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Estimating stochastic volatility models using daily returns and realized volatility simultaneously

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Author Info

  • Takahashi, Makoto
  • Omori, Yasuhiro
  • Watanabe, Toshiaki

Abstract

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 bias in the realized volatility. On the other hand, daily returns are less subject to noise and therefore may provide additional information on the true volatility. From this point of view, modeling realized volatility and daily returns simultaneously based on the well-known stochastic volatility model is proposed. Empirical studies using intraday data of Tokyo stock price index show that this model can estimate realized volatility biases and parameters simultaneously. The Bayesian approach is taken and an efficient sampling algorithm is proposed 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 and that asymmetry is crucial in stochastic volatility models. The proposed Bayesian approach provides an estimate of the entire conditional predictive distribution of returns under consideration of the uncertainty in the estimation of both biases and parameters. Hence common risk measures, such as value-at-risk and expected shortfall, can be easily estimated.

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Bibliographic Info

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

Volume (Year): 53 (2009)
Issue (Month): 6 (April)
Pages: 2404-2426

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Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2404-2426

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References

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Citations

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Cited by:
  1. Peter Reinhard Hansen & Zhuo Huang, 2012. "Exponential GARCH Modeling with Realized Measures of Volatility," CREATES Research Papers 2012-44, School of Economics and Management, University of Aarhus.
  2. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
  3. Pierre Chausse & Dinghai Xu, 2012. "GMM Estimation of a Stochastic Volatility Model with Realized Volatility: A Monte Carlo Study," Working Papers 1203, University of Waterloo, Department of Economics, revised May 2012.
  4. Asuka Takeuchi-Nogimori, 2012. "An Empirical Analysis of the Nikkei 225 Put Options Using Realized GARCH Models," Global COE Hi-Stat Discussion Paper Series gd12-241, Institute of Economic Research, Hitotsubashi University.
  5. Makoto Takahashi & Toshiaki Watanabe & Yasuhiro Omori, 2014. "Volatility and Quantile Forecasts by Realized Stochastic Volatility Models with Generalized Hyperbolic Distribution," CIRJE F-Series CIRJE-F-921, CIRJE, Faculty of Economics, University of Tokyo.
  6. Trojan, Sebastian, 2013. "Regime Switching Stochastic Volatility with Skew, Fat Tails and Leverage using Returns and Realized Volatility Contemporaneously," Economics Working Paper Series 1341, University of St. Gallen, School of Economics and Political Science.
  7. Masato Ubukata & Toshiaki Watanabe, 2011. "Pricing Nikkei 225 Options Using Realized Volatility," IMES Discussion Paper Series 11-E-18, Institute for Monetary and Economic Studies, Bank of Japan.
  8. Mike So & Rui Xu, 2013. "Forecasting Intraday Volatility and Value-at-Risk with High-Frequency Data," Asia-Pacific Financial Markets, Springer, vol. 20(1), pages 83-111, March.
  9. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3674-3689.
  10. Siem Jan Koopman & Marcel Scharth, 2011. "The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures," Tinbergen Institute Discussion Papers 11-132/4, Tinbergen Institute.
  11. Masato Ubukata & Toshiaki Watanabe, 2013. "Pricing Nikkei 225 Options Using Realized Volatility," Global COE Hi-Stat Discussion Paper Series gd12-273, Institute of Economic Research, Hitotsubashi University.
  12. Takahashi, Makoto & Omori, Yasuhiro & Watanabe, Toshiaki, 2013. "News impact curve for stochastic volatility models," Economics Letters, Elsevier, vol. 120(1), pages 130-134.
  13. Siem Jan Koopman & Marcel Scharth, 2011. "The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures," Tinbergen Institute Discussion Papers 11-132/4, Tinbergen Institute.
  14. Strid, Ingvar, 2010. "Efficient parallelisation of Metropolis-Hastings algorithms using a prefetching approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2814-2835, November.
  15. Minchul Shin & Molin Zhong, 2013. "Does realized volatility help bond yield density prediction?," PIER Working Paper Archive 13-064, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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