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QUESTION

Should the value (premium) of an option increase with the
volatility of the price of the underlying asset?


ANSWER

Yes, as increasing volatility means increasing risk or uncertainty
in the price of the underlying asset. If you are the holder of a
call option the more volatile the asset, the more valuable the
stabilizing option will be for you. Likewise for the holder of a
put option. Therefore you will pay more for the stability, hence
the premium should be greater. Could argue also from issuers point
of view.




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