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Latent Integrated Stochastic Volatility, Realized Volatility, and Implied Volatility: A State Space Approach

Author

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  • Christian Bach

    (Aarhus University, School of Economics and Management and CREATES)

  • Bent Jesper Christensen

    (Aarhus University, School of Economics and Management and CREATES)

Abstract

We include simultaneously both realized volatility measures based on high-frequency asset returns and implied volatilities backed out of individual traded at the money option prices in a state space approach to the analysis of true underlying volatility. We model integrated volatility as a latent fi?rst order Markov process and show that our model is closely related to the CEV and Barndorff-Nielsen & Shephard (2001) models for local volatility. We show that if measurement noise in the observable volatility proxies is not accounted for, then the estimated autoregressive parameter in the latent process is downward biased. Implied volatility performs better than any of the alternative realized measures when forecasting future integrated volatility. The results are largely similar across the stock market (S&P 500), bond market (30-year U.S. T-bond), and foreign currency exchange market ($/£ ).

Suggested Citation

  • Christian Bach & Bent Jesper Christensen, 2011. "Latent Integrated Stochastic Volatility, Realized Volatility, and Implied Volatility: A State Space Approach," CREATES Research Papers 2010-61, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2010-61
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    File URL: https://repec.econ.au.dk/repec/creates/rp/10/rp10_61.pdf
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    Cited by:

    1. Kleppe, Tore Selland & Liesenfeld, Roman, 2011. "Efficient high-dimensional importance sampling in mixture frameworks," Economics Working Papers 2011-11, Christian-Albrechts-University of Kiel, Department of Economics.

    More about this item

    Keywords

    Autoregression; bipower variation; high-frequency data; implied volatility; integrated volatility; Kalman fi?lter; moving average; option prices; realized volatility; state space model; stochastic volatility.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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