Level Shifts in Volatility and the Implied-Realized Volatility Relation

Bent Jesper Christensen, Paolo Santucci de Magistris

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    We propose a simple model in which realized stock market return volatility and implied volatility backed out of option prices are subject to common level shifts corresponding to movements between bull and bear markets. The model is estimated using the Kalman filter in a generalization to the multivariate case of the univariate level shift technique by Lu and Perron (2008). An application to the S&P500 index and a simulation experiment show that the recently documented empirical properties of strong persistence in volatility and forecastability of future realized volatility from current implied volatility, which have been interpreted as long memory (or fractional integration) in volatility and fractional cointegration between implied and realized volatility, are accounted for by occasional common level shifts.
    Original languageEnglish
    Place of publicationAarhus
    PublisherInstitut for Økonomi, Aarhus Universitet
    Number of pages38
    Publication statusPublished - 2010


    • Common level shifts, fractional cointegration, fractional VECM, implied volatility, long memory, options, realized volatility.


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