institute of Economic Research, Hitotsubashi University)

Realized volatility, which is the sum of squared intraday returns over a certain interval such as a day, has recently attracted the attention of financial economists and econometricians as an accurate measure of the true volatility. In the real market, however, the presence of non-trading hours and market microstructure noise in transaction prices may cause the bias in the realized volatility. On the other hand, daily returns are less subject to the noise and therefore may provide additional information on the true volatility. From this point of view, we propose modeling realized volatility and daily returns simultaneously based on well-known stochastic volatility model. Using intraday data of Tokyo stock price index, we show that this model can estimate realized volatility biases and parameters simultaneously.We take a Bayesian approach and propose an efficient sampling algorithm to implement the Markov chain Monte Carlo method for our simultaneous model. The result of the model comparison between the simultaneous models using both naive and scaled realized volatilities indicates that the effect of non-trading hours is more essential than that of microstructure noise but still the latter has to be considered for better fitting. Our Bayesian approach has an advantage over the conventional two-step correction procedure in that we are able to take the uncertainty in estimation of both biases and parameters into account for the prediction and the evaluation of Value-at-Risk.

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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2007/2007cf515.pdf
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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-515.

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Length: 32 pages
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:tky:fseres:2007cf515
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  1. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
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  11. Hasbrouck, Joel, 2007. "Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading," OUP Catalogue, Oxford University Press, number 9780195301649.
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