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Modelling H-Volatility with Fractional Brownian Bridge

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Sergio Bianchi

    (Sapienza University of Rome, Department of MEMOTEF)

  • Massimiliano Frezza

    (Sapienza University of Rome, Department of MEMOTEF)

  • Augusto Pianese

    (University of Cassino and Southern Lazio, QuantLab)

  • Anna Maria Palazzo

    (University of Cassino and Southern Lazio, QuantLab)

Abstract

We express the realized volatility in terms of the Hurst exponent of the trajectory drawn by the market index. By analyzing distribution, stationarity, and (partial) sample autocorrelation of the estimated paths, and exploiting the empirical law of return to the central value 1/2, we model the dynamics of H(t) (and hence of the volatility) through a fractional Brownian bridge of appropriate parameter H.

Suggested Citation

  • Sergio Bianchi & Massimiliano Frezza & Augusto Pianese & Anna Maria Palazzo, 2022. "Modelling H-Volatility with Fractional Brownian Bridge," Springer Books, in: Marco Corazza & Cira Perna & Claudio Pizzi & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 96-102, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-99638-3_16
    DOI: 10.1007/978-3-030-99638-3_16
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