Journal of Quantitative Economics

, Volume 17, Issue 1, pp 57–91 | Cite as

Robust Volatility Estimation with and Without the Drift Parameter

  • Muneer ShaikEmail author
  • S. Maheswaran
Original Article


We find the closed form solution for the joint probability of the running maximum and the drawdown of the Brownian motion with a non-zero drift parameter at a random time that is exponentially distributed and independent of the Brownian motion. This characterization leads us to come up with a robust method of estimating volatility using open, high, low and closing prices. We rigorously show the independence of robust volatility estimators based on extreme values of asset prices relative to the standard robust volatility estimator based on closing price alone. We further prove that the proposed robust volatility ratio is unbiased with no drift parameter. Moreover, we find that the robust volatility ratio with a non-zero drift parameter has only a second order effect. We have shown that our proposed extreme value robust volatility estimator is 2–3 times relatively more efficient when compared to the classical robust volatility estimator based on Monte Carlo simulation experiment. On the empirical side, we test the proposed robust volatility ratio based on high and low prices on different asset classes like stock indices, exchange rate and precious metals.


Robust volatility modeling Extreme value estimators Radon Nikodym derivative Brownian motion Drawdown Absolute returns 

JEL Classification

C13 C51 C58 G12 


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Copyright information

© The Indian Econometric Society 2018

Authors and Affiliations

  1. 1.Institute for Financial Management and ResearchChennaiIndia

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