To quote John Maynard Keynes, “The market can stay irrational longer than you can stay solvent"
An option's value is its intrinsic value, plus its time value. The time value of an option is mostly sigma, yes.
https://en.wikipedia.org/wiki/Option_time_value#Time_value
To quote John Maynard Keynes, “The market can stay irrational longer than you can stay solvent"