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Volatility estimators and the inverse range process in a random volatility random walk and Wiener processes

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  • Vallois, Pierre
  • Tapiero, Charles S.

Abstract

The purpose of this paper is to study the mean, the variance, the probability distribution and the hazard rate of the inverse range process of an a-priori unknown volatility random walk. Motivation for this process arises when it is necessary to obtain statistics that pertain to a process volatility in addition to the usual variance statistics. As a result, range process statistics are indicated as an additional source of information in the study of processes’ volatility. Examples and applications are considered.

Suggested Citation

  • Vallois, Pierre & Tapiero, Charles S., 2008. "Volatility estimators and the inverse range process in a random volatility random walk and Wiener processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2565-2574.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:11:p:2565-2574
    DOI: 10.1016/j.physa.2007.12.018
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    References listed on IDEAS

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    1. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    2. Pierre Vallois & Charles Tapiero, 1997. "Range reliability in random walks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 325-345, October.
    3. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    6. Michael W. Brandt & Francis X. Diebold, 2006. "A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," The Journal of Business, University of Chicago Press, vol. 79(1), pages 61-74, January.
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    Cited by:

    1. Tapiero, Charles S. & Vallois, Pierre, 2016. "Fractional randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1161-1177.

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    Keywords

    Volatility; Range process; Risk;
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