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It comes from options. A common way to do it is from ATM (at the money) put and call and the Black Scholes formula. There are also other ways that use a larger number of options and more complicated maths.


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For historical volatility I actually like this article: http://www.todaysgroep.nl/media/236846/measuring_historic_volatility.pdf it provides several of the better known methods for calculating historical vol, which of course could be done manually. Just being aware of the upsides and downsides of each method. As for implied vol, yes as onlyvix has said it'...



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