A new unbiased additive robust volatility estimation using extreme values of asset prices

Abstract

We propose a new unbiased robust volatility estimator based on extreme values of asset prices. We show that the proposed Add Extreme Value Robust Volatility Estimator (AEVRVE) is unbiased and is 2–3 times more efficient relative to the Classical Robust Volatility Estimator (CRVE). We put forth a novel procedure to remove the downward bias present in the data even without increasing the number of steps in the stock price path. We perform Monte Carlo simulation experiments to show the properties of unbiasedness and efficiency. The proposed estimator remains exactly unbiased relative to the standard robust volatility estimator in the empirical data based on global stock indices namely CAC 40, DOW, IBOVESPA, NIKKEI, S&P 500 and SET 50.