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I know that annualized historical volatility calculated with closing prices is a much rougher estimate than implied volatility for the correct "volatility" parameter in options pricing models. However, implied volatility requires knowing the market price of the option in question, which is not feasible for my application. Is there a widely used better estimate for the volatility parameter than annualized historical volatility? Thanks.

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If you want to estimate volatility from historical data, the only best linear unbiased estimator (BLUE) is $$\sigma=\sqrt{\frac{1}{T-1}\sum_{i=1}^T (r_i-E(r_i))^2}$$ Any other estimator will hence either be biased or not consistent.

Another approach could be to estimate volatility via a GARCH model, which has shown good empirical results in the past.

It is also possible to transform the sample data before estimation, i.e. filter for outliers and such.

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All option pricing formulas except this one and this one use some sort of historical volatility . I can't see how you can use the Black Sholes framework and not use some sort of historical volatility

  1. uses an order book

  2. uses geometric shapes and volume

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    $\begingroup$ Welcome to the site. An upvote for a good, if (somewhat) brief answer. $\endgroup$ – Tom Au Nov 9 '14 at 15:19

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