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Most Efficient Homogeneous Volatility Estimators


  • A. Saichev
  • D. Sornette
  • V. Filimonov


We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We introduce the "quasi-unbiased estimators", that can address any type of desirable constraints. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval in the form of the joint distributions of the high-minus-open, low-minus-open and close-minus-open values, whose analytical expression is derived exactly for Wiener processes with drift. The distributions can be calculated to yield the most efficient estimators associated with any statistical properties of the underlying log-price stochastic process. Applied to Wiener processes for log-prices with drift, we provide explicit analytical expressions for the most efficient point-wise volatility and variance estimators, based on the analytical expression of the joint distribution of the high-minus-open, low-minus-open and close-minus-open values. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass, Roger-Satchell and maximum likelihood estimators.

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  • A. Saichev & D. Sornette & V. Filimonov, 2009. "Most Efficient Homogeneous Volatility Estimators," Papers 0908.1677,
  • Handle: RePEc:arx:papers:0908.1677

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    References listed on IDEAS

    1. Donald MacKenzie, 2006. "An Engine, Not a Camera: How Financial Models Shape Markets," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262134608, January.
    2. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
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    Cited by:

    1. Andreea Röthig & Andreas Röthig & Carl Chiarella, 2015. "On Candlestick-based Trading Rules Profitability Analysis via Parametric Bootstraps and Multivariate Pair-Copula based Models," Research Paper Series 362, Quantitative Finance Research Centre, University of Technology, Sydney.

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