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A Threshold Stochastic Volatility Model with Realized Volatility

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  • Dinghai Xu

    (Department of Economics, University of Waterloo)

Abstract

Rapid development in the computer technology has made the financial transaction data visible at an ultimate limit level. The realized volatility, as a proxy for the "true" volatility, can be constructed using the high frequency data. This paper extends a threshold stochastic volatility specification proposed in So, Li and Lam (2002) by incorporating the high frequency volatility measures. Due to the availability of the volatility time series, the parameters estimation can be easily implemented via the standard maximum likelihood estimation (MLE) rather than using the simulated Bayesian methods. In the Monte Carlo section, several mis-specification and sensitivity experiments are conducted. The proposed methodology shows good performance according to the Monte Carlo results. In the empirical study, three stock indices are examined under the threshold stochastic volatility structure. Empirical results show that in different regimes, the returns and volatilities exhibit asymmetric behavior. In addition, this paper allows the threshold in the model to be flexible and uses a sequential optimization based on MLE to search for the "optimal" threshold value. We find that the model with a flexible threshold is always preferred to the model with a fixed threshold according to the log-likelihood measure. Interestingly, the "optimal" threshold is found to be stable across different sampling realized volatility measures.

Suggested Citation

  • Dinghai Xu, 2010. "A Threshold Stochastic Volatility Model with Realized Volatility," Working Papers 1003, University of Waterloo, Department of Economics, revised May 2010.
    • Handle: RePEc:wat:wpaper:1003
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    File URL: http://economics.uwaterloo.ca/documents/10-003DX.pdf
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    References listed on IDEAS

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    Cited by:

    1. Heejoon Han & Eunhee Lee, 2020. "Triple Regime Stochastic Volatility Model with Threshold and Leverage Effects," Korean Economic Review, Korean Economic Association, vol. 36, pages 481-509.
    2. Mao, Xiuping & Ruiz, Esther & Veiga, Helena, 2017. "Threshold stochastic volatility: Properties and forecasting," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1105-1123.

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    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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