Volatility is the standard deviation of the continuously compounded returns of an asset in a specific time horizon. Since an option contract gives the option buyer a right to buy or sell an asset from a pre defined price level, if the volatility of the asset increases the probability of the option to be in the money in the future increases.

If the volatility is calculated by the previous price data of an underlying asset, it is called historical volatility. Historical volatility can give an idea about the past price behaviour of an asset but does not give any idea about the future. That’s why historical volatility is not used for pricing the options.

In fact for the options market volatlity is not a statistical result of a historical data, but a tradeable instrument showing the expectation of the market about the future volatility of the asset. Volatility is traded in the options market according to its tenor and called implied volatility.
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