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Long memory and the relation between implied and realized volatility

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  • Federico Bandi

    (The University of Chicago)

  • Benoit Perron

    (Université de Montréal)

Abstract

We argue that the conventional predictive regression between implied volatility (regressor) and realized volatility over the remaining life of the option (regressand) is likely to be a fractional cointegrating relation. Since cointegration is associated with long-run comovements, this finding modifies the usual interpretation of such regression as a study towards assessing option market efficiency (given a certain option pricing model) and/or short-term unbiasedness of implied volatility as a predictor for realized volatility, thereby rendering the conventional tests invalid. We use spectral methods and exploit the long memory in the data to design an econometric methodology which is robust to the various issues that the literature on the relation between implied and realized volatility has proposed as plausible explanations for an estimated slope coefficient less than one, implying biasedness, in the standard predictive regression (measurement errors and presence of an unobservable time-varying risk premium, for instance). Even though little can be said about market efficiency and/or short-term unbiasedness, which were the objects of the previous studies, our evidence in favor of a long-run one-to-one correspondence between implied and realized volatility series is rather strong. Simulation results confirm our findings.

Suggested Citation

  • Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics 0305004, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:0305004
    Note: Type of Document - pdf; prepared on PC; to print on HP Laserjet; pages: 49; figures: included
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    References listed on IDEAS

    as
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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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